10/08/2008ky ccs seminar strangeness and glue in the nucleon from lattice qcd takumi doi (univ. of...

10/08/2008 KY CCS seminar

Strangeness and glue in the nStrangeness and glue in the nucleon from lattice QCDucleon from lattice QCD

Takumi Doi(Univ. of Kentucky)

In collaboration withUniv. of Kentucky:M. Deka, S.-J. Dong, T. Draper, K.-F. Liu, D. MankameTata Inst. of Fundamental Research:N. MathurUniv. of Regensburg:T. Streuer

QCD Collaboration


Introduction

Nucleon structure Fundamental particle as only stable baryons:

the structure is crucial to understand not only nucleons themselves but also to understand the QCD

Electric/Magnetic structure

GE: electric form factor GM: magnetic form factor

electron

1950s


Introduction

Nucleon structure Fundamental particle as only stable baryons:

the structure is crucial to understand not only nucleons themselves but also to understand the QCD

Deep Inelastic Scattering (DIS)

W1 F1 structure function W2 F2 structure function Weak Q2 dependence & 2xF1=F2 Parton model

electron

1960s


Introduction

Nucleon structure Parton model

P

xP

Parton carry (xP) momentum

Q2 evolution QCD interaction


Introduction Nucleon structure

Yet, whole understanding of its structure has not been obtained

Q2-dependence QCD pert. calc., but x-dependence ??

Spin “crisis” The EMC experiments (1989) quark spin is only 30% Orbital angular momentum and/or gluon must carry the rest

Exciting results are coming from experiments RHIC, JLAB, DESY, … Inputs from theoretical prediction are necessary for

some quantities: e.g., strangeness <x2>


Introduction The ingredients: valence/sea quark and gluon

Quark “connected” insertion diagrams Quark“disconnected insertion” diagrams Glue what is suitable “glue” operator ?

Glue terms Glue in <x> Glue contribution to nucleon spin necessary to complete (angular) momentum su

m rules

Tough calculation in lattice


Outline Lattice QCD and our methodology Energy-momentum tensor

<x> and spin <x> from disconnected insertion <x> from glue

Glue operator from overlap operator Strangeness magnetic/electric form

factor Outlook


Non-perturbative fluctuations are included via Path-Integral

Monte Carlo calculation(Weighted sum is taken)

1

2

3

tim

e

space

det=1: quenched

det≠1: full QCD

Lattice QCD


Lattice QCD Various fermion formulations

Wilson fermion, clover fermion Calculation cost is cheap Chiral symmetry broken explicitly

Staggered fermion Calculation cost is cheaper Part of Chiral symmetry respected Flavor cannot identified, Rooting problem

Domain Wall / Overlap fermion Calculation cost is expensive Good Chiral symmetry


Lattice QCD Various fermion formulations

Wilson fermion, clover fermion Calculation cost is cheap Chiral symmetry broken explicitly

Staggered fermion Calculation cost is cheap Part of Chiral symmetry respected Flavor cannot identified, Rooting problem

Domain Wall / Overlap fermion Calculation cost is expensive Good Chiral symmetry

Symmetry and (spontaneous) broken symmetry

Nobel Prize 2008

Nambu Maskawa-Kobayashi


Methodology

Matrix elements

Requires 4pt function calc.

Operator Product Expansion (OPE) 3pt calc.


Disconnected Insertion (DI)

Why are DI diagrams important ? Strangeness in nucleon Strangeness electric/magnetic form factor Structure function, <x>, <x2> Quark spin and angular momentum in nuleon Pion-Nucleon-Sigma term

Now is the full QCD Era: dynamical sea quark ! Challenging subject

All-to-all propagator is necessary Straightforward calculation impossible

O(105) inversion for O(106)XO(106) matrix

Rich Physics !


Stochastic Method for DI Use Z(4) (or Z(2)) noises such that

DI loop can be calculated as

Introduce new source for noises (“off-diagonal” part) Unbiased subtraction using hopping parameter expansion

(HPE)

Off-diagonal contaminations are estimated by HPE and subtracted (in unbiased way)

Disconnected Insertion (DI)

S.-J.Dong, K.-F.Liu, PLB328(1994)130


Analysis for <x> (D.I.)


Methodology The energy momentum tensor can be decomposed int

o quark part and gluon part gauge invariantly

Nucleon matrix elements can be decomposed as

(angular) momentum sum rules (reduce renormalization consts.)

X.Ji (1997)

Orbital part


Methodology <x> can be obtained by

q

pp’=p-qt1

t2t0


Methodology We take the ratio of 3pt to 2pt

q

pp’=p-q t1

t2t0

To improve S/N, we take a sum over t1=[t0+1, t2-1]

Slope wrt. t2 (sink time) corresponds to the signal


Methodology Spin components can be obtained by

q

pp’=p-q

N.B. we use one more equation to extract T1 and T2 separately(q^2 dependence could be different)


Analysis (1) Nf=2+1 dynamical clover fermion + RG impro

ved gauge configs (CP-PACS/JLQCD) About 800 configs Beta=1.83, (a^-1=1.62GeV, a=0.12fm) 16^3 X 32 lattice, L=2fm Kappa(ud)=0.13825, 0.13800, 0.13760

M(pi)= 610 – 840 MeV Kappa(s)=0.13760 (Figures are for kappa(ud)=0.13760)


Analysis (2)

Wilson Fermion + Wilson gauge Action 500 configs with quenched approximation Beta=6.0, (a^-1=1.74GeV, a=0.11fm) 16^3 X 24 lattice, L=1.76fm kappa=0.154, 0.155, 0.1555

M(pi)=480-650 MeV Kappa(s)=0.154 , kappa(critical)=0.1568 (Figures are for kappa=0.154)


D.I. calculation

D.I. diagrams are estimated Z(4) noise (color, spin, space-time) method #noise = 300 (full), 500 (quenched) (To

reduce the possible autocorrelation, we take different noise for different configurations)

We also take many nucleon sources (full: #src=64/32 (lightest mass/others), quenched: #src=16 ) We found that this is very effective (autocorrelation between different sources is small) CH, H and parity symmetry:

(3pt)=(2pt) X (loop)(3pt) = Im(2pt) X Re(loop) + Re(2pt) X Im(loop)


Results for <x>(s)

Linear slope corresponds to signal

#src = 1

Nf=2+1

Somewhat large errors


Many nucleon sources

Further improvement

q

pp’=p-q

S/N improve by √Nnoise

S/N improve by √Nsrc

N.B. The calculations of loop part and 2pt part are independent !


Results for <x>(s)

Linear slope corresponds to signalBy increasing the nucleon sources #src = 1 32, the signal becomes prominent

Nf=2+1

Error bar reduced more than factor 5 !


Chiral Extrapolation

Note: The values are not renormalized

<x>(ud) [D.I.] <x>(s)

Nf=2+1

We expect we can furhter reduce the error by subtraction technique using clover-fermion HPE


Ratio of <x>(s) and <x>(ud)[D.I.]

<x>(s) / <x>(ud)[D.I.] =0.857(40)

Note: The values are not renormalized

Preliminary

<x>(s) / <x>(ud)[D.I.] =0.88(7)

Nf=2+1

c.f. Quenched

M. Deka


Glue calculation Gluon Operator

Glue operator constructed from link variables are known to be very noise

Smearing ? (Meyer-Negele. PRD77(2008)037501, glue in pion)

Field tensor constructed from overlap operator

Ultraviolet fluctuation is expected to be suppressed In order to estimate D_ov(x,x), Z(4) noise method is us

ed, where color/spin are exactly diluted, space-time are factor 2 dilution + even/odd dilution, #noise=2

K.-F.Liu, A.Alexandru, I.Horvath PLB659(2008)773


Results for <x>(g) (quenched)


First time to obtain the signal of glue in nucleon !

c.f. M.Gockeler et al., Nucl.Phys.Proc.supp..53(1997)324


Strangeness form factor

Very poor information available even today Experiments

Even the sign of GM(Q2=0) unknown Only few direct lattice QCD

Dong-Liu, PRD58(1998)074504

Mathur-Dong, NP.Proc.Suppl.94(2001)311

Lewis-Wilcox-Woloshyn, PRD67(2003)013003

arXiv:0805.2889 [hep-ex]


Strangeness form factor: Latt Operator

Point-split operator conserved, no RG factor

Electric/Magnetic form factorElectric

Magnetic


Strangeness magnetic moment


#src = 32



Q^2 dependence

#src = 32

At each Q^2, s.m.m. is basically consistent with zero



Q^2 dependence

#src = 64

At each Q^2, s.m.m. is basically consistent with zero



Chiral Extraplation

s.m.m. is basically consistent with zero



Improvement ? Dilution in color/spin in stochastic method

did not work : probably because current is point-splitted Dilution in even/odd

Does work, but unbiased subtraction w/ HPE compensate Unbiased subtraction w/ HPE not w/ Wilson-type but

w/ clover-type Does work, but not so much

Deflation for the next overlap/domain-wall calc.


Summary/Outlook We have studied the <x> from strangeness,

u, d (disconnected insertion[D.I.]) and glue Nf=2+1 clover fermion and quenched for <x>(q) <x>(s) is as large as <x>(ud) [D.I.]

Renormalization is necessary for quantitative results Glue <x> has been studied using overlap operator

We have obtained a promising signal ! Strangeness magnetic/electric form factor

Outlook Angular momentum is being studied origin of nuc spin Various quantities of D.I., pi-N-sigma term, etc.


Renormalization

We have two operators: T4i(q), T4i(G) It is known that the RG can be parametrized

as

Two unknown parameters can be determined by two sum rules

Momentum sum rule: Spin sum rule:

X.Ji, PRD52 (1995) 271

10/08/2008ky ccs seminar strangeness and glue in the nucleon from lattice qcd takumi doi (univ. of...

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