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Πανεπιστήμιο Κύπρου. Κ. Αλεξάνδρου. Hadron Physics on the Lattice. Outline . The Highlight of Lattice 2007- Reaching the chiral regime - Results using light dynamical fermions Twisted mass - ETMC (Cyprus, France, Germany, Italy, Netherlands, UK, Spain, Switzerland) - PowerPoint PPT Presentation
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C. Alexandrou, University of Cyprus PSI, December 18th 2007
Hadron Physics on the Lattice
Πανεπιστήμιο ΚύπρουΚ. Αλεξάνδρου
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Outline
The Highlight of Lattice 2007- Reaching the chiral regime
- Results using light dynamical fermions
Twisted mass - ETMC (Cyprus, France, Germany, Italy, Netherlands, UK, Spain, Switzerland)
Clover improved dynamical fermions - QCDSF/UKQCD
Overlap fermions - JLQCD
Hybrid approach - LHPC and Cyprus
Staggered fermions:Charm Physics - HPQCD
- Chiral extrapolation of lattice results
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Lattice 2007: Highlights
• Impressive progress in unquenched simulations using various
fermions discretization schemes
C. Alexandrou, University of Cyprus PSI, December 18th 2007
a
μ
Uμ(n)=eigaAμ(n)
ψ(n)
€
SF = ψ (k)D(k,n)ψ (n)k,n∑
€
S = SG + SF Difficult to simulate -->
90’s Det[D]=1 : quenched
⟨O⟩=∫ dUndψ ndψ n O[U,ψ ,ψ ]e−S
n∏
Z=
∫ dUndet[D]O[U,D−1]e−SG
n∏
Z
Integrate out
It is well known that naïve discretization of Dirac action
leads to 16 speciesSF = d4x ψ(x) γμ∂μ +μ⎡⎣ ⎤⎦ψ(x)∫ → ∂μψ(x)=ψ(x +μ)-ψ(x -μ)
2a
Lattice fermionsBasics:
A number of different discretization schemes have been developed to avoid doubling:
Wilson : add a second derivative-type term --> breaks chiral symmetry for finite a
Staggered: “distribute” 4-component spinor on 4 lattice sites --> still 4 times more species,
take 4th root, non-locality Nielsen-Ninomiya no go theorem: impossible to have doubler-free, chirally symmetric, local, translational invariant fermion lattice action BUT…
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Chiral fermions
Instead of a D such that {γ5, D}=0 of the no-go theorem, find a D such that {γ5,D}=2a D γ5D Ginsparg - Wilson relation
Luescher 1998: realization of chiral symmetry but NO no-go theorem!
Kaplan: Construction of D in 5-dimensions Domain Wall fermions
Left-handed fermionright-handed fermion
L5
Neuberger: Construction of D in 4-dimensions but with use of sign function Overlap fermions
D =
1+ε(D w )2
, ε(D w )=D w
D w+D w
Equivalent formulations of chiral fermions on the lattice
But still expensive to simulate despite progress in algorithms
Compromise: - Use staggered sea (MILC) and domain wall valence (hybrid) - LHPC
- Twisted mass Wilson - ETMC
- Clover improved Wilson - QCDSF, UKQCD, PACS-CS
Rely on new improved algorithms
C. Alexandrou, University of Cyprus PSI, December 18th 2007
QuickT
ime™ a
nd aTIFF
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pressed
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pressor
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ee this
picture.
Simulation of dynamical fermions
Results from different discretization schemes must agree in the continuum limit
Clark
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Lattice 2007: Highlights Impressive progress in unquenched simulations using various
fermions discretization schemes
With staggered, Clover improved and Twisted mass dynamical fermions results are reported with pion mass of ~300 MeV
PACS-CS reported simulations with 210 MeV pions! But no results shown yet
RBC-UKQCD: Dynamical NF=2+1 domain wall simulations reaching ~300 MeV on ~3 fm volume are underway
JLQCD: Dynamical overlap NF=2 and NF=2+1, ml ~ms/6, small volume (~1.8 fm)
Progress in algorithms for calculating D-1 as mπ physical value
Deflation methods: project out lowest eigenvalues Lüscher, Wilcox, Orginos/Stathopoulos
C. Alexandrou, University of Cyprus PSI, December 18th 2007
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Deflation methods in fermion inverters -Wilcox
Twisted mass 203x32 at κcr
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C. Alexandrou, University of Cyprus PSI, December 18th 2007
Lattice 2007: Highlights Impressive progress in unquenched simulations using various
fermions discretization schemes
With staggered, Clover improved and Twisted mass dynamical fermions results are reported with pion mass of ~300 MeV
PACS-CS reported simulations with 210 MeV pions! But no results shown yet
RBC-UKQCD: Dynamical NF=2+1 domain wall simulations reaching ~300 MeV on ~3 fm volume are underway
JLQCD: Dynamical overlap NF=2 and NF=2+1, ml ~ms/6, small volume (~1.8 fm)
Progress in algorithms for calculating D-1 as mπ physical value
Deflation methods: project out lowest eigenvalues Lüscher, Wilcox, Orginos/Stathopoulos
Chiral extrapolations
Using lattice results on fπ/mπ yield LECs to unprecedented accuracy
Begin to address more complex observables e.g. excited states and resonances, decays, finite density
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Chiral extrapolationsControlled extrapolations in volume, lattice spacing and quark masses: still needed for reaching the physical world
Quark mass dependence of observables teaches about QCD - can not be obtained from experiment
Lattice systematics are checked using predictions from χPT
Chiral perturbation theory in finite volume:
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Correct for volume effects depending on pion mass and lattice volume
Like in infinite volume
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Pion sectorApplications to pion and nucleon mass and decay constants
e.g.
mπ −μ π (L)
μ π
=-x2λ
Iμ π
(2) (λ)+ xIμ π
(4) (λ)⎡⎣ ⎤⎦|rn|≠0∑
fπ - fπ (L)fπ
= - xλ
I fπ(2)(λ)+ xI fπ
(4)(λ)⎡⎣ ⎤⎦|rn|≠0∑
x =μ 0
2
(4πfπ0 )2
, λ =μ π |rn |L
G. Colangelo, St. Dürr and Haefeli, 2005
Applied by QCDSF to correct lattice data
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r0=0.45(1)fm
NLO continuum χPT
Pion decay constant
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Twisted mass dynamical fermions
Consider two degenerate flavors of quarks: Action is
SF =a4 ψ(x) D w [U] +μ 0 + iμγ5τ3( )
x∑ ψ(x)
Wilson Dirac operator untwisted mass
Twisted mass μ τ3 acts in flavor space
Advantages: - Automatic O(a) improvement (at maximal twist)
- Only one parameter to tune (zero PCAC mass at smallest μ)
- No additional operator improvement
Disadvantages: - explicit chiral symmetry breaking (like in all Wilson)
- explicit breaking of flavour symmetry appears only at O(a2) in practice only affects π0
Physics results reported for ~300 MeV pions on spatial size of about 2.7 fm with a < 0.1fm
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Pion decay constant with twisted mass fermionsSimultaneous chiral fits to mπ and fπ Extract low energy constants
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r0=0.441(14)fm
l3,4 ≡λoγL3,4
2
μπ±2
⎛⎝⎜
⎞⎠⎟
λ3 =3.44(28), λ4 =4.61(9)
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S. Necco, Lat07NF=2
C. Alexandrou, University of Cyprus PSI, December 18th 2007
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Leutwyler (hep-ph/0612112)ETMC
ππ s-wave length a00 and a0
2
ππ-scattering lengths
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C. Alexandrou, University of Cyprus PSI, December 18th 2007
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π-π scatteringLüscher’s finite volume approach:
Calculate the energy levels of two particle states in a finite box
DEn =En - 2μ =2 πn2 +μ 2 - 2μ with pn given by
p cotδ(π)= 1πL
f(rn)
rn2 −
πL2π
⎛⎝⎜
⎞⎠⎟2rn
∑
Expand ΔE0 about p~0: DE0 =-
4πaμ L3
1+c1aL+c2
aL
⎛⎝⎜
⎞⎠⎟2⎡
⎣⎢⎢
⎤
⎦⎥⎥+O
1L6
⎛⎝⎜
⎞⎠⎟
where we use particle definition for the scattering length: a = lim
p→ 0
τanδ(π)π
Applied to I=2 two-pion system within the hybrid approach (staggered sea and domain wall fermions)
mπa02 =-0.0426(27)
S. Beans et al. PRD73 (2006)
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Other applications: I=1 KK scattering
N-N scattering - too noisy
no new LECs
form independent of sea quarks if valence are chiral
π-π scattering - improved
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More statistics
mixed action χPT formulamπa0
2 =-0.04330(42)
A. Walker-Loud, arXiv:0706.3026
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C. Alexandrou, University of Cyprus PSI, December 18th 2007
Pion form factor Sh. Hashimoto
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Dynamical overlap, L~1.8 fm
Fπ (q
2 )=1
1−q2 / μ r2+δ1q
2 + ...
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Fπ (q2 )=1−
16< r2 > q2 + ...
< r2 >=c0 −1
(4πfπ )2λn
μ π2
(4πfπ )2
⎛⎝⎜
⎞⎠⎟+c1μ π
2
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Set initial and final pion momentum to zero --> no disadvantage in applying the one-end trick
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G. Koutsou, Lat07
q-q
4-point function: first application of the one-end trick (C. Michael):
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S. Simula, ETM Collaboration
one-trick for 3pt function
VMD :
11−q2 / μ r
2
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Wilson
Pion form factor
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Pion form factor
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Comparison with experiment
S. Simula , Lat07
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Rho form factors
<ρ(p’)|jμ|ρ(p)> decomposed into three form factors Gc(Q2), GM(Q2), GQ(Q2)
Related to the ρ quadrupole moment GQ(0)=mρ
2 Qρ
Adelaide group: Qρ non-zero --> rho-meson deformed in agreement with wave function results using 4pt functions
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|Ψ(y)|2
One-end trick improves signal, application to baryons is underway
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Decreasing quark mass
G. Koutsou, Lat07
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Baryon sector
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Twisted mass and Staggered results
Two fit parameters: m0=0.865(10), c1=-1.224(17) GeV-1 to be compared with ~-0.9 GeV-1 (π-N sigma term)
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C. Alexandrou, University of Cyprus PSI, December 18th 2007
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Delta mass splittingSymmetry: u d --> Δ++ is degenerate with Δ- and Δ+ with Δ0
Check for flavour breaking by computing mass splitting between the two degenerate pairs
Splitting consistent with zero in agreement with theoretical expectations that isospin breaking only large for neutral pions (~16% on finest lattice)
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Baryon structure
Coupling constants: gA, gπNN, gπΝΔ, …
Form factors: GA(Q2), Gp(Q2), F1(Q2),….
Parton distribution functions: q(x), Δq(x),…
Generalized parton distribution functions: H(x,ξ,Q2), E(x,ξ,Q2),…
Need to evaluate three-point functions: <J(p’,tsink) O (t,q) J†(p,0)>
O(t,rq)= δ3x ε−irx.rq∫ ψ(x) ΓD μ1 D μ2 ...( )ψ(x)
Four-point functions: yield detailed info on quark distribution
only simple operators used up tp now - need all-to-all propagators
Hybrid actions
Wilson fermions
In addition:
Masses: two-point functions <J(tsink) J†(0)> QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
C. Alexandrou, University of Cyprus PSI, December 18th 2007
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Nucleon axial charge
HBχPT with Δ Hemmert et al. , Savage & Beane
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Finite volume dependence
Forward nucleon axial vector matrix element: < N | uγμγ5u - δγμγ5δ |N >=γAv(π)γμγ5v(π)
Improved Wilson (QCDSF)
Pleiter, Lat07
accurately measured
no-disconnected diagrams
chiral PT
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Nucleon form factors
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Isovector form factors obtained from connected diagram
Isovector Sachs form factors:
G E =Γ Eπ −Γ E
n
Γ M =Γ Mπ −Γ M
n
Disconnected diagram not evaluated
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with GE and GM given in terms of F1 and F2
G E (q2 ) =F1(q2 )+
q2
(2μ N )2F2(q
2 )
Γ M (q2 )=F1(q
2 )+ F2(q2 )
In last couple of years better methods have become available, dilution, one-end trick,…
Evaluation of 3pt function using the fixed sink approach --> any current to be inserted with no additional computational cost
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Nucleon EM form factors
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Results using dynamical Wilson fermions and domain wall valence on staggered sea (from LHPC) are consistent
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QCDSF/UKQCD
Cyprus/MIT Collaboration, C. A., G. Koutsou, J. W. Negele, A. Tsapalis
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Fp =23Fu −
13Fδ
Fn =−13Fu +
23Fδ Dirac FF
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Nucleon axial form factors
Within the fixed sink method for 3pt function we can evaluate the nucleon matrix element of any operator with no additional computational cost
Aμ
a =ψγμγ5
τa
2ψ use axial vector current to obtain the axial form factors
pseudoscalar density to obtain GπN(q2) Pa =ψiγ5
τa
2ψ
< N(r
′π , ′s)|Aμ3 |N(
rπ,s) >=i
μ N2
EN ( ′π )EN (π)
⎛⎝⎜
⎞⎠⎟1/2
u( ′π ) Γ A(Q2 )γμγ5 +
qμγ5
2μ N
Γ π (Q2 )
⎡⎣⎢⎢
⎤⎦⎥⎥τ3
2u(π)
2mq < N(r
′π , ′s)|P3 |N(rπ,s) >=
μ N2
EN( ′π )EN(π)
⎛⎝⎜
⎞⎠⎟1/2
fπμ π2Γ πNN (Q
2 )
μ π2 +Q2
u( ′π ) iγ5
τ3
2u(π)
PCAC relates GA and Gp to GπNN:
GA (Q2 ) - Q2
4mN2 Gp (Q2 ) = 1
2mN
fπmπ2GπNN (Q2 )
mπ2 + Q2
Generalized Goldberger-Treiman relation
Pion pole dominance:
12mN
Gp (Q2 ) ~2GπNN (Q2 )fπ
mπ2 + Q2
→ Γ πNN (Q2 )fπ =μ NΓ A(Q
2 ) Goldberger-Treiman relation
Th. Korzec
C. Alexandrou, University of Cyprus PSI, December 18th 2007
GA and Gp
monopole fit
pion pole dominance
monopole fit to experimental results
Results in the hybrid approach by the LPHC in agreement with dynamical Wilson results
Unquenching effects large at small Q2 in line with theoretical expectations that pion cloud effects are dominant at low Q2
Cyprus/MIT collaboration
C. Alexandrou, University of Cyprus PSI, December 18th 2007
N to Δ transition form factors
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Electromagnetic N to Δ: Write in term of Sachs form factors:
< D(r′π , ′s)|jμ |N(
rπ,s) >=i
23
μ Dμ N
ED ( ′π )EN (π)
⎛⎝⎜
⎞⎠⎟1/2
us (r′π , ′s)Osμ u(
rπ,s)
Osμ =Γ M1(q2 )Ksμ
M1 +Γ E2(q2 )Ksμ
E2 +Γ C2(q2 )Ksμ
C2
Magnetic dipole: dominant
Electric quadrupole
Coloumb quadrupole
Axial vector N to Δ: four additional form factors, C3A(Q2), C4
A(Q2), C5A(Q2), C6
A(Q2)
Dominant: C5A GA
C6A GpPCAC relates C5
A and C6A to GπΝΔ :
C5
A (Q2 )−Q2
μ N2C6
A(Q2 )=1
2μ N
fπμ π2Γ πND (Q
2 )
μ π2 +Q2
Generalized non-diagonal Goldberger-Treiman relation
Pion pole dominance:
1mN
C6A (Q2 ) :
12
G πND (Q2 )fπ
μ π2 +Q2
→ Γ πND (Q2 )fπ =2μ NC5
A(Q2 ) Non-diagonal Goldberger-Treiman relation
C. Alexandrou, University of Cyprus PSI, December 18th 2007
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Quadrupole form factors and deformationQ2=0.127 GeV2
Large pion effects
Quantities measured in the lab frame of the Δ are the ratios:
R EM (EMR) =−Γ E2(Q
2 )
Γ M1(Q2 )
R SM (CMR )=−|rq |
2μ D
Γ C2(Q2 )
Γ M1(Q2 )
Precise experimental data strongly suggest deformation of Nucleon/Δ
First conformation of non-zero EMR and CMR in full QCD
C. N. Pananicolas, Eur. Phys. J. A18 (2003)
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Axial N to Δ
Bending seen in HBχPT with explicit Δ - Procura et al.
SSE to O(ε3):
C5A(Q2,mπ)=a1+a2mπ
2+a3Q2+loop
C6A
mN2 =a4 −
1μ π
2 +Q2
a5 +a6μ π2 +a7Q
2
+λooπ(μ π ,cA ,γA ,γ1,fπ ,D)
⎡⎣⎢⎢
⎤⎦⎥⎥
Again large unquenching effects at small Q2
C. Alexandrou, University of Cyprus PSI, December 18th 2007
GπΝN and GπΝΔ
GπΝ=a(1-bQ2/mπ2)
GTR: GπΝ=GAmN/fπ
GπΝΔ=1.6GπΝ
Q2-dependence for GπΝ (GπΝΔ) extracted from GA (C5
A) using the Goldberger-Treiman relation deviates at low Q2
Small deviations from linear Q2-dependence seen at very low Q2 in the case of GπΝΔ
GπΝΔ/GπΝ = 2C5A/GA as predicted by taking
ratios of GTRs
GπΝΔ/GπΝ=1.60(1)
Curves refer to the quenched data
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Goldberger-Treiman Relations
Deviations from GTR
Improvement when using chiral fermions
1mN
C6A (Q2 ) :
12
G πND (Q2 )fπ
μ π2 +Q2
→ Γ πND (Q2 )fπ =2μ NC5
A(Q2 )
12mN
G p (Q2 ) :2G πN (Q
2 )fπμ π
2 +Q2
→ Γ πN (Q2 )fπ =μ NΓ A(Q
2 )
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Δ electromagnetic form factors
< D(r′π , ′s)|jμ |D(rπ,s) >=i
μ D2
ED ( ′rπ )ED (
rπ)us ( ′π , ′s)Osμτuτ(π,s)
Osμτ =δsτ a1iγμ +
a2
2μ D
( ′π μ +πμ )⎡⎣⎢
⎤⎦⎥- q
sqτ
2μ D2
c1iγμ +
c2
2μ D
(r′π μ +
rπμ )
⎡⎣⎢
⎤⎦⎥
Four form factors: GE0, GE2,GM1, GM3 given in terms of a1, a2,c1,c2
Like for the nucleon form factors only the connected diagram is evaluated --> isovector part
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GE0
mπ=0.56 GeVmπ=0.49GeVmπ=0.41 GeV
Q2 (GeV2)
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GM1
mπ=0.56 GeVmπ=0.49 GeV
mπ=0.41 GeV
Q2 (GeV2)
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Accurate results for the dominant form factors calculated in the quenched approximation. Unquenched evaluation is in progress - Cyprus/MIT Collaboration, C. A., Th. Korzec, Th. Leontiou J. W. Negele, A. Tsapalis
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Electric quadrupole Δ form factor
GE2 connected to deformation of the Δ: G E2 (Q2 =0) : μ D2 δ3rψ(r)∫ 3z2 −r2⎡⎣ ⎤⎦ψ(r)
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Q2 (GeV2)
mπ=0.56 GeVmπ=0.49 GeVmπ=0.41 GeV
GE2 <0 Δ oblate in agreement with what is observed using density correlators to extract the wave function, C. A., Ph. de Forcrand and A. Tsapalis, PRD (2002)
GM3 also evaluated, small and negative
C. Alexandrou, University of Cyprus PSI, December 18th 2007
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Moments of parton distributions
< N(p, s) | Oqμ1 ...μn{ } |N(π,s) >~ δx∫ xn-1q(x)
Forward matrix elements:
< xn >q= δx xn q(x)+ (-1)n+1q(x)⎡⎣ ⎤⎦-1
1
∫ q =q↓ +q↑
< xn >Dq= δx xn
-1
1
∫ Dq(x)+ (-1)nDq(x)⎡⎣ ⎤⎦ Dq =q↓ - q↑
< xn >δq= δx xn
-1
1
∫ δq(x)+ (-1)n+1δq(x)⎡⎣ ⎤⎦ δq =qT +q⊥
unpolarized moment
polarized moment
transversity
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Parton distributions measured in deep inelastic scattering
Oqμ1 ...μn =q γμ1 i
τD μ2 ...i
τD μn }⎡⎣ ⎤⎦q
O5qμμ1 ...μn =q γ5γ
μ iτD μ1 ...i
τD μn }⎡⎣ ⎤⎦q
OTqμnμ1 ...μn =q γ5s
μn iτD μ2 ...i
τD μn }⎡⎣ ⎤⎦q
τD =
12(rD −
sD)
3 types of operators:Moments of parton distributions
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Moments of Generalized parton distributions
Off diagonal matrix element Genelarized parton distributions
GPD measured in Deep Virtual Compton Scattering
< N(p', s') | Oqμ1 ...μn{ } |N(π,s) >=u( ′π ) Ani
q (τ)K niA +Bni
q (τ)K niB{ } +δn,εvεnCni
q (τ)K nC
i=0εvεn
n-1
∑⎡
⎣⎢⎢⎢
⎤
⎦⎥⎥⎥u(π)
Generalized FF
Hn (x, τ)≡ δx-1
1
∫ xn-1 H(x, x, τ)
En (x, τ)≡ δx-1
1
∫ xn-1 E(x, x, τ)
Hn (0, τ)=An0(τ) A10(τ)=F1(τ)
En (0, τ)=Bn0(τ) B10(τ)=F2(τ)
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GPDs
p =12
π+ ′π( ), q =(x + x)π, ′q =(x −x)π
τ=−Q2 =D2 t=0 (forward) yield moments of parton distributions
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Transverse quark densities Fourier transform of form factors/GPDs gives probability
dx xn-1 -1
1
∫ q(x,rb⊥ )=
δ 2D⊥
(2π )2∫ ε-irb⊥ .
rD⊥ An0
q (-rD⊥
2 )
q(x → 1,rb⊥ ) ∝δ 2(b⊥ )
Transverse quark distributions:
M. Burkardt, PRD62 (2000)QuickTime™ and a
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q(x,
rb⊥
2 )=δ 2D⊥
(2π )2∫ ε-irb⊥ .
rD⊥ H(x,x =0, -D⊥
2 )
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NLO: gA,0--> gA,lat, same with fπ
Self consistent HBχPT
<x>u-d
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LHPCas n increases slope of An0 decreases
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C. Alexandrou, University of Cyprus PSI, December 18th 2007
Spin structure of the nucleon
Jq = 1
2< x >q +B20
q (0)( ) Lq =Jq -12DSq DS =%A10
q (0)
QCDSF/UKQCD Dynamical Clover
For mπ~340 MeV: Ju=0.279(5) Jd=-0.006(5)
Lu+d=-0.007(13) ΔΣu+d=0.558(22)
In agreement with LPHC, Ph. Hägler et al., hep-lat/07054295
Total spin of quark:
Spin of the nucleon: 12=Lu+δ +
12DSu+δ + Jγ
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A20(0)
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Transverse spin density
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Unpolarized
u
d
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N
N
u
d
q unpolarized N unpolarized
C. Alexandrou, University of Cyprus PSI, December 18th 2007
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C. Alexandrou, University of Cyprus PSI, December 18th 2007
Charm PhysicsHPQCD: C. Davies et al.
Determination of CKM matrix, Test unitarity triangleWeak decays - calculate in lattice QCD
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Nf=2+1 dynamical staggered fermions
0.9 1.0 1.1 0.9 1.0 1.1
Quenched
Full QCD results show impressive agreement with experiment across the board - from light to heavy quarks
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Lattice QCD First message: Use unquenched QCD
Bench mark
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Weak Decays and CKM matrix
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Leptonic D-meson decays:
Lattice results versus experiment - CLEO-c
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c
d
l
ν
For charm use highly improved staggered action remove further cut off effects at α(amc)2 and (amc)4
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fDs/fD=1.164(11)fDs
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Semi-leptonic: in progress
C. Alexandrou, University of Cyprus PSI, December 18th 2007
B-decays
Use non-relativistic QCD for b-quark with mb fixed from mΥ
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mq/ms
fBs/fBq
Log- dependence on light quark mass
fB = 216(22) MeV,
fBs
fB
= 1.20(3)
to be compared with experiment ICHEP 06: fB=229(36)(34)MeV
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Semileptonic B-decays
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Unitarity triangle
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Using lattice input
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Expectation: errors on lattice results should halve in the next two years
C. Alexandrou, University of Cyprus PSI, December 18th 2007
Conclusions
Accurate results on coupling constants, Form factors, moments of generalized parton distributions are becoming available close to the chiral regime (mπ~300 MeV).
More complex observables are evaluated e.g excited states, polarizabilities, scattering lengths, resonances, finite density
First attempts into Nuclear Physics e.g. nuclear force
• Lattice QCD is entering an era where it can make significant contributions in the interpretation of current experimental results.
• A valuable method for understanding hadronic phenomena
• Computer technology and new algorithms will deliver 100´s of Teraflop/s in the next five years
Provide dynamical gauge configurations in the chiral regime
Enable the accurate evaluation of more involved matrix elements
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