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Toward a fully realistic simulation of QCD – three flavor QCD project by CP-PACS/JLQCD K. Kanaya

2003/12 Nagoya. Toward a fully realistic simulation of QCD – three flavor QCD project by CP-PACS/JLQCD K. Kanaya for CP-PACS and JLQCD Collab.s kanaya@rccp.tsukuba.ac.jp. SR8000 (2000, 1.2TFlops) @ KEK. JLQCD

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Toward a fully realistic simulation of QCD – three flavor QCD project by CP-PACS/JLQCD K. Kanaya

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  1. 2003/12 Nagoya Toward a fully realistic simulation of QCD – three flavor QCD project by CP-PACS/JLQCD K. Kanaya for CP-PACS and JLQCD Collab.s kanaya@rccp.tsukuba.ac.jp SR8000 (2000, 1.2TFlops) @ KEK JLQCD T.Onogi N.Tsutsui N.Yamada (H.Mino) (S.Kaya) (S.Tominaga) .... S.Aoki M.Fukugita S.Hashimoto K-I.Ishikawa N.Ishizuka Y.Iwasaki KK T.Kaneko Y.Kuramashi M.Olawa A.Ukawa T.Yoshie (R.Burkhalter) ... Y.Taniguchi K.Ide T.Ishikawa Y.Namekawa T.Yamazaki (A.AliKhan) (G.Boyd) (S.Ejiri) (V.Leske) (T.Manke) (K-I.Nagai) (J-I.Noaki) (M.Okamoto) (T.Umeda) .... CP-PACS CP-PACS (1996, 614GFlops) @ CCP, Univ.Tsukuba

  2. Introduction • Low energy properties of hadrons • difficult to calculate analytically due to strong coupling. • Lattice QCD: • The only systematic way to calculate non-perturbative properties –– directly from the first principles of QCD. • Precise calculation of hadron properties • critical test of QCD as the theory of quarks • determination of fundamental parameters (mq, a, CKM, ...) • predictions for hadron physics, QGP, ... QCD corrections important for quarks.

  3. a La Introduction (2) • Lattice QCD • Quarks and gluons formulated on space-time lattice with • finite lattice spacing a • finite lattice size L • Physics is defined in the limit • a ––> 0"continuum extrapolation" • keeping La sufficiently large (or ––> ∞) • lattice size L ––> ∞ • Core calculations: quark matrix inversion D–1 • large sparse matrix 12L4x12L4 ≈ typically 107 x 107 (12 = color x spin) • condition number µ 1/mqa • Difficult to calculate u, d quarks directly. • mq ––> mu,d "chiral extrapolation"

  4. Introduction (3) • For a precise and reliable prediction for the real world, good control of these extrapolations, based on systematic large scale simulations, is required. • Large computer power indispensable! • ß ˜ (dedicated) parallel computers • Steps toward a realistic simulation • Quenched approximation (no quark pair creation/annihilations) • Dynamical u,d quarks (degenerate) NF = 2 full QCD • Dynamical s quark NF = 2+1 fQCD • Sea u,d quark mass difference • Dynamical c quark ... Thus, "3" is the last major step toward reality. Expect only small effects in most processes

  5. Yes q q q q No! Systematic studies of LQCD by CP-PACS and JLQCD sea Step 1: NF = 0 (quenched) QCD quench: disregard pair creation/annihilation of sea quarks Important properties of QCD (confinement, AF, ChSB) retained. O(10%) error in the spectrum expected. Computer time < 1/100. valence • First study: Hamber and Parisi ('81), Weingarten ('82) • First systematic study performing all extrapolations: GF11 Collab. ('93) • Light hadron spectrum consistent with experiment within estimated errors of O(10%) • Quality of extrapolation not tested. • Quenching artifacts not identified.

  6. qQCD simulations Hamber and Parisi ('81) Weingarten ('82) GF11 ('93)

  7. Systematic studies by CP-PACS/JLQCD (2) • CP-PACS, PRL 84(00)238, PR D67(03)034503 • plaq. gauge + standard Wilson quark • lattice ba [fm] Ls a [fm] Niter • --------------------------------------------------------------- • 323´56 5.90 0.102(1) 3.26(3) 160,000 • 403´70 6.10 0.078(1) 3.10(3) 240,000 • 483´84 6.25 0.064(1) 3.08(3) 420,000 • 643´112 6.47 0.050(1) 3.18(6) 300,000 • ----------------------------------------------------------------- • 1 iter. = HB + 4 x OR • ≈100 more computations than the GF11. • First well-controlled chiral and continuum extrapolations • ––> a problem in GF11 extrapolation found. Errors in light hadron spectra ≤ 1-3% (statistical + systematic, except for quenching) • Experiment approximately • reproduced. • Deviations of O(10%) • Limitation of quenched approx.

  8. qQCD simulations CP-PACS ('98)

  9. CP-PACS Systematic studies by CP-PACS/JLQCD (3) • Step 2: NF = 2 full QCD • dynamical degenerate u, d, but quenched s • Naively, several hundreds more computer power required. • ß • CP-PACS PRL 85(00)4674 [E: 90(03)029902], PR D65(02)054505 [E: D67(03)059901] • JLQCD PR D68(03)0504502 • Improved lattice action • computation ≈ 1/10 Not enough => lattice ≈ 2.5 fm CPPACS: a = 0.2–0.1 fm mqsea ≥ 70 MeV [Mps/Mv ≥ 0.6] mqval ≥ 40 MeV [Mps/Mv ≥ 0.5] • The 1st cont. extrap. • ~ GF11 in qQCD. •  Deviations largely reduced ◇ ：Experiment ●： NF = 2 QCD ■□: quenched QCD

  10. Toward a realistic simulation But still small gaps?? Among many possible origins (e.g. syst. err. from chiral extrap., small volume etc.) quarks:udscbt 3 MeV 7 MeV 70-100 MeV 1.2 GeV 4 GeV 175 GeV ÝÝ QCD scalesLQCD, TC Step 3: NF = 2+1 full QCD dynamical s-quark Large computer power required: * Calculation of s quark * More parameters to be scanned/adjusted as a joint project of CP-PACS and JLQCD collabs.

  11. Computing Facilities machines full machine for LQCD GF/node #Node GFlops #Node GFlops SR8000/F1 12 100 1200 ~ 64 ~768 @ KEK CP-PACS 0.3 2048 614 2048 614 @ CCP, U.Tsukuba SR8000/G1 14.4 12 173 12 173 @ CCP, U.Tsukuba VPP5000 9.6 80 768 ~ 24 ~230 @ SIPC, U.Tsukuba Earth Simulator 64 640 40960 ~ 10 ~640 @ ES Center

  12. Algorithm Conventional Hybrid MC algorithm exact only for NF = 2 n for Wilson-type quarks NF = 4 n for staggered-type quarks mu ~ md << ms single (odd) flavor algorithm needed to avoid unexpected systematic errors. (cf.) other groups adopting approximate algorithms. • Exact algorithms based on polynomial approx. for quark matrix D or det D • multiboson algorithm (Alexandrou et al., PR D60(99)034504) • HMC (Takaishi and de Forcrand, Int. J. Mod. Phys. C13(02)343) A systematic test of various alternativesAoki et al., PR D65(02)094507 We adopt: HMC for u, d PHMC for s ~ 1.5 times more CPU time than NF = 2 HMC Implementation+optimization: performance ~ 20-44% in production runs!

  13. Computing Facilities machines full machine for LQCD GF/node #Node GFlops #Node GFlops / [*] SR8000/F1 12 100 1200 ~ 64 ~768 @ KEK 35% CP-PACS 0.3 2048 614 2048 614 @ CCP, U.Tsukuba20% SR8000/G1 14.4 12 173 12 173 @ CCP, U.Tsukuba44% VPP5000 9.6 80 768 ~ 24 ~230 @ SIPC, U.Tsukuba44% Earth Simulator 64 640 40960 ~ 10 ~640 @ ES Center31% [*] performance of PHMC code on 203x40 (T. Yoshié, Lattice 2003)

  14. Action Test study: a-1 ~ 1.5--2.5 GeV, 83x16, 123x32 S. Aoki et al., Nucl. Phys. B(PS)106(02)263 Plaquette gauge + Clover v.s. RG-improved gauge + Clover • b = 4.6, 4.8, ... 6.0; 83x16 b = 1.5, 1.55, ..., 2.25; 83x16 • With clover-improved Wilson quarks, •  severe lattice artifact with the plaquette gauge action • at a-1 < 2 GeV • Effective adjoint coupling due to the clover term? (No such phenomena with naive Wilson quarks.) •  improvement of the gauge action (RG or Symanzik) important ~

  15. Action (2) We adopt: • RG-improved gauge action (Iwasaki, '83) Sg = (b/6) {c0S + c1S } c0 + 8c1 = 1, c1 = –0.331 • clover-improved Wilson quarks with cSW non-perturbatively evaluated using the Schrödinger functional method (Lüscher et al., '96, Jansen and Sommer, '98)  at fixed physical lattice size L* = 6 x ab=1.9 to ensure full O(a)-improvement K.-I. Ishikawa, Lattice 2002; 2003

  16. Simulation Parameters • a-1 ~ 2 GeV (b = 1.9, cSW = 1.715) as the 1st point towards the continuum limit • 163x32 (La ~ 1.6 fm) 203x40 (La ~ 2.0 fm) on-going • mud: 5–6Kud points (L) mPS(LL) / mV(LL) ~ 0.64-0.77 • ms: 2Ks points (S) mPS(SS) / mV(SS) ~ 0.72, 0.77 slightly missed the phys. pt. (0.68) • 3000 traj. at each (Kud, Ks) on 163x32 ≥5000 203x40 had. meas. every 10 traj., jackknife-bin = 50 traj. for 16, 100 traj. for 20 163x32

  17. Simulation Parameters (2) 163x32, b = 1.9, cSW = 1.715 (3000 traj. each) Kud Ks dt Npoly mPS/mV(LL) mPS/mV(SS) 0.1358 0.1358 1/100 110 0.768(4) 0.768(4) 0.1361 1/100 100 0.745(5) 0.766(4) 0.1364 1/125 100 0.717(5) 0.766(4) 0.1366 1/125 100 0.691(4) 0.761(4) 0.1368 1/125 100 0.663(6) 0.762(4) 0.1370 1/140 100 0.639(6) 0.769(4) 0.1358 0.1364 1/100 130 0.763(5) 0.716(5) 0.1361 1/100 130 0.743(4) 0.718(4) 0.1364 1/125 130 0.716(5) 0.716(4) 0.1366 1/125 130 0.694(5) 0.716(5) 0.1368 1/125 130 0.662(7) 0.712(6) 0.1370 1/140 130 0.636(7) 0.715(6)

  18. Simulation Parameters (3) 203x40, b = 1.9, cSW = 1.715 (5000 traj. each) Kud Ks dt Npoly mPS/mV(LL) mPS/mV(SS) 0.1358 0.1358 1/125 110 0.767(2) 0.1361 1/125 110 0.742(2) 0.764(2) 0.1364 1/140 110 0.721(3) 0.770(2) 0.1368 1/160 110 0.675(4) 0.771(2) 0.1370 1/180 110 0.639(3) 0.769(2) 0.1358 0.1364 1/125 140 0.767(2) 0.722(2) 0.1361 1/125 140 0.746(2) 0.720(2) 0.1364 1/140 140 0.714(3) 0.1368 1/180 140 0.665(4) 0.715(3) 0.1370 1/180 140 0.623(4) 0.708(3) Preliminary ! 163x32 data will be discussed, unless otherwise stated.

  19. Meson masses In this study, Kval = one of Ksea(L or S) only "diagonal" mPS(LL) obtained atKud = 0.1366, Ks=0.1364 [mPS(LL)/mV(LL)=0.694(5), mPS(SS)/mV(SS) =0.716(4)]  Doubly-smeared source & single exp. fit mV(LL)

  20. Meson masses (2) • Chiral extrapolation: quadratic polynomial fits • (PS) • (V1) • (V2) • [1] = (PS)+(V1) • [2] = (PS)+(V2) • central value = weighted average of [1] & [2]; syst. error = [1] - [2] • Identification of the physical point a , Kud , Ks • K-input:Mp , Mr , MK • f-input:Mp , Mr , Mf • 

  21. Meson masses (3) K-input K-input At a ~ 0.1 fm  consistent with Experiment  K- and f-inputs agree Similar results also for J. Assuming small a-dep. (due to non-pert. improvement)  quenching artifacts removed in NF=3 QCD

  22. J : influence of the chiral extrapolation not strong • consistent with Experiment

  23. J Preliminary ! • consistent with Experiment

  24. Light meson decay constants Using MF-improved 1-loop ZA, cA, bA • Systematic errors? • scaling violation • chiral extrapolation • non-perturbative effects in Z 's

  25. MF-improved 1-loop matching with MS at m = a-1 • 4-loop running to m = 2 GeV Quark masses K-input K-input  mq(NF=3) < mq(NF=2) < mq(NF=0) VWI and AWI disagree  K- and f-inputs agree

  26. Assuming small a-dep. in mqAWI (as seen in the NF=2 case), in the MS scheme at m = 2 GeV, Quark masses (2)  10-15% smaller than NF=2  consistent with 1-loop ChPT 24.4(1.5)(Leutwyler, PL B378(96)313)

  27. Tentative conclusions and future plans • NF=2+1 QCD • RG-improved gauge + clover-improved Wilson quark with non-perturbative cSW • exact NF=2+1 algorithm (PHMC) • 163x32, a-1 ~ 2 GeV, 6Kud x 2Ks x 3000traj.'s finished  light meson spectrum ~ experiment already at a-1~2GeV assuming small scaling violation in AWI-mq  mq 10-15% lighter than NF = 2  decay constants ?  further study needed • next • 203x40, a-1 ~ 2 GeV jobs  finite volume effects • two more a-1 points  continuum extrapolation

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