1. 10/08/2008KY CCS seminar 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  QCD Collaboration

2. 10/08/2008KY CCS seminar 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 G E : electric form factor G M : magnetic form factor electron 1950s

3. 10/08/2008KY CCS seminar 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) W 1  F 1 structure function W 2  F 2 structure function Weak Q 2 dependence & 2xF 1 =F 2  Parton model electron 1960s

4. 10/08/2008KY CCS seminar Introduction Nucleon structure Parton model P xP Parton carry (xP) momentum Q 2 evolution  QCD interaction

5. 10/08/2008KY CCS seminar Introduction Nucleon structure Yet, whole understanding of its structure has not been obtained Q 2 -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

6. 10/08/2008KY CCS seminar 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 Glue contribution to nucleon spin  necessary to complete (angular) momentum sum rules Tough calculation in lattice

7. 10/08/2008KY CCS seminar Outline Lattice QCD and our methodology Energy-momentum tensor and spin from disconnected insertion from glue Glue operator from overlap operator Strangeness magnetic/electric form factor Outlook

8. 10/08/2008KY CCS seminar Non-perturbativ e flu ctuations are included via Path-Integral Monte Carlo calculation (Weighted sum is taken) 1 23 time space det=1: quenched det≠1: full QCD Lattice QCD

9. 10/08/2008KY CCS seminar 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

10. 10/08/2008KY CCS seminar 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 NambuMaskawa-Kobayashi

11. 10/08/2008KY CCS seminar Methodology Matrix elements Requires 4pt function calc. Operator Product Expansion (OPE)  3pt calc.

12. 10/08/2008KY CCS seminar Disconnected Insertion (DI) Why are DI diagrams important ? Strangeness in nucleon Strangeness electric/magnetic form factor Structure function,, 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(10 5 ) inversion for O(10 6 )XO(10 6 ) matrix Rich Physics !

13. 10/08/2008KY CCS seminar 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

14. 10/08/2008KY CCS seminar Analysis for (D.I.)

15. 10/08/2008KY CCS seminar 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) Orbital part

16. 10/08/2008KY CCS seminar Methodology can be obtained by q p p ’ =p-q t1 t2t0

17. 10/08/2008KY CCS seminar Methodology We take the ratio of 3pt to 2pt q p p ’ =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

18. 10/08/2008KY CCS seminar Methodology Spin components can be obtained by q p p ’ =p-q N.B. we use one more equation to extract T1 and T2 separately (q^2 dependence could be different)

19. 10/08/2008KY CCS seminar 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)

20. 10/08/2008KY CCS seminar 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)

21. 10/08/2008KY CCS seminar 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)

22. 10/08/2008KY CCS seminar Results for (s) Linear slope corresponds to signal #src = 1 Nf=2+1 Somewhat large errors

23. 10/08/2008KY CCS seminar Many nucleon sources Further improvement q p p ’ =p-q S/N improve by √Nnoise S/N improve by √Nsrc N.B. The calculations of loop part and 2pt part are independent !

24. 10/08/2008KY CCS seminar Results for (s) Linear slope corresponds to signal By increasing the nucleon sources #src = 1  32, the signal becomes prominent Nf=2+1 Error bar reduced more than factor 5 !

25. 10/08/2008KY CCS seminar Chiral Extrapolation Note: The values are not renormalized (ud) [D.I.] (s) Nf=2+1 We expect we can furhter reduce the error by subtraction technique using clover-fermion HPE

26. 10/08/2008KY CCS seminar Ratio of (s) and (ud)[D.I.] (s) / (ud)[D.I.] =0.857(40) Note: The values are not renormalized Preliminary (s) / (ud)[D.I.] =0.88(7) Nf=2+1 c.f. Quenched M. Deka

27. 10/08/2008KY CCS seminar 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

28. 10/08/2008KY CCS seminar Results for (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

29. 10/08/2008KY CCS seminar Strangeness form factor Very poor information available even today Experiments Even the sign of G M (Q 2 =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]

30. 10/08/2008KY CCS seminar Strangeness form factor: Latt Operator Point-split operator  conserved, no RG factor Electric/Magnetic form factor Electric Magnetic

31. 10/08/2008KY CCS seminar Strangeness magnetic moment Linear slope corresponds to signal #src = 32

32. 10/08/2008KY CCS seminar Strangeness magnetic moment Q^2 dependence #src = 32 At each Q^2, s.m.m. is basically consistent with zero

33. 10/08/2008KY CCS seminar Strangeness magnetic moment Q^2 dependence #src = 64 At each Q^2, s.m.m. is basically consistent with zero

34. 10/08/2008KY CCS seminar Strangeness magnetic moment Chiral Extraplation s.m.m. is basically consistent with zero

35. 10/08/2008KY CCS seminar Strangeness magnetic moment 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.

36. 10/08/2008KY CCS seminar Summary/Outlook We have studied the from strangeness, u, d (disconnected insertion[D.I.]) and glue Nf=2+1 clover fermion and quenched for (q) (s) is as large as (ud) [D.I.] Renormalization is necessary for quantitative results Glue 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.

37. 10/08/2008KY CCS seminar Renormalization We have two operators: T 4i (q), T 4i (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