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Dependence of the decay width
for exotic pentaquark Θ+(1540) on its mass
and the mass of N(1685) in a chiral soliton model
Ghil-Seok Yang Yongseok Oh Hyun-Chul Kim
NTG (Nuclear Theory Group)
Inha University
HEP (Center for High Energy
Physics) Kyungpook Natlsquol
University
ldquoNew Frontiers in QCDrdquo 27th ndash 28th October 2011 Engineering Research Park Yonsei University Seoul Republic of Korea
bull Prehistory of SU(3) Baryons
bull Motivation (Θ+ N )
bull Chiral Soliton Model
bull Masses and Decay Width
bull Summary
Outline
Naiumlve Quark Model (up down strange light quarks)
SU(3) scheme to classify particles with the same spin
and parity
Fundamental Particles
multiplets (proton neutron) isospin [ SU(2) ] rarr higher symmetry (Σ
K) SU(3)
SU(3) Baryons SU(3) Baryons
Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet
Why not 4 5 6 hellip quark states
representation 10 (10)
Nothing prevents such states to exist
Y s Oh and H c Kim Phys Rev D 70 094022 (2004)
1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)
(uddss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32
Ξ032Ξ-32Ξ--32
Σ-10
Σ010
Σ+10
(uudss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Motivation Motivation
S = -1
S = -2
Successful searches for Θ+ (2003~2005) 2007 PDG
Motivation Motivation
Unsuccessful searches for Θ+ (2006~2008) 2010 PDG
Motivation Motivation
Motivation Motivation
Experimental Status
New positive experiments (2005 - 2010)
DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010
MeV
(K+n rarr K0p higher statistical significance 6σ - 8σ)
[Signals are confirmed by LEPS SVD KEK hellip]
GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
bull Prehistory of SU(3) Baryons
bull Motivation (Θ+ N )
bull Chiral Soliton Model
bull Masses and Decay Width
bull Summary
Outline
Naiumlve Quark Model (up down strange light quarks)
SU(3) scheme to classify particles with the same spin
and parity
Fundamental Particles
multiplets (proton neutron) isospin [ SU(2) ] rarr higher symmetry (Σ
K) SU(3)
SU(3) Baryons SU(3) Baryons
Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet
Why not 4 5 6 hellip quark states
representation 10 (10)
Nothing prevents such states to exist
Y s Oh and H c Kim Phys Rev D 70 094022 (2004)
1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)
(uddss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32
Ξ032Ξ-32Ξ--32
Σ-10
Σ010
Σ+10
(uudss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Motivation Motivation
S = -1
S = -2
Successful searches for Θ+ (2003~2005) 2007 PDG
Motivation Motivation
Unsuccessful searches for Θ+ (2006~2008) 2010 PDG
Motivation Motivation
Motivation Motivation
Experimental Status
New positive experiments (2005 - 2010)
DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010
MeV
(K+n rarr K0p higher statistical significance 6σ - 8σ)
[Signals are confirmed by LEPS SVD KEK hellip]
GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Naiumlve Quark Model (up down strange light quarks)
SU(3) scheme to classify particles with the same spin
and parity
Fundamental Particles
multiplets (proton neutron) isospin [ SU(2) ] rarr higher symmetry (Σ
K) SU(3)
SU(3) Baryons SU(3) Baryons
Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet Hadron [ baryon (qqq) meson (qq) ] SU(3) color singlet
Why not 4 5 6 hellip quark states
representation 10 (10)
Nothing prevents such states to exist
Y s Oh and H c Kim Phys Rev D 70 094022 (2004)
1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)
(uddss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32
Ξ032Ξ-32Ξ--32
Σ-10
Σ010
Σ+10
(uudss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Motivation Motivation
S = -1
S = -2
Successful searches for Θ+ (2003~2005) 2007 PDG
Motivation Motivation
Unsuccessful searches for Θ+ (2006~2008) 2010 PDG
Motivation Motivation
Motivation Motivation
Experimental Status
New positive experiments (2005 - 2010)
DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010
MeV
(K+n rarr K0p higher statistical significance 6σ - 8σ)
[Signals are confirmed by LEPS SVD KEK hellip]
GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
1997 Diakonov Petrov and Polyakov Narrow 5-quark resonance (q4q Θ+) ( M = 1530 Γ~ 15 MeV from Chiral Soliton Model)
(uddss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32
Ξ032Ξ-32Ξ--32
Σ-10
Σ010
Σ+10
(uudss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Motivation Motivation
S = -1
S = -2
Successful searches for Θ+ (2003~2005) 2007 PDG
Motivation Motivation
Unsuccessful searches for Θ+ (2006~2008) 2010 PDG
Motivation Motivation
Motivation Motivation
Experimental Status
New positive experiments (2005 - 2010)
DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010
MeV
(K+n rarr K0p higher statistical significance 6σ - 8σ)
[Signals are confirmed by LEPS SVD KEK hellip]
GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Successful searches for Θ+ (2003~2005) 2007 PDG
Motivation Motivation
Unsuccessful searches for Θ+ (2006~2008) 2010 PDG
Motivation Motivation
Motivation Motivation
Experimental Status
New positive experiments (2005 - 2010)
DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010
MeV
(K+n rarr K0p higher statistical significance 6σ - 8σ)
[Signals are confirmed by LEPS SVD KEK hellip]
GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Unsuccessful searches for Θ+ (2006~2008) 2010 PDG
Motivation Motivation
Motivation Motivation
Experimental Status
New positive experiments (2005 - 2010)
DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010
MeV
(K+n rarr K0p higher statistical significance 6σ - 8σ)
[Signals are confirmed by LEPS SVD KEK hellip]
GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Motivation Motivation
Experimental Status
New positive experiments (2005 - 2010)
DIANA 2010 (Θ+) M = 1538plusmn2 Γ= 039plusmn010
MeV
(K+n rarr K0p higher statistical significance 6σ - 8σ)
[Signals are confirmed by LEPS SVD KEK hellip]
GRAAL (N ) M = 1685plusmn0012 MeV (CBELSATAPS LNS-Sendai hellip)
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model Chiral Soliton Model
Effective and relativistic low energy theory
Large Nc limit meson field
rarr soliton
Quantizing SU(3) rotated-meson fields rarr Collective Hamiltonian model baryon states
Chiral Soliton Model
Hedgehog Ansatz
Collective quantization
SU(2) Witten imbedding into SU(3) SU(2) X U(1)
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Model baryon state
Constraint for the collective quantization
Mixings of baryon states
Chiral Soliton Model Chiral Soliton Model
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Mixing coefficients
Chiral Soliton Model Chiral Soliton Model
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
-frac12 frac12
940
11161193
1318
Mass
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Collective Hamiltonian for flavor symmetry breakings
α β γ
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Two advantages offered by the model-independent approach in the χSM
1 the very same set of dynamical model-parameters allows us
to calculate the physical observables of all SU(3) baryons regardless of different
SU(3) flavor representations of baryons namely octet decuplet antidecuplet
and so on
2 these dynamical model-parameters can be adjusted to the experimental data
of
the baryon octet which are well established with high precisions
Chiral Soliton Model Chiral Soliton Model
Mass α β γ (for octet decuplet antide-cuplethellip)
Vector transitions wi (i=12hellip6)
Axial transitions ai (i=12hellip6)
[10] [10]
Baryonsl = l0(1 + c ΔT) linear expansion coefficient of a wire c
[8]
model-parame-tersHowever
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Octet (8) J p = 12 + Decuplet (10) J p = 32 +
Y
T3
YY
T3
-1
1 N
Ξ
Λ
Σ0
1
-1
-2
Δ
Σ
Ξ
Ω-
( udd ) n p ( uud )
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12 frac12
940
11161193
1318
Mass
( ddd )Δ- Δ++ ( uuu )Δ0 Δ+
Ω-( sss )
Ξ- Ξ0
Σ- Σ0 Σ+
-frac12 frac12-32 -32
1232
1385
1533
1673
Mass
SU(3) flavor symmetry breaking+ Isospin symmetry breaking
Chiral Soliton Model (mass) Chiral Soliton Model (mass)Collective Hamiltonian for flavor symmetry breakings
α β γ
+ α β γ
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
In order to determine the values of model parame-ters ldquoModel-independent approachrdquo needs more informa-tion(at least 2 inputs for antidecuplet baryons)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Formulae for Baryon Decuplet Masses
hadronic mass part in terms of δ1 and δ2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Formulae for Baryon Anti-Decuplet Masses
hadronic mass part in terms of δ3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Motivation Motivation
DPP EKP χQSM
Considered Effects SU(3) H SU(3) H SU(3) H
Input Masses
[MeV]
N(1710 )Θ+(1539plusmn2)
Ξ--
(1862plusmn2 )
ΣπN [MeV] 45 73 Predicted rarr 41
Results
I2 [fm] 04 049 048
msα [MeV]
msβ [MeV]
msγ [MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for symDPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches1
2
3
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In order to take fully into account the masses of
the baryon octet as input it is inevitable to consider
the breakdown of isospin symmetry
Two sources for the isospin symmetry breaking
1 mass differences of up and down quarks (hadronic part)
2Electromagnetic interactions (EM part)
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
ΔMB = MB1 ndash MB2
= (ΔMB )H + (ΔMB )EM
B(p) B(p)
k
p pp - k
EM mass corrections
Electromagnetic (EM ) self-energy
EM [MeV] Exp
(p ndash n)EM 076plusmn030
(Σ+ ndash Σ-)EM-017plusmn030
(Ξ0 ndashΞ-)EM-086plusmn030
( p ndash n )exp~ ndash 1293 MeV ( p ndash n ) EM ~076 MeV
9383 9396
1197 1189
1321 1315
( udd ) n p ( uud )
T3
( dss)Ξ- Ξ0 ( uss )
Σ- Σ+
Λ
Σ0
-frac12-1 1frac12
-1
1
Y
Gasser Leutwyler PhysRep 87 77 ldquoQuark Massesrdquo
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
In the ChSM
It can be further reduced to
Because of Bose symmetry
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Weinberg-Treiman formulaM EM(T3) = αT3
2 + βT3 + γDashen ansatzΔM EM ~ κT3
2 ~ κrsquoQ 2
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Coleman-Glashow relation
EM [MeV] Exp [input]
(Mp ndash Mn)EM076plusmn030
(MΣ+ ndash MΣ-)EM-017plusmn030
(MΞ0 ndashMΞ-)EM-086plusmn030
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
EM [MeV] Exp [input] reproduced
(Mp ndash Mn)EM076plusmn030 074plusmn022
(MΣ+ ndash MΣ-)EM-017plusmn030 -015plusmn023
(MΞ0 ndashMΞ-)EM-086plusmn030 -088plusmn028
Coleman-Glashow relation
Χ 2 fit
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
[ DWThomas et al]
[ PDG 2010 ]
[ GW 2006 ]
[ Gatchina 1981 ]
Physical mass differences of baryon decuplet
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (mass) Chiral Soliton Model (mass)
Mass splittings within a Chiral Soliton Model
Formulae for Baryon Octet Masses
(ΔM)EM(ΔM)H
hadronic mass part in terms of δ1 and δ2
G S Yang H-Ch Kim and M V Polyakov Phys Lett B 695 214 (2011)
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Motivation Motivation
DPP EKP χQSM This Work
Considered Effects SU(3) H SU(3) H SU(3) H EM + iso H + SU(3) H
Input Masses
[MeV]
N(1710 )
Θ+(1539plusmn2)
Ξ--(1862plusmn2 )
Θ+ 1500-1580 MeV
ΣπN [MeV] 45 73 Predicted rarr 41
Re-sults
I2 [fm] 04 049 048
msα [MeV]
msβ
[MeV]
msγ
[MeV]
-218-156-107
-605-23152
-197-94-53
c10 0084 0088 0037
ΓΘ+ [MeV] 15 for sym
111 for sym
071 for sym
DPP Diakonov Petrov Polyakov Z Physics A 359 305-314 (1997)EKP Ellis Karliner Praszalowicz JHEP 0405 002 (2004)χQSM Tim Ledwig H-Ch Kim K Goeke Phys Rev D 78 054005 amp Nucl Phys A 811 353 2008
Problems in the previous solitonic approaches
1
2
3
(ud-dss)
T3
1
Θ+(uudds)
frac12-frac12
-1
2
Ξ+32Ξ0
32Ξ-32Ξ--32
Σ-10 Σ010 Σ+
10
(u-udss)
p ( uud )( udd ) n
Y
S = 1
S = 0
Anti-decuplet (10)
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
with
The full expression for the axial-vector transitions g 1BBrsquo = g 1BBrsquo
(0) + g 1BBrsquo(op)
+ g 1BBrsquo(wf)
SU(3) baryons Motivation Mass splitting Vector Axial-vector Summary
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model (axial-vector) Chiral Soliton Model (axial-vector)
Axial-vector transitions
036plusmn008
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
ResultsResults
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Baryon octet masses
ResultsResults
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Baryon decuplet masses
ResultsResults
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Various experimental data for Θ+
and N
Mass of Θ+ 1525 ndash 1565 MeV
Mass of N 1665 ndash 1695 MeV
DIANALEPS
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
NA49 Mass of Ξ--32 = 1862 MeV
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
DIANALEPS
GRAALSAID
MAMI
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
DIANA
LEPS DIANA
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Chiral Soliton Model ldquomodel-independent approachrdquo
Mass splittings SU(3) and isospin symmetry breakings with EM
in the range of MΘ+ = 1500-1600MeV used as input
Masses of octet and decuplet are not sensitive to the MΘ+ input rarr very good agreement with experimental data
Small value of pion-nucleon sigma term is estimated (ΣπN = 35 - 40MeV)
MΘ+ = 1524 MeV [LEPS]
MN = 1685 MeV [GRAAL]
ΓΘ+ = 038plusmn011 MeV [DIANA]
reliable values within a chiral soliton model
Summary Summary
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH
Спасибо
Thank you
ありがとうございます 감사합니다
Danke schoumln
謝謝TERIMA KASIH