1 / 32

Nucleon sigma term and strange quark content from dynamical overlap simulations

Nucleon sigma term and strange quark content from dynamical overlap simulations. arXiv:0806.4744 [hep-lat] . Lattice 2008 @ College of William and Mary. Hiroshi Ohki (YITP and Kyoto University) for JLQCD Collaboration. Outline .

azana
Download Presentation

Nucleon sigma term and strange quark content from dynamical overlap simulations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Nucleon sigma term and strange quark contentfrom dynamical overlap simulations arXiv:0806.4744[hep-lat] Lattice 2008@ College of William and Mary Hiroshi Ohki(YITP and Kyoto University) forJLQCD Collaboration

  2. Outline • Introduction and motivation • Methods • Simulation details • Results • Summary

  3. JLQCD collaboration KEK S. Hashimoto, H. Ikeda, T. Kaneko, H. Matsufuru, J. Noaki, E. Shintani, N. Yamada Niels Bohr H. Fukaya Tsukuba S. Aoki, T. Kanaya, N. Ishizuka, K.Takeda, Y. Taniguchi,A. Ukawa, T. Yoshie Hiroshima K.-I. Ishikawa, M. Okawa YITP H. Ohki,T. Onogi, T. Yamazaki KEK BlueGene (10 racks, 57.3 TFlops)

  4. Introduction • What is sigma term? • Strange quark content of Nucelon scalar form factor of the nucleon at zero recoil and Low energy parameter of ChPT

  5. H, h Motivation • Y and f parameters are quite important phenomenologically. Neutralino Dark matter search The interaction with nucleon is mediated by the higgs boson exchange in the t-channel. K. Griest, Phys.Rev.Lett.62,666(1988) Phys,Rev,D38, 2375(1988) Baltz, Battaglia, Peskin, Wizanksy Phys. Rev. D74, 103521 (2006). heavy quark loop strange quark strange quark contribution is dominant and important.

  6. Introduction • y (and f) parameters are calculated by connected and disconnected contributions. It is necessary for the determination of y parameter to calculate each contribution separately.

  7. How well are the parameters known? c.f. Recent work of nucleon mass for plenary talk of Walker-Loud The strange quark content has an almost 100% uncertainty.

  8. Previous lattice calculations (Wilson type fermion). Mixing of connected and disconnected contributions (Matrix methods and spectrum methods) due to lattice artifact. The most crucial uncertainty is the additive mass shift. c.f. C. Michael et.al. Nucl. Phys. Proc. Suppl. 106, 293 (2002) Sea quark mass derivative with fixed bare valence quark mass is contaminated by physical valence quark mass derivative Which is unwanted lattice artifact ( red arrow). Spectrum methods with Wilson type fermions Uncertainties in y parameter • ChPT: Low Energy Constants (higher order).

  9. Our strategy Determine the nucleon sigma term in unquenched QCD using the dynamical quark (overlap fermion), which has an exact chiral symmetry on the lattice. • The advantage of the exact chiral symmetry • No mixing of connected and disconnected contributions • In this study, we work in nf=2 unquenched QCD. Result for nf=2+1 QCD will also soon appear.

  10. Our method the sigma term from the nucleon mass spectrum. Feynman - Hellman theorem partial derivatives with respect to the valence and sea quark masses give contributions from ‘connected’ and ‘disconnected’ diagrams. no additive mass shift which causes dangerous lattice artifact Exact chiral symmetry

  11. Numerical simulation Nf=2 overlap fermion configurations • 16^3 x 32, a=0.12 fm, L=1.9 fm • 6 values of sea quark mass • fixed topology • At Q=0 accumulated 10,000 trajectories Measurement of the nucleon 2pt function • 6pts(sea) and 9pts(valence) for quark masses • Low mode averaging is employed (#eigenmodes=100)

  12. Results • Nucleon masses from 2-pt functions Effective mass plot for amq=0.035 Solid lines are the mass from the fit

  13. Chiral extrap. (unitary point) extraction of nucleon sigma term • Fit without lightest quark mass data(5pts) • several fit forms to study chiral extrapolation errors • Fit with finite volume correction (5 and 6pts) • fits including finite volume effects estimated by ChPT.

  14. ChPT Fit of nucleon mass spectrum Fit formula with Heavy Baryon chiral perturbation theory c.f. E. E. Jenkins et. al., PLB255,558 (1991) M. Procura et. al. PRD69, 034505(2004) I : II : with input , III : with input , (0 : simplified version of Fit I)

  15. Fit results with and without finite volume corrections raw data Finite volume corrected(Fit 0) Solid …fit 0 dot…fit I Dashed…Fit II dot-dashed…Fit III Raw data Finite volume corrected data Nicely fit to the ChPT formula without lightest point. Fit uncertainty is O(10)%. Successful with all data point

  16. Results of sigma term 1. The systematic error is mainly the chiral extrap. error. 2. Finite volume effect (FVE) is sub-leading (~ 9%). 3. We quate final results from Fit 0(FVE uncorrected).

  17. PQChPT fit (partially quenched data points) extraction of y parameter • Fit with partially quenched ChPT (5 X 8 data points) • consistency check of the unitary point fit • interpolation to the strange quark mass. • Separate extraction of connected and disconnected contributions

  18. Fit a: 6 parameters • Fit b: 7 parameters • Fit b: 8 parameters PQChPT fit function J.W. Chen et al.,PRD65,094001(2002) S.R. Beane et al.NPA709,319 (2002)

  19. Fit results (PQChPT) PQChPT fit works very well. It gives consistent results with the unitary point fit.

  20. valence Sea The disconnected contribution (sea quark content) is always smaller than the connected contribution (valence quark content). Connected and disconnected contributions at

  21. Connected and disconnected contributions at • Strictly speaking, it is not possible to extract the strange quark content within two-flavor QCD. For the final result, we should wait for 2+1-flavor QCD result (coming soon). • We present semi-quenched estimate of the y parameter Semi quenched estimate of y

  22. Comparison with other results • Our results of is consistent with ChPT . • Finite Volume correction is controllable. • Previous lattice result of sea/valence is larger than 1. Our result is 0~0.3. • ChPT predicts • Previous lattice results due to large sea quark contribution without removing lattice artifact. • After removing lattice artifact previous y is -0.3(3) • Our result gives

  23. 6. summary • We studied the nucleon mass spectrum for nf=2 unquenched QCD using exactly chiral symmetric fermions. • Our calculation is free from the dangerous lattice artifacts (mixing of connected and disconnected contributions) • Our result of sigma term is consistent with the ChPT prediction. • We found that the disconnected (strange quark content) part is tiny.

  24. Thank you

  25. Backup slide

  26. Fit of the quark mass dependence (5pt) a means fit with input gA B means fit with gA free The solid, dot, dashed, dot-dashed curves represent the Fit 0a, Ia, II, and III, respectively.

  27. Fit of the quark mass dependence (5 and 6pt) Box size of L=1.9 fm is rather small for baryon with light quarks. We can estimate the Finite Size Effect(FSE) using ChPT. ＦＶＣ　Ｒｅｆする After correcting the lattice data including FSE, we can redo the ChPT fit. Raw data Finite volume corrected data

  28. Results of sigma term 5ｐｔと６ｐｔ • Although there are finite size effects (FSE), sigma term gets only about 5% change. • ChPT fit (gA fixed) without considering FSE gives reasonable result. • We take ChPT fit (gA fixed, FSE uncorrected) as our best fit, assuming possible 10% finite size error.

  29. JLQCD’s Simulations • Overlap fermion ( explicit construction by Neuberger) Exact chiral symmetry on the lattice(index theorem) Hasenfratz, Laliena and Niedermayer, Phys.Lett. B427(1998) 125 Luscher, Phys.Lett.B428(1998)342.

  30. Our analysis • Fit 5 pt data without finite volume correction • Fit 0a and 0b: 3 and 4 parameters fit • Fit Ia and Ib: 3 and 4 parameters fit • Fit II : 3 parameters with c_2=3.2[GeV-1] and c_3=-3.4[GeV-1] • Fit III : 3 parameters with c_2=3.2[GeV-1] and c_3=-4.7[GeV-1] a means fit with input gA=1.267, B means fit with gA free • Fit 5 and 6 pt data with finite volume correction • Fit 0a: 3 parameters fit • Fit Ia: 3 parameters fit • Fit II : 3 parameters with c_2=3.2[GeV-1] and c_3=-3.4[GeV-1] • Fit III : 3 parameters with c_2=3.2[GeV-1] and c_3=-4.7[GeV-1]

  31. Fit of the quark mass dependence (5pt) The solid, dot, dashed, dot-dashed curves represent the Fit 0a, Ia, II, and III, respectively.

  32. Fit the finite volume corrected data (5 and 6pt) Box size of L=1.9 fm is rather small for baryon with light quarks. We can estimate the Finite Size Effect(FSE) using ChPT. c.f. A. Ali Khan et al.,Nucl, Phys.B 689,175(2004) For the input parameter, we use the nominal values of gA, c1, c2 and c3, after correcting the lattice data including FSE, we carry out the ChPT fit. Raw data Finite volume corrected data

More Related