1. 1 Lattice QCD Activities at CCS Yoshinobu Kuramashi Center for Computational Sciences (CCS) University of Tsukuba

2. 2 Contents §1. Members of Particle Physics Group §2. Introduction to Lattice QCD §3. PACS-CS Project PRD79(2009)034503, PRD80(2009)054502, arXiv:0911.2561 §4. Summary and Future Perspectives

3. 3 Members of Particle Physics Group Staff N.Ishizuka, Y.K., Y.Taniguchi, T.Yoshié PD Y.Namekawa, N.Ukita, T.Yamazaki OB Y.Iwasaki: ex-President of the University of Tsukuba (2004-2009) ex-Director of CCP (1992-1998) A.Ukawa: Executive Advisor to the President ex-Director of CCP and CCS (1998-2007) Collaborative members S.Aoki, K.Kanaya

4. 4 Introduction to Lattice QCD investigate nonperturbative effects of the strong interaction through numerical simulations with lattice QCD strong interaction one of the fundamental forces in Nature (gravity, electromagnetic, strong, weak) dynamics between quarks and gluons quark protonneutron nucleon

5. 5 6 Flavors of Quarks and Gluons dsb uct charge +2/3 1/3 s quark (R,B,G) gluons

6. 6 Various Hadrons p, n, Δ, Λ, Σ, Σ, Ξ, Ξ, Ω, Λc, Ξc, Λc,... π, K, K, ρ, ω, η, φ, a, b, f, D, B,... meson (quark and anti-quark) baryon (3 quarks)

7. 7 QCD Lagrangian determine kinematics and interactions of quarks and gluons quark mass m q (q=u,d,s,c,b,t) are free parameters Is it possible to quantitatively describe the hierarchical structures with an appropriate tuning of m q ? quarks hadrons nuclei

8. 8 Lattice QCD nonperturbative investigation of strong interactions with respect to QCD Lagrangian

9. 9 Path Integral Formalism numerical integration with Monte Carlo method on discretized 4-dim. space-time lattice average over the values evaluated on configurations

10. 10 History before PACS-CS 1981 first calculation of hadron masses in quenched approx. (Hamber-Parisi) demonstrate the possibility of first principle calculations 1996-2000 precision measurements in quenched approx. (CP-PACS) clear deviation from experimental values 2000-2005 embark on 2+1 flavor QCD simulations (CP-PACS/JLQCD, MILC, RBC, …) attempt of first principle calculations

11. 11 2+1 flavor QCD simulations with HMC algoriyhm CP-PACS/JLQCD project looks impossible to reach the physical point in near future CP-PACS/JLQCD m ud =0m ud =

12. 12 aim to make simulations at the physical point of 2+1 flavor QCD PACS-CS project Physicists S.Aoki, N.Ishizuka, K.Kanaya, Y.K. Tsukuba Y.Namekawa, Y.Taniguchi, A.Ukawa, N.Ukita, T.Yamazaki, T.Yoshié K.-I.Ishikawa, M.Okawa Hiroshima T.Izubuchi BNL Computer scientists T.Boku, M.Sato, D.Takahashi, O.Tatebe Tsukuba T.Sakurai, H.Tadano

13. 13 Parallel Array Computer System for Computational Sciences 2560 nodes, 14.3 Tflops peak, 5.12 TB memory operation started on 1 July 2006 at CCS in U.Tsukuba PACS-CS

14. 14 Tukuba-Tokyo-Kyoto open supercomputer alliance 648 nodes, 95.4 Tflops peak, 20.7 TB memory operation started on 2 June 2008 at CCS in U.Tsukuba T2K-Tsukuba

15. 15 drastic reduction of computational cost thanks to DDHMC algorithm Algorithmic Improvements physical point simulations are within reach

16. 16 nontrivial curvature = log dependence expected from chiral symmetry Toward the Physical Point importance of simulations at smaller ud quark masses

17. 17 m π, m K, m Ω inputs consistent within 2-3 % error bars Comparison with Experiment hadron masses extrapolated at the physical point

18. 18 Fine Tuning to the Physical Point reweighting method simulation: (m ud,m s ) physical point: (m´ ud,m´ s ) with m ud m´ ud and m s m´ s reweighting factors

19. 19 m π /m Ω, m K /m Ω are properly tuned (Δm ud <1 MeV, Δm s <3MeV) Comparison with Experiment hadron masses normalized by m Ω

20. 20 Summary and Future Perspective peak machine target physics < 1TF CP-PACS embark on 2+1 flavor QCD 10 TF PACS-CS physical point simulation 100 TF T2K-Tsukuba determination of QCD parameters light nuclei in quenched QCD (Yamazaki et al., arXiv:0912.1383) 10 PF NGSC light nuclei in 2+1 flavor QCD finite temperature and finite density 1 EF NNGSC weak hadron matrix elements w/o OPE heavy nuclei in 2+1 flavor QCD

21. 21 Why Physical Point Simulations? simulations at heavier quark masses (m >200~300MeV) and extrapolations to the physical point with ChPT current most popular strategy due to computational cost whats wrong with cheaper strategy? guiding principle for chiral extrapolation? ChPT is not always valid for all the physical quantities polynomial is valid only near the physical point difficult to precisely trace logarithmic curvatures different dynamics at unphysically heavy quark masses ρππ decay is not allowed final destination is 1+1+1 flavor QCD simulations