Strangeness and glue in the nucleon from lattice QCD Takumi Doi (Univ. of Kentucky) In collaboration with Univ. of Kentucky: M. Deka, S.-J. Dong, T. Draper, K.-F. Liu, D. Mankame Tata Inst. of Fundamental Research: N. Mathur Univ. of Regensburg: T. Streuer cQCD Collaboration 07/17/2008 Lattice 2008

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> 07/17/2008 Lattice 2008

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 07/17/2008 Lattice 2008

Outline Energy-momentum tensor <x> from disconnected insertion <x> and spin <x> from disconnected insertion <x> from glue Glue operator from overlap operator Outlook 07/17/2008 Lattice 2008

Methodology The energy momentum tensor can be decomposed into quark part and gluon part gauge invariantly Nucleon matrix elements can be decomposed as (angular) momentum sum rules (reduce renormalization consts.) Orbital part X.Ji (1997) 07/17/2008 Lattice 2008

Methodology <x> can be obtained by q p p’=p-q To improve S/N, we take a sum over t1=[t0+1, t2-1] t1 t0 t2 07/17/2008 Lattice 2008

Methodology Spin components can be obtained by q p’=p-q N.B. we use one more equation to extract T1 and T2 separately (q^2 dependence could be different) 07/17/2008 Lattice 2008

Analysis for <x> (D.I.) c.f. Analysis for <x> (connected)  talk by D. Mankame (Mon.) 07/17/2008 Lattice 2008

Analysis (1) Nf=2+1 dynamical clover fermion + RG improved 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) 07/17/2008 Lattice 2008

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) 07/17/2008 Lattice 2008

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) 07/17/2008 Lattice 2008

Results for <x>(s) Nf=2+1 Linear slope corresponds to signal By increasing the nucleon sources #src = 1  32, the signal becomes prominent Error bar reduced more than factor 5 ! 07/17/2008 Lattice 2008

Chiral Extrapolation <x>(s) <x>(ud) [D.I.] Nf=2+1 <x>(s) <x>(ud) [D.I.] We expect we can furhter reduce the error by subtraction technique using hopping parameter expansion Note: The values are not renormalized 07/17/2008 Lattice 2008

Ratio of <x>(s) and <x>(ud)[D.I.] Nf=2+1 <x>(s) / <x>(ud)[D.I.] =0.857(40) Preliminary c.f. Quenched <x>(s) / <x>(ud)[D.I.] =0.88(7) M. Deka Note: The values are not renormalized 07/17/2008 Lattice 2008

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 used, 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 07/17/2008 Lattice 2008

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 07/17/2008 Lattice 2008

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. 07/17/2008 Lattice 2008

Supplement 07/17/2008 Lattice 2008

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 07/17/2008 Lattice 2008