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Recent results from lattice QCD

Recent results from lattice QCD. Tetsuya Onogi (YITP, Kyoto Univ.) for JLQCD collaboration. JLQCD Collaboration. KEK S. Hashimoto, T. Kaneko, H. Matsufuru, J. Noaki, M. Okamoto E. Shintani, N. Yamada RIKEN/Niels Bohr H. Fukaya

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Recent results from lattice QCD

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  1. Recent results from lattice QCD Tetsuya Onogi (YITP, Kyoto Univ.) for JLQCD collaboration

  2. JLQCD Collaboration KEK S. Hashimoto, T. Kaneko, H. Matsufuru, J. Noaki,M. Okamoto E. Shintani, N. Yamada RIKEN/Niels Bohr H. Fukaya Tsukuba S. Aoki, T. Kanaya, Y. Kuramashi, N. Ishizuka, Y. Taniguchi,A. Ukawa, T. Yoshie Hiroshima K.-I. Ishikawa, M. Okawa YITP H. Ohki, T. Onogi TWQCD Collaboration National Taiwan U. T.W.Chiu, K. Ogawa, KEK BlueGene (10 racks, 57.3 TFlops)

  3. Outline • Introduction • Method for dynamical overlap simulation • Applications • QCD vacuum Chiral symmetry breaking, topological susceptibility • Spectrum and Chiral Perturbation Theoy (ChPT) • Flavor Physics • New directions • Summary

  4. 1. Introduction Many unquenched simulations are performed or starting now. New era for lattice QCD. Lattice QCD with dynamical quark having exact chiral symmetry enables us to attack new problems which was impossible otherwise.

  5. Advantage of exact chiral symmetry • Exact results from chiral symmetry can be reproduced good for Chiral symmetry breaking • Exact chiral anomaly relations good for topological susceptibility • Chiral behavior is correct at finite lattice spacing fit with Chiral Perturbation Theory (ChPT) is valid good for chiral extrapolation for • Operator mixing with wrong chirality is prohibited. good for • No extra divergence due to lack of chiral symmetry appears good for • No O(a) error good for scaling and nonperturbative renormalization

  6. Overlap fermion • Neuberger’s overlap fermion • Ginsparg-Wilson relation Ginsparg and Wilson, Phys.Rev.D 25(1982) 2649. • Exact chiral symmetry on the lattice(index theorem) Hasenfratz, Laliena and Niedermayer, Phys.Lett. B427(1998) 125 Luscher, Phys.Lett.B428(1998)342.

  7. Problems in dynamical overlap simulation • [1] Cost grows towards chiral limit as • [2] Numerical implementation by rational approximation Nrationallarge : huge numerical cost. • [3] Sign function discontinuity at Hw=0. • Special care is need to make reflection/refraction at the discontinuity • Additional numerical cost. Becomes much more serious with larger volume. 300 years or more on 10Tflops supercomputer with naïve algorithm. We should reduce it to one year

  8. 2. Method for dynamical overlap fermion simulation H. Matsufuru, Plenary talk at lattice 2007 • KEK Blue/Gene 57Tflops ( x 5 ) • Algorithm • Hasenbusch mass preconditioning ( x 5 ) solves the problem [1] by separating the low and high modes • 5 dimensional solver ( x 4 ) solves the problem [2] by more efficient rationalization • Gauge action ( x 3 or much more ) solves the problem [3] by prohibiting the topology change. Speed up by factor 5 x 5 x 4 x 3 = 300 !!

  9. Suppressing near-zero modes of HW Topology fixing term: extra Wilson fermion/ghost (Vranas, 2000, Fukaya, 2006, JLQCD, 2006)‏ avoids zero mode of Hw during MD evolution • No need of reflection/refraction • Cheeper sign function Nf = 2, a~0.125fm, msea ~ ms , withSE withoutSE

  10. 2. Applications

  11. Runs • Run 1 (epsilon-regime) Nf=2: 163x32, a=0.11fm e-regime (msea ~ 3MeV)‏ • 1,100 trajectories with length 0.5 • 20-60 min/traj on BG/L 1024 nodes • Q=0 • Run 2 (p-regime) Nf=2: 163x32, a=0.12fm 6 quark masses covering (1/6~1) ms • 10,000 trajectories with length 0.5 • 20-60 min/traj on BG/L 1024 nodes • Q=0, Q=−2,−4 (msea ~ ms/2)‏ • Run 3 (p-regime) Nf=2+1 : 163x48, a=0.11fm (in progress)‏ • 2 strange quark masses around physical ms • 5 ud quark masses covering (1/6~1)ms • Trajectory length = 1 • About 2 hours/traj on BG/L 1024 nodes

  12. Mass parameters for Run 2 (p-regime Nf=2) We have 6 sea quark masses and 9 valence quark masses.

  13. QCD vacuum

  14. Chiral condensate • Banks-Casher relation(Banks & Casher, 1980)‏ • Accumulation of low modes Chiral SSB : spectral density of D • epsilon-regime: at finite V • Low-energy effective theory • Q-dependence is manifest • Random Matrix Theory (RMT)‏ Finite V

  15. Result in the-regime (JLQCD, 2007, JLQCD and TWQCD, 2007)‏ Low-lying spectrum of D(m)‏ • Nf=2, 163x32, a=0.11fm • m~3MeV • Good agreement with RMT • lowest level distrib. • Flavor-topology duality • Chiral condensate: • Nonperturbative renorm. effect: correctable by meson correlator H.Fukaya et al.

  16. Simulation at fixed topology S. Aoki et al.‏ Out of the-regime, fixing topology could be a problem • In the infinite V limit, • Fixing topology is irrelevant • Local fluctuation of topology is active • In practice, V is finite • Topology fixing finite V effect • Theta vacuum physics can be reconstructed (see below)‏ • Must check local topological fluctuation topological susceptibility • Questions: Ergodicity ?

  17. Physics at fixed topology Reconstruct QCD in vacuum from fixed topology (Bowler et al., 2003, Aoki, Fukaya, Hashimoto, & Onogi, 2007)‏ • Partition function at fixed topology for , Q distribution is Gaussian • Physical observables • Saddle point analysis for • Example: pion mass

  18. Topological susceptibility • Topological susceptibility can be extracted from correlation functions(Aoki et al., 2007)‏ where Numerical result at Nf=2, a=0.12fm mP0mP0 ma=0.025 t m

  19. Mass Spectrum and Test with Chiral Perturbation Theory

  20. Low-mode averaging J.Noak, lattice 2007 proceedings Technical improvement: • 50 pairs of eigenmodes of D predetermined • Solver with low mode projection (8 times faster)‏ • Low-mode averaging (DeGrand, 2004, Giusti et al., 2004)‏ • Averaging over source points only for low mode contrib. Nf=2, a=0.12fm, Q=0 3 smallest msea=mval.

  21. Two-loop ChPT test J.Noaki lattice 2007 proceedings Chiral extrapolation • Fit parameter: • NLO vs NNLO of ChPT --- NLO tends to fail; NNLO successful • Low energy constants: Nf=2, a=0.12fm, Q=0

  22. Finite volume effect Finite volume correction • R: finite size effect from 2-loop ChPT(Colangelo et al, 2005)‏ • T: Fixed topology effect (Aoki et al, 2007)‏ • At most 5% effect --- largely cancel between R and T • No Q-dependence (consistent with expectation)‏ Q=-2,-4 (msea=0.05)‏ (ampi)2 Nf=2, a=0.12fm, Q=0 afpi

  23. Flavor Physics

  24. BK N.Yamada, lattice 2007 proceedings Indirect CP violation for K Problems unquenched lattice calculations Wilson fermion : huge operator mixing wrong chirality. Staggered fermion : How to treat doubler contribution ? Domain-wall fermion: Exponentially suppressed but sizable operator mixing Overlap fermion is free from operator mixing problem

  25. Bare Bag parameter is obtained by the simultaneous fit of 2-pt, 3-pt functions • Contaminations from other states can be removed using fits with different • Fit the mass dependence with Partially Quenched Chiral Perturbation (PQChPT) formula

  26. Renormalization factor is obtained nonperturbatively with RI-MOM scheme (off-shell quark amplitude in Landau gauge) Use continuum perturbation theory to convert to MS bar scheme • Nf=2, a=0.12fm, preliminary result:

  27. Pion form factor T.Kaneko lattice 2007 proceedings‏ • Precisely calculated with the all-to-all technique(J.Foley et al., 2001)‏ • Pion charge radius Nf=2, a=0.12fm, preliminary result: This method also applies to Kl3

  28. New directions

  29. Vacuum polarizations Talk by E.Shintani • Das-Guralnik-Mathur-Low-Young sum rule(1967)‏ • Vacuum polarization • Low Q2: pole dominance • High Q2: OPE Nf=2, a=0.12fm Cf. exp. 1242 MeV2 Exact chiral symmetry plays essential role !

  30. Nucleon sigma term Definitions of the nucleon sigma term • sigma term = scalar form factor of the nucleon at zero recoil • related quantities

  31. Why sigma term is important? • A crucial parameter for the WIMP dark matter detection rate. The interaction with nucleon is mediated by the higgs boson exchange in the t-channel. • Also related to the chromo-electric contributions to neutron EDM assuming (1) PCAC + (2) QCD sum rule with saturation by lightest O++ state ex.J. Hisano and Y. Shimizu, Phys.Rev.D70, 093001(2004) heavy quark loop strange quark K. Griest, Phys.Rev.Lett.62,666(1988) Phys,Rev,D38, 2375(1988)

  32. Previous results

  33. Basic Methods Nucleon mass spectrum Feynman - Hellman theorem From now on we will denote as for referring for the sake of brevity.

  34. Nucleon masses from 2-pt functions Nice plateau for t >4 We fit the 2-pt function with a single expoential function with fitting range t=5-10 Effective mass plot for amq=0.035 Solid lines are the mass from the fit

  35. Sea and valence quark mass dependences The valence quark mass dependence is very clear, while the seaquark mass dependence is small.

  36. Fit of the quark mass dependence • Fit forinterpolation using polynomial • Fit for chiral extrapolation with diagonal (unitary) points Chiral Perturbation Theory (ChPT)

  37. valence quark contribution to (polynomial)

  38. Sea quark contribution to (polynomial fit)

  39. Sea and valence quark contribution to (ChPT) Nucleon mass in the chiral limit is consistent with the experimental value. similar analysis was done by Procula et al.(2004)

  40. sigma term • ChPT fit Preliminary

  41. (polynomial) Preliminary

  42. Comparison with other results • ChPT results and previous results are consistent. • Our results with ChPT is consistent • Previous lattice calculation sea/valence. Is larger than 1 • Our lattice calculation sea/valence n is about 0.1 • ChPT predicts • Previous lattice results due to large sea quark contribution • Our results with ChPT gives

  43. Comparison with other results • ChPT results and previous results are consistent. • Our results with ChPT is consistent • Previous lattice calculation sea/valence. Is larger than 1 • Our lattice calculation sea/valence n is about 0.1 • ChPT predicts • Previous lattice results due to large sea quark contribution • Our results with ChPT gives

  44. Additive mass shift and sigma term Wilson fermion has an additive mass shift through tadpole diagram which mimics mass operator insertion to the valence quark due to the lack of chiral symmetry Normal disconnected contribution (long distance effect) Operator mixing induced connected contribution (short distance effect)

  45. Additive mass shift and sigma term Same phenomena can be understood in the mass spectrum approach Fixing the bare valence quark mass and changing the sea quark mass effectively induces the change of the ‘physical’ valence quark mass due to the additive mass shift.

  46. Summary/Outlook We are performing dynamical overlap project at fixed topological charge • Nf=2 on 163x32, a~0.12fm: producing rich physics results • Nf=2+1 on 163x48, a~0.11fm: in progress • Understanding chiral dynamics with exact chiral symmetry • Application to matrix elements in progress • Opens new directions for phenomenological study from lattice QCD Outlook • More measurements planned • Larger lattices 243x48: need further improved algorithms

  47. Backup

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