ハドロン分光 Hadron spectroscopy

Aug 7-9, 2008 WS@KEK 1

ハドロン分光Hadron spectroscopy

保坂　淳　Hosaka, Atsushi, RCNP Osaka Univ

構成クォークとメソンダイナミックス

Aug 7-9, 2008 WS@KEK 2

Contents

1. General discussions Quark model Mathematical tool or realisti

c Quark excitation, minimal+qq, pentaquarks

2. Meson(s) in a baryon (1)Virtual, (2)Almost “real” mesons

3. Multiquarks

4. Summary

Aug 7-9, 2008 WS@KEK 3

1. General discussions

Aug 7-9, 2008 WS@KEK 4

QCDL =q(i /∂−m)q−

14

Fμν2

At high energies = Asymptotic freedom Success of perturbative QCD Quarks at deep inside hadrons are well understood

At low energies = Infrared slavery • Quarks are confined • Hadron masses (~1 GeV) >> Quark masses (~10 MeV) • Chiral symmetry is spontaneously broken

Aug 7-9, 2008 WS@KEK 5

Scale

Energy scale of hadrons is similar to that of nuclei

Thus

Hadron structure is very important to (Hyper) Nuclei

Historically: Constituent quark model seems to work well

Aug 7-9, 2008 WS@KEK 6

Quark model

Convenient method for flavor & spin symmetrySU(3) SU(2)

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Aug 7-9, 2008 WS@KEK 7

B[Q /Aμ , B]

FB[QFμνσμν , B] + DB{QFμνσ

μν , B}

D/(F+D) ratio of SU(6) = 3/5 = 0.6 fit ~ 0.58

μB ~1

mq→ mq ~ 300 MeV

So far quarks are convenient tool for realization of SU(3)/SU(6) algebra

Minimal

Anomalous

• Success of Gell-Mann Okubo mass formula

• Magnetic moments

Aug 7-9, 2008 WS@KEK 8

Lattice calculation for mBBErkol-Takahashi-Oka, 0805.3068[hep-lat]


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D/(F+D) = 0.616 ~ 0.6

Aug 7-9, 2008 WS@KEK 9

Constituent quarks seem at work for qq and qqq ground states minimal

What about other states?

• Quark excitation (single particle levels) • Minimal + qq • Multiquarks

genuine nonminimal, tetra, penta, …

Aug 7-9, 2008 WS@KEK 10

Excitation of a quark

Effective dynamical degrees of freedom

Realistic

Ground

Excited

RR

Aug 7-9, 2008 WS@KEK 11

2000

1500

1000

500

0

28 S

28 S

28 S

410

S

410

S

N Λ Σ Δ

P11 (1440)

F15 (1680)

P 13 (1720)

H19 (2220)

P11 (1710)P 01 (1600)

F05 (1820)

P 03 (1890)

H09 (2350)

P01 (1810)

F05 (2110)

P 11 (1660)

F15 (1915)

* P 13 (1840)

F17 (2030)

* F15 (2070)

** P 13 (2080)

P33 (1600)

F37 (1950)

F35 (1905)

P33 (1920)

P31 (1910)

H3 11 (2420)

P11 (939) P 01 (1116) P 11 (1189) P 13 (1385) P33 (1232)

=0L

=0L

=2L

=4L

** P13 (1900)

** F17 (1990)

** F15 (2000)

* F07 (2020)

** F37 (2390)

** P11 (1880)

8MS 8 MS28 MS

• Measured from the ground state • 8MS states are shifted downward by 200 MeV

Positive parity baryons

Takayama-Toki-Hosaka, PTP101, 1271(1999)

Aug 7-9, 2008 WS@KEK 12

Negative parity baryons

Aug 7-9, 2008 WS@KEK 13

12 のののののののののののの

Λ(1405) が軽すぎる

負パリティー状態にばらつきがある

光の結合もよくわかっていない（東北）　 S11(1535, 1650), D13(1520, 1700)

Aug 7-9, 2008 WS@KEK 14

Minimal + qq

ΔE ~1

R ~ m, m1/0.5 ~ 400 MeV

Aug 7-9, 2008 WS@KEK 15

Minimal + qq

ΔE ~1

R 1/0.5 ~ 400 MeV ~ m, m

B = qqq + qqq qq( )1 + qqq qq( )2 +L

Constituent model Penta(multi)quarkButNonmimimal

Aug 7-9, 2008 WS@KEK 16

σ(0+), a1(1+) … mesons

1/2–, 3/2–, … baryons

For one quanta (hbar omega) ~ one qq pair

Aug 7-9, 2008 WS@KEK 17

Virtual mesons

• Nucleon spin

• Neutron charge radius • Nuclear force

l = 0l = 1l = 0

sz <1 / 2

r2 < 0

Aug 7-9, 2008 WS@KEK 18

Almost real mesons

E,

Π(E) = dt∫ exp(itE) 0 Jα (t)Jα (0) 0

m

M

m

M

E*

Free Correlated

EB

q*

E(m+M)

Aug 7-9, 2008 WS@KEK 19

1

1.5

GeV

KΣ

KΛ

N

N(1440)

N(1710)

N(940)

Δ(1232)

Λ(1405)

Λ(1520) Σ

KN

Σ

P-wave

N(1535)

N(1650)

N

S-waveOpenchannels

s −wave: d3x∫ j0 (qr)ρ(r)

p−wave: d3x∫ j1(qr)ρ(r)

Aug 7-9, 2008 WS@KEK 20

2. Meson(s) in a baryon

A problem in Photoproduction N -> KΛ

Ozaki-Nagahiro-HosakaPhys.Lett.B665:178-181,2008. e-Print: arXiv:0710.5581 [hep-ph]

2-1. Virtual mesons

Aug 7-9, 2008 WS@KEK 21

N -> KΛ

Effective Lagrangian approach

NN Y, Q, …Y, Q, …

K*-exchange

Too strong?

A problem in Photoproduction

Aug 7-9, 2008 WS@KEK 22

Strong K* ?

Also discussed by Guidal et al. NPA627 (1997) 645



Bennhold et al.NPA695 (2001) 237

Aug 7-9, 2008 WS@KEK 23

Asymmetry

A =

σ⊥ −σP

σ⊥ +σP

+ Magnetic– Electric

=

K

K*K

MagneticElectric

Aug 7-9, 2008 WS@KEK 24

Asymmetry

A =

σ⊥ −σP

σ⊥ +σP

+ Magnetic– Electric

=

LEPS dataSumihama et al. PRC73,035214 (2006)

SU(3)

K

K*K

MagneticElectric

Aug 7-9, 2008 WS@KEK 25

WZW induced processMeson clouds

WZW term

• Strength is determined by QCD• Contains => Magnetic• Triangle can not be K*• Energy dependent, raising

εμνβ

p Λ

K

K

Actual computation (Ozaki) Covariant loop integral Cutoff ~ 1 GeV

Aug 7-9, 2008 WS@KEK 26

0.60.70.80.91

cosθcm

-1-0.500.5 LEPSdataphotonasymmetry

2.109GeV2.196GeV

withWZW term

w/oWZW term

A =

σ⊥ −σP

σ⊥ +σP

Asymmetry

0.6 0.7 0.8 0.9 1

0

0.5

– 0.5

LEPS data, Sumihama et al

Aug 7-9, 2008 WS@KEK 27

2-2. Almost real mesons

p の

K

Kの

の

p

K

K

の

の

As energy is increased

Aug 7-9, 2008 WS@KEK 28

Dynamically generated resonanceWeakly bound system of mBExample: Λ(1405) and N(1535)

Aug 7-9, 2008 WS@KEK 29

T ( s ) =V +VG( s)T( s)

KN-Σ scattering for Λ(1405)Oset and Ramos, NPA635, 99 (1998)

• Input V and • Suitably renormalize G(√s)

S-channel unitarityApprox. cross. symm.

Chiral Unitary model

V V G V V G V G V

+ • • •+ +

散乱方程式を解く

Aug 7-9, 2008 WS@KEK 30

L =tr(Bi /DB) + ... Dμ =∂μ +i2(∂μξ

†ξ + ∂μξξ† )

LWT =1

4 f2 trBiμ [φ∂μφ−∂μφφ,B] ~

s−M2 f

2 BBφφ

Contact, S-wave

V: WT interaction

B =

Σ0

2+

Λ6

Σ+ p

Σ− −Σ0

2+

Λ6

n

Ξ− Ξ0 −26Λ

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟

φ =

0

2+

η

6π + K +

π − −π 0

2+

η

6K 0

K − K 0 −2

6η

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟

ξ =exp(iφ / 2)

Aug 7-9, 2008 WS@KEK 31

G( s ) ~1

s −Enn

Λ

∑ =1

s− m2 +q2 − M 2 +q2q

Λ

∑


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a-parameter, subtraction constantis chosen suitably => apheno

G(√s): Loop function

G is divergent for the contact interaction VWT

Aug 7-9, 2008 WS@KEK 32







Mass spectrum Σ

σ K–p) σ Σ)

Oset and Ramos, NPA635, 99 (1998)

Aug 7-9, 2008 WS@KEK 33

Two poles

Σ -> Σ -> Σ

1426 + 16i (KN)

1390 + 66i (Σ

Jido-Oller-Oset-Ramos-Meissner, Nucl.Phys.A725:181-200,2003: nucl-th/0303062

Re Im

Aug 7-9, 2008 WS@KEK 34

疑問 :

メソンとバリオンの成分だけで記述できるか

他の成分（３ｑ）は要らない？

Aug 7-9, 2008 WS@KEK 35

To answer these questions:

We use the ambiguity (a-parameter) in G(E)

G( s ) =2MT

(2 )2a+ ln

MT2

μ2 +m2 −MT

2 + s2s

lnm2

MT2 +L

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

→2MT

(2 )2apheno + ln

MT2

μ2 +m2 −MT

2 + s2s

lnm2

MT2 +L

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

=2MT

(2 )2{ apheno −anatural

Δa1 24 4 34 4

+ anatural + lnMT

2

μ2 +m2 −MT

2 + s2s

lnm2

MT2 +L

Gnatural

1 24 4 4 4 4 4 44 34 4 4 4 4 4 4 4}

データから決める

a-parameter の決め方

Aug 7-9, 2008 WS@KEK 36



μ

G( s ) < 0G( s =μ) =0

Determination of anatural

(1)(2)

Thereshold

Aug 7-9, 2008 WS@KEK 37

(1) Physics of MB scattering

For M < s < M + m(threshold), G( s) < 0

G( s ) ~1

s −Enn∑ ~i

d4q

(2 )42M

P −q( )2 −M 2 + iε1

q2 −m2 + iε∫

(2) Boundary condition (matching)

Near the threshold

Choose this point at μ = M for LET

T (μ) =VχPT G( s =μ) =0

Aug 7-9, 2008 WS@KEK 38

apheno neq anatural

T ( s ) =1

VWT−1 −G( s)

=1

VWT−1 −ΔA

Vnatural

1 24 34 −Gnatural ( s)

How to interpret the difference

G( s ) =2MT

(2 )2{ apheno −anatural

Δa1 24 44 34 4 4

+ anatural + lnMT

2

μ2 +m2 −MT

2 + s2s

lnm2

MT2 +L

Gnatural

1 24 4 4 4 4 4 44 34 4 4 4 4 4 4 4}

Aug 7-9, 2008 WS@KEK 39

Modify the interaction

Vnatural−1 ≡VWT

−1 + ΔA⇒

Vnatural ( s) =1

VWT−1 + ΔA

=VWT +C

2 f 2s−M( )

2

s−Meff

• The deviation from the natural value (different a) is absorbed into the interaction as a pole term (1) of mass Meff and (2) of higher order

• If Δa is small (close to natural), Meff –> large Δa is large (different from natural), Meff ~ MT



Aug 7-9, 2008 WS@KEK 40

Λ(1405) N(1535) with realistic parameters

Coupled channel



S = -1, I = 0

Vnatural( s )

=1

VWT−1 + ΔA

is a matrix equation.

Pole in √s are complex.

Vnatural( s ) ~gig j

s −zeff gi g j

i j

Cha

nnel

i

Aug 7-9, 2008 WS@KEK 41

Subtraction constants



For S =-1 (~Λ(1405)), apheno ~ anatural Meff ~ 8 GeV

For S = 0 (~N(1535)), apheno ≠anatural Meff ~ 1.6 GeV

Λ(1405)

N*(1535)

Aug 7-9, 2008 WS@KEK 42

Couplings of N*(1535)Full amplitude = Pole + Dynamical(phenomenological) (Meson Cloud)

= +

Dynamical







Full

Pole

Aug 7-9, 2008 WS@KEK 43

4. Multiquarks

Aug 7-9, 2008 WS@KEK 44

4. Multiquarks • Large impact on hadron physics

• New form of matter

• Very difficult to observe and predict (and explain) Maybe as difficult as solving the problems of QCD?

• So far candidates are 1(1400, 1600, 2000) ~ can be hybrid +(1520), Z+(4430)

Aug 7-9, 2008 WS@KEK 45

PentaquarksLEPS (Nakano et al) exp. SPring-8, 2002

Q = + 1, S = +1 => Minimally 5 quarks

In the quark model M ~ 1.7 MeV, Fall apart width ~ very wideBUT exp M ~ 1.52 MeV, Width ~ very narrow < ~10 MeV

Fall apart

n → K– +

Aug 7-9, 2008 WS@KEK 46

Current status

Exp: • Many positive results until ~ 2004 • Many negative results appear CLAS

2003

Aug 7-9, 2008 WS@KEK 47

Current status

Exp: • Many positive results until ~ 2004 • Many negative results appear CLAS

2003The peak here disappears in 2006 PRL 97, 032001



Aug 7-9, 2008 WS@KEK 48

New LEPS exp

Deuteron target

• Fermi motion => Minimal momentum prescription

• Optimal cut

• No reflection from Λ(1520)QuickTime˛ Ç∆

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Aug 7-9, 2008 WS@KEK 49

Tohoku N*(1675)

proton neutron

Aug 7-9, 2008 WS@KEK 50

Theory

Accumulated properties of in various models

• No explanation everybody agrees

• Chiral soliton model can predict the mass and width JP = 1/2+

• In the quark model, JP = 3/2– is likely, but light mass seems difficult to explain

Color singlet vs. colored correlations

Must be in multiquarks states

Aug 7-9, 2008 WS@KEK 51

• For quark excitations like Δ, N*(1535), and others Many tools can excite them

• But if they are molecular type, e.g., KN K with a suitable energy should be used

For : On-shell K of p ~ 220 MeVFor Λ(1420): Off-shell K of E* ~ 475 MeV and of small p

Producing of Resonances

Aug 7-9, 2008 WS@KEK 52

Production

LEPS experiment tells that quasi-free seems working

K

K

s ~ M

N

Correlated KK



= 20 MeV

10 MeV

1 MeV

Aug 7-9, 2008 WS@KEK 53

For

K

Kのののののののののの

Nの

For Λ

K

の

vs

K

N

Λ

ΛNucleus

Aug 7-9, 2008 WS@KEK 54

5. Summary

• How do hadrons look like? Mass, size; Ground & excited states • Can excited orbit survive under the qq creation? • If qq (qq) has strong correlation, hadrons may form

molecule like structure • + seems alive in Spring-8 • Structure of such resonances is important

for many-body nuclear dynamics • If strangeness (kaon) is regarded heavy

similar phenomena can be seen in c, b, t hadrons

Aug 7-9, 2008 WS@KEK 55

4. Other topics

(1) Chiral symmetry

Vacuum properties: qq , f , MN , mV , etc

Spectroscopy, chiral multipletsSU(N f )×SU(N f )

(σ, ), (ρ,a1), (N,N* ), (N, Δ), etc

Aug 7-9, 2008 WS@KEK 56

Pattern of breaking

Example of SU(2) x SU(2) -> SU(2)

H = I = aIL IR[ IL , IR]

I

IL , IR

∑

cf: good SU(2) x SU(2) H = IL , IR

Coefficients carry information of breakingaIL IR

Also they determine some hadron properties (Larger symmetry has more constraints)

Aug 7-9, 2008 WS@KEK 57

• (N(939), N(1535))

DeTar-Kunihiro, Jido-Oka-Hosaka

Left: (1/2,0) => a1 (1/2,0) + a2 (0,1/2)

• (D(1232), D(1700), N(1520), N(1720))

Jido-Hatsuda-Kunihiro

Mirror baryon

• (N(939), N(1440), D(1232))

Weinberg, Beane

• (N(939), Quartet)

Quartet model

Nagata-Hosaka-Dmitrasinovic, to appear in PRL

Aug 7-9, 2008 WS@KEK 58

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Where to study

Aug 7-9, 2008 WS@KEK 59

dσdcosθ

[μb]

p –> K+Λ

W = 2.164 GeV

w/o WZW

Aug 7-9, 2008 WS@KEK 60



Poles

++

+

Dynamically generated (= VWT + Natural G)

+ Phenomenological

Documents

ハドロン分光 Hadron spectroscopy