L.C Physics Charged/Neutral hadron separation and energies at 0.5 and 3 TeV

# Hadron Physics on the Lattice

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### Transcript of Hadron Physics on the Lattice

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

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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