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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

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Introduction Nucleon structure

Fundamental particle, but a whole understanding of its structure has not been obtained yet

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>

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Introduction The ingredients: valence/sea quark and gluon

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

Disconnected Insertion (D.I.) terms Now is the full QCD Era: dynamical sea quark ! Strangeness in <x>, <x2>, electric/magnetic form factors

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

Tough calculation in lattice

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Outline

Energy-momentum tensor <x> and spin

<x> from disconnected insertion <x> from glue

Glue operator from overlap operator Outlook

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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

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Methodology <x> can be obtained by

q

pp’=p-qt1

t2t0

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

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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)

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Analysis for <x> (D.I.)

c.f. Analysis for <x> (connected) talk by D. Mankame (Mon.)

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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)

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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)

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D.I. calculation

Disconnected 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)

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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 !

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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 hopping parameter expansion

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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

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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

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Results for <x>(g) (quenched)

Linear slope corresponds to signal

First time to obtain the signal of glue in nucleon !

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

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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 ! Outlook

Angular momentum is being studied origin of nuc spin Various quantities of D.I., strangeness electric/magnetic

form factor, pi-N-sigma term, etc.

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Supplement

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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