1. 1 2+1 Flavor lattice QCD Simulation on K computer Y.Kuramashi U. of Tsukuba/RIKEN AICS August 2, 2013 @ Mainz

2. 2 Plan of talk §1. K computer and Strategic Field Program §2. Physics Plan §3. Simulation Parameters §4. Preliminary results §5. Summary

3. 3 §1. K computer and Strategic Field Program Tokyo Kobe Tsukuba Kyoto Advanced Institute for Computational Science (Note: independent of RIKEN-BNL-Columbia Collab.) RIKEN AICS Peak=11.28PFlops Logo Computer room

4. 4 Strategic Field Program For strategic use of K computer Government selected 5 strategic fields in science and technology for importance from national view point For each field, Government also selected a core institute Each core institute is responsible for organizing research and supercomputer resources in the respective field and its community, for which they receive − priority allocation of K computer resources − funding to achieve the research goals Strategic FieldCore Institute Life Science & MedicineRIKEN New Materials & EnergyISSP at U. Tokyo Global Change PredictionJAMSTEC Next Generation EngineeringIIS at U. Tokyo Matter and UniverseCCS at U. Tsukuba

5. 5 §2. Physics Plan Scientific target 2+1 flavor QCD ⇒ 1+1+1 flavor QCD+QED Various physical quantities Investigation of resonances Direct construction of light nuclei Determination of baryon-baryon potentials

6. 6 Light Nuclei in 2+1 Flavor QCD (1) 2+1 flavor QCD, m π ＝ 0.5 GeV, m N =1.32 GeV 4He3HeNN(3S1)NN(1S0) Binding energy [MeV]43(12)(8)20.3(4.0)(2.0)11.5(1.1)(0.6)7.4(1.3)(0.6 ) Exp. value [MeV]28.37.722.220 Successful construction of helium nuclei in 2+1 flavor QCD Yamazaki-Ishikawa-YK-Ukawa 12 Ukawa @this conference

7. 7 Light Nuclei in 2+1 Flavor QCD (2) NN( 3 S 1 ) and NN( 1 S 0 ) channels Both 3 S 1 and 1 S 0 channels are bound at m π =0.5 GeV |ΔE( 3 S 1 )| > |ΔE( 1 S 0 )| is observed Important to investigate quark mass dependence Target on K computer: construction of nuclei at the physical point

8. 8 Baryon-Baryon Potentials (1) based on equal-time BS amplitude Quenched QCD, m N =1.34GeV Ishii-Aoki-Hatsuda 07 Phenomenological model BS wave function with lattice QCD ⇒ NN Potential

9. 9 Baryon-Baryon Potentials (2) 2+1 flavor QCD, lattice size=32 3 ×64, m π ＝ 0.70, 0.57, 0.41 GeV Attractive phase shift, though the magnitude is just 10% of exp. value (no bound state ⇒ inconsistency against the direct method) Phase shift becomes smaller, as quark mass decreases ⇒ need direct comparison with exp. values at the physical point HAL-QCD @FB12

10. 10 Collaboration members N.Ishii, N.Ishizuka, Y.Kuramashi, Y.Namekawa, Tsukuba H.Nemura, K.Sasaki, Y.Taniguchi, N.Ukita T.Hatsuda, T.Doi RIKEN-Wako T.Yamazaki Nagoya S.Aoki Kyoto Y.Nakamura RIKEN-AICS K.-I.Ishikawa Hiroshima HAL QCD Collab. joins to determine baryon-baryon potential

11. 11 §3. Simulation Parameters 2+1 flavor QCD Wilson-clover quark action + Iwasaki gauge action Stout smearing with α=0.1 and N smear =6 NP C SW =1.11 determined by SF β=1.82 ⇒ a 〜 0.1 fm Lattice size=96 4 ⇒ ( 〜 9 fm) 4 Hopping parameters: (κ ud,κ s )=(0.126117,0.124790) Simulation algorithm − (HB) 2 DDHMC w/ active link for ud quarks, UVPHMC for s quark − Block size=12 4 ⇒ ( 〜 1 fm) 4 − HB parameters: (ρ 1,ρ 2 )=(0.99975,0.9940) − Multi-time scale integrator: (N 1,N 2,N 3,N 4,N 5 )=(15,2,2,2,8) − trajectory length: τ=1 − N poly =310 − Chronological inverter guess: N chrono =16 − Solver: mixed precision nested BiCGStab

12. 12 Performance on K computer Kernel (MatVec) performance: >50% Solver performance: 〜 26% (mixed precision nested BiCGStab) Weak scaling test − 6 3 ×12/node fixed − 16 nodes (V=12 3 ×24) ⇒ 12288 nodes (V=48×72×96 2 ) 16 256 2048 12288 #nodescalability 16 ⇒ 256 98% 256 ⇒ 2048 98% 2048 ⇒ 12288 96% good weak scaling B/F=0.5 on K computer

13. 13 Non-Perturbative Determination of C SW (1) Schördinger functional method − L 3 ×T=8 3 ×16 (L 3 ×T=12 3 ×24 for volume dependence check) − Choose β such that the lattice spacing becomes around 0.1 fm Taniguchi @Lattice2012 C SW =1.11 at β=1.82 ⇒ 1/a 〜 2.1 GeV κ C is close to 0.125 at β=1.82

14. 14 Non-Perturbative Determination of C SW (2) N smear dependence of C SW and Kc C SW monotonically decreases as N smear increases κ C shows a similar behavior

15. 15 §4. Preliminary results Meson and baryon effective masses for smeared-local correlators Smearing function: Aexp(−Br) − (A,B)=(1.2,0.06) for ud quarks − (A,B)=(1.2,0.12) for s quarks

16. 16 Hadron spectrum Further tuning to the physical point is planned with reweighting method Clear deviation is already observed for unstable particles (ρ,K*) Comparison with experiment (normalized by m Ω )

17. 17 ρ Meson Effective Mass It is hard to find a reasonable plateau (same for Δ baryon effective mass) Analysis of 2×2 correlation matrix (ρ,ππ) is necessary Decay channel is open: m ρ >2√{m π 2 +(π/48) 2 } m ρ =776 MeV 2√{m π 2 +(π/48) 2 }

18. 18 §5. Summary ・ K computer and strategic field program ・ 2+1 flavor QCD simulation at the physical point on ( 〜 9 fm) 4 lattice ・ Preliminary results for hadron spectrum