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Strangeness and glue in the nucleon from lattice QCD

Takumi Doi (Univ. of Kentucky). Strangeness and glue in the nucleon from lattice QCD. 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. c QCD Collaboration.

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Strangeness and glue in the nucleon from lattice QCD

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  1. Takumi Doi (Univ. of Kentucky) Strangeness and glue in the nucleon from lattice QCD 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 Lattice 2008

  2. 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> Lattice 2008

  3. 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 Lattice 2008

  4. Outline • Energy-momentum tensor • <x> and spin • <x> from disconnected insertion • <x> from glue • Glue operator from overlap operator • Outlook Lattice 2008

  5. Orbital part 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.) X.Ji (1997) Lattice 2008

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

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

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

  9. 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) Lattice 2008

  10. 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) Lattice 2008

  11. 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) Lattice 2008

  12. 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 ! Lattice 2008

  13. Chiral Extrapolation 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 Lattice 2008

  14. 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 Lattice 2008

  15. 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 Lattice 2008

  16. 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 Lattice 2008

  17. 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. Lattice 2008

  18. Supplement Lattice 2008

  19. 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 Lattice 2008

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