Unquenched spectroscopy with dynamical up, down and strange quarks

Transcription

1 Unquenched spectroscopy with dynamical up, down and strange quarks CP-PACS and JLQCD Collaborations Tomomi Ishikawa Center for Computational Sciences, Univ. of Tsukuba 4th ILFTN Workshop Lattice QCD via International Research Network 8th-11th, March

2 Nf=2+1 full QCD project members (CP-PACS and JLQCD) S. Aoki, M. Fukugita, S. Hashimoto, K-I. Ishikawa, T. Ishikawa, N. Ishizuka, Y. Iwasaki, K. Kanaya,T. Kaneko, Y. Kuramashi, M. Okawa,T. Onogi, Y. Taniguchi, N. Tsutsui, N. Yamada, A. Ukawa and T. Yoshie 2

3 Nf=2+1 full QCD project CP-PACS and JLQCD joint project Wilson quark formalism Chiral symmetry is violated at finite lattice spacing. Computational cost is large. Theoretical ambiguity is less. Dynamical up, down and strange quark Up and down are degenerate. Strange has a distinct mass. 3

4 Large scaled simulations in Nf=0 and Nf=2 QCD by CP-PACS and JLQCD Quenched (Nf=0) CP-PACS : Plaquette gauge + Wilson quarks, continuum limit Phys.Rev.D67(2003)034503, Phys.Rev.Lett.84(2000)238. CP-PACS : RG improved gauge + clover quarks with PT Phys.Rev.D65(2002) c SW, continuum limit Dynamical up and down quarks (Nf=2) strange : quenched JLQCD : Plaquette gauge + clover quarks with NPT Phys.Rev.D68(2003) CP-PACS : RG improved gauge + clover quarks with PT c SW c SW Phys.Rev.D65(2002)054505, Phys.Rev.Lett.85(2000)4674., continuum limit 4

5 Nf=0 and Nf=2 results meson masses [GeV] Nf=0(RG+PT clover) Nf=2(RG+PT clover) experiment φ (K-input) K* (K-input) K* (φ-input) K (φ-input) a [fm] meson spectrum Nf=0 Systematic deviation from experiment is O(5-10%). Nf=2 The deviation is considerably reduced. the effect of dynamical up and down quarks RG+clover (Phys.Rev.D65(2002)054505) c SW : perturbation N f = 0 : a = fm, La = fm N f = 2 : a = fm, La = fm 5

6 Baryon spectrum 1.8 Nf=0 large volume systematic deviation from experiment (5-10%) Nf=2 small Finite Size Effect (FSE) small volume for heavier baryons good agreement with exp. dynamical ud quark effect for lighter baryons large discrepancy from exp. FSE mass [GeV] PS spin 0 K Vector spin 1 K * φ N experiment Nf=0 (K-input) Nf=0 (φ-input) Nf=2 (K-input) Nf=2 (φ-input) Octet spin 1/2 Decuplet spin 3/2 RG+clover (Phys.Rev.D65(2002)054505) Λ PLQ+Wilson (Phys.Rev.D67(2003)034503) N f = 0 : a = fm, La = fm Σ Ξ c SW : perturbation N f = 2 : a = fm, La = fm Δ Σ Ξ Ω

7 ud quark masses Nf=0 Nf=2 : ud quark mass is reduced. dynamical ud quark effects m ud MS (µ=2gev) [MeV] Nf=0,VWI Nf=2,VWI Nf=0,AWI Nf=2,AWI a [fm] RG+clover (Phys.Rev.D65(2002)054505) 7

8 s quark masses Nf=0 Nf=2 : strange quark mass is largely reduced. discrepancy between K- and φ-input vanish. dynamical ud quark effects How is the results in the fully unquenched QCD (Nf=2+1)? 8 m s MS (µ=2gev) [MeV] m s MS (µ=2gev) [MeV] RG+clover (Phys.Rev.D65(2002)054505) K-input Nf=2,VWI Nf=2,AWI a [fm] Nf=0,AWI Nf=2,VWI φ-input a [fm] Nf=0,VWI Nf=0,AWI Nf=0,VWI Nf=2,AWI

9 Lattice action gauge : RG improved action (Iwasaki,1985) quark : non-perturbatively c SW Strategy for Nf=2+1 O(a) is non-perturbatively determined. improved Wilson action (Nucl.Phys.Proc.Suppl.129(2004)444, Phys.Rev.D73(2006)034501) Algorithm standard HMC algorithm for up and down quarks usual pseudo-fermion method Polynomial HMC (PHMC) algorithm for strange quark odd flavor algorithm exact algorithm (Phys.Rev.D65(2002)094507) 9

10 δτ, N poly δτ, N poly P HMC 85%, P GMP 90% κ ud κ s dτ N poly κ ud κ s dτ N poly / / / / / / / / / / β = 1.83 κ ud κ s dτ N poly κ ud κ s dτ N poly / / / / / / / / / / β = 1.90 κ ud κ s dτ N poly κ ud κ s dτ N poly / / / / / / / / / / β =

11 Simulation parameters Lattice spacing, size, etc a 2 β = 2.05 (a fm) c SW = L 3 T = HMC traj. = β = 1.90 (a fm) c SW = L 3 T = HMC traj. = β = 1.83 (a fm) c SW = L 3 T = HMC traj. = fixed physical volume (2 fm) 3 11

12 Quark mass parameters 5 ud quark parameters m ps /m V (0.18 : exprriment) 2 s quark parameters m ps /m V 0.7 (0.68 : 1-loop ChPT) 0.05 β=1.83, L 3 xt=16 3 x β=1.90, L 3 xt=20 3 x40 β=2.05, L 3 xt=28 3 x56 Ks= Ks= Ks= a m S VWI physical point a m S VWI 0.04 physical point a m S VWI physical point 0.03 Ks= Ks= Ks= a m ud VWI a m ud VWI a m ud VWI 12

13 Gauge configuration generation Production runs 2003 Earth β=1.90 β=1.83 Univ. of Tsukuba Univ. of Tsukuba β= Univ. of Tsukuba

14 Computing facilities for Nf=2+1 machines GF/node total for Nf=2+1 QCD # of node GFlops # of node GFlops use Univ. of Tokyo ~2 ~122 measurement Univ. of Tsukuba Univ. of Tsukuba Univ. of Tsukuba ~24 ~ ~64 ~768 production (β=1.83, 1.90), measurement production (β=1.83, 1.90) production (β=1.83, 1.90) production (β=1.90, 2.05), measurement Earth ~14 ~896 production (β=1.90, 2.05) total ~2.8TFlops 14

15 Measurement of the meson masses Procedure We perform the measurements at only unitarity points. m valence = m sea Physical volume (2 fm) 3 is not large to calculate baryon masses. We mainly focus on the meson sector. FSE is comparable to or slightly larger than statistical error of the meson spectrum at physical points. It does not change conclusions. Measurements are performed at every 10 HMC trajectories. 2 source points Smearing: Doubly (exponentialy) smeared source - point sink 15

16 Statistics for the measurement β=1.83 κ ud κ s traj. m π /m ρ m ηs /m φ κ ud κ s traj. m π /m ρ m ηs /m φ (13) (15) (14) (19) (21) (21) (14) (16) (18) (17) (18) (18) (22) (16) (23) (20) (24) (15) (32) (21) β=1.90 κ ud κ s traj. m π /m ρ m ηs /m φ κ ud κ s traj. m π /m ρ m ηs /m φ (15) (15) (16) (21) (18) (17) (15) (17) (19) (15) (16) (16) (27) (17) (21) (17) (21) (15) (28) (20) β=2.05 κ ud κ s traj. m π /m ρ m ηs /m φ κ ud κ s traj. m π /m ρ m ηs /m φ (26) (29) (23) (32) (23) (23) (29) (39) (30) (23) (34) (34) (34) (25) (45) (43) (38) (28) (47) (46) 16 jackknife bin size = 100 HMC traj.

17 Effective mass plot am eff (t) = ln G(t + 1) G(t) G(t) : correlation function effective mass plot beta=2.05, Kud= , Ks= effective mass plot beta=2.05, Kud= , Ks= π (smeared source - point sink) 0.38 ρ (smeared source - point sink) effective mass effective mass T T 17

18 Chiral extrapolation Fitting procedure Polynomial fit functions in quark masses are used. include up to quadratic terms interchanging symmetry among 3 sea quarks Chiral fits are made to among 2 valence quarks light-light (LL), light-strange (LS) and strange-strange (SS) meson simultaneously. ignoring correlations among LL, LS and SS 18

19 Polynomial fit forms using the VWI quark mass definition m 2 P S = BS P S (2m ud + m s ) + BV P S (m val1 + m val2 ) + DSV P S (2m ud + m s )(m val1 + m val2 ) + C P S S1 (2m 2 ud + m 2 s) + C P S S2 (m 2 ud + 2m ud m s ) + C P S V 1 (m 2 val1 + m 2 val2) + C P S V 2 m val1 m val2 m V = A V + B V S (2m ud + m s ) + B V V (m val1 + m val2 ) m q = D V SV (2m ud + m s )(m val1 + m val2 ) + C V S1(2m 2 ud + m 2 s) + C V S2(m 2 ud + 2m ud m s ) + C V V 1(m 2 val1 + m 2 val2) + C V V 2m val1 m val2 ( 1 K q 1 K C ) # of fit parameters = 16 m ud, m s : sea quarks m val1, m val2 : valence quarks 19

20 0.4 β=1.90, L 3 xt=20 3 x40, quadratic 0.8 β=1.90, L 3 xt=20 3 x40, quadratic χ 2 /d.o.f.=0.94 χ 2 /d.o.f= (a m PS ) a m V Ks= Ks= VWI a m ud Ks= Ks= VWI a m ud 20

21 Fitting form from Wilson ChPT (WChPT) chiral log behavior m 2 π ln m 2 π Wilson ChPT (WChPT) (Sharpe et al. 98, Lee et al. 99) include explicit chiral symmetry breaking effect of Wilson quark Nf=2+1 version (Phys.Rev.D73(2006)014511), hep-lat/

22 for and (O(a) improved theory) π ρ m 2 π = x + 2y + 1 f 2 m ρ = m O + λ x x + 2λ y y 2 3πf 2 [ L π ( x 2 + y + 5C) + L K 4C + L η ( x 6 y 3 + C) ] (D x x + 2D y y + E xx x 2 + Eyyy π 2 + 2Exy) [ (g g2 )(x + 2y) 3/2 +2g 2 2(x y) 3/ g2 2(x 2y) 3/2 ] L ψ = m2 ψ 16π 2 ln m2 ψ, m 2 π = x + 2y, m 2 K = x y, m 2 η = x 2y x = 2B 3 (2m ud + m s ), y = B 3 (m ud m s ) # of fit parameters = 16 fitting is very difficult due to highly non-linear form (in progress) 22

23 Physical point and lattice spacing Inputs to fix the quark masses and the lattice spacing K-input φ-input lattice spacings m π, m ρ, m K m π, m ρ, m φ m ρ to set s quark mass K-input φ-input β a 1 [GeV] a[fm] a 1 [GeV] a[fm] (22) (17) 1.598(26) (20) (38) (19) 1.980(37) (19) (11) (26) 2.84(10) (26) K-input and φ-input give consistent results. 23

24 Light meson spectrum Prediction K-input m K, m φ φ-input m K, m K The calculation of m η, m η is in progress. disconnected diagram is needed. Continuum extrapolation We use the non-perturbatively O(a) improved Wilson quark, thus meson spectrum should scale as a 2. m(a) = A + Ba 2 24

25 Results In the continuum, meson spectrum is consistent with experiment. The statistical error in the continuum limit is large. meson masses [GeV] Quenched(RG+PT clover) Nf=2(RG+PT clover) Nf=2+1(RG+NPT clover) experiment φ (K-input) K* (K-input) K* (φ-input) K (φ-input) a 2 [fm 2 ] a 2 [fm 2 ] In the Nf=2,0 case, extrapolation function is m(a)=a+ba, because clover action is perturbatively O(a) improved. 25

26 Scaling violations Is the scaling violations in Nf=2+1 larger than that in Nf=2 and Nf=0? N f = : NPT c SW, N f = 2, 0 : PT c SW K* (K-input) a 2 [fm 2 ] m K (a) = m K (0)(1 + c(λa) 2 ), Λ 300 MeV c O(1) The scaling violation in Nf=2+1 is reasonable. The small scaling violation in Nf=2 and 0 is accidental. 26

27 VWI quark mass VWI quark mass can be negative due to lack of chiral symmetry of the Wilson quark. AWI quark mass The scaling violation is smaller than that of VWI in Nf=2 case. Renormalization tad-pole improved 1-loop matching with 4-loop running to Light quark masses m V W I q = 1 2 ( 1 K 1 K c 27 ) K c m π (K ud, K s ) Kud =K s =K c = 0 m AW I q = 4A 4 (t)p (0) 2 P (t)p (0) m LAT q µ = 2 GeV (a 1 ) m MS q (µ = 2 GeV) MS at µ = a 1

28 up and down quarks We assume that the O(a) contribution is small and use the extrapolation function which is same as in the meson spectrum (linear in a 2 ). In the continuum limit, the VWI definition gives a positive value. m MS ud (µ = 2GeV) = 3.49(15) MeV (AWI, combined K with φ-input) m ud MS (µ=2gev) [MeV] m ud MS (µ=2gev) [MeV] Nf=2+1 (K-input) AWI VWI a 2 [fm 2 ] Quenched,VWI Nf=2+1,AWI (K-input) Quenched,AWI Nf=2,AWI Nf=2,VWI a 2 [fm 2 ] (Nf=2, 0 : RG+clover(PT)) 28

29 strange quark All definitions of strange quark mass gives consistent results in the continuum limit. The difference between Nf=2+1 and Nf=2 is invisible in the continuum limit as in the ud quark. m MS s (µ = 2GeV) = 90.9(3.7) MeV (AWI, combined K with φ-input) m s MS (µ=2gev) [MeV] m s MS (µ=2gev) [MeV] K-input Nf=2+1,VWI φ-input Nf=2+1,AWI Nf=2,VWI Nf=2,AWI Nf=0,VWI Nf=2,VWI Nf=0,AWI Nf=2,AWI Nf=0,VWI Nf=0,AWI Nf=2+1,AWI Nf=2+1,VWI a 2 [fm 2 ] (Nf=2, 0 : RG+clover(PT))

30 NPT Comment : PT and NPT renormalization factor In Nf=2 we can see systematic deviation of strange quark mass between PT and NPT renormalization factor. NPT renormalization factor is very important. MeV our result MeV our result NPT NPT QCDSF!UKQCD AWI, NPR ALPHA AWI, NPR SPQcdR AWI, NPR CP!PACS AWI, TB!PT JLQCD AWI, TB!PT QCDSF!UKQCD VWI, NPR SPQcdR VWI, NPR CP!PACS VWI, TB!PT JLQCD VWI, TB!PT HPQCD!MILC!UKQCD, TB!PT HPQCD, TB!PT a 2 [fm 2 ] figure from hep-lat/ (QCDSF-UKQCD) 30

31 PS meson decay constants PS decay constant f π, f K 0 A 4 π = f π m π renormalization tad-pole improved one-loop renormalization factor definitions for the calculation We test two different definitions. P P (t)p P (0) C P P P P P (t)p S (0) C P S P P S (t)p S (0) C SS P A P 4 (t)p S (0) C P S A P : point, e m πt e m πt e m πt e m πt S : exponential f π = CP A S CP P S f π = C P S A 2C P P P m π (method 1) 2 m π C SS P (method 2) 31

32 Two methods are consistent each other within the large statistical error K K K K f PS [GeV] π π K-input π π K-input, method 1 K-input, method a 2 [fm 2 ] a 2 [fm 2 ] f PS [GeV] 0.15 K π f π (Nf=2+1) f K (Nf=2+1) f π (Nf=2) f K (Nf=2) experiment The continuum limit values are consistent with experiment. f π = 140.7(9.3) MeV f K = 160.9(9.1) MeV a 2 [fm 2 ] (Nf=2 : RG+clover(PT)) (method 2, K-input) (preliminary) 32

33 Baryon spectrum Effective mass plot effective mass plot beta=1.90, Kud= , Ks= effective mass plot beta=2.05, Kud= , Ks= N (octet) effective mass effective mass 0.6 Δ (decuplet) T T Signal is not good. Volume (2.0 fm) 3 is too small (?) 33

34 Ξ mass [GeV] Ξ Σ Λ Σ Λ 1.6 experiment Nf=2+1 (K-input) Nf=0 (K-input) Σ Ξ Ω N N octet (φ-input) a 2 [fm 2 ] mass [GeV] N Λ Σ Ξ Δ mass [GeV] Ω Ω Ξ * Σ * Ξ * Σ * Δ decuplet (φ-input) a 2 [fm 2 ] The data points rampage widely. Δ octet decuplet spin 1/2 spin 3/2 (preliminary) Pattern of the spectrum is reproduced. But the precise spectrum and FSE are unclear.

35 Static quark potential V (r) = V 0 α r + σr Sommer scale 2 dv (r) r dr In our calculation through Sommer scale = 1.65 r=r0 R 0 = ar fm phenomenological model r 0 = r α σ r string model ( α=π/12 ) is obtained [ V(r) - V(r 0 ) ] r 0 [ V(r) - V(r 0 ) ] r 0 [ V(r) - V(r 0 ) ] r β = 1.83 β = 1.90 r / r 0 string model ( α=π/12 ) r / r β = 2.05 string model ( α=π/12 ) r / r 0

36 0.25 Chiral extrapolation 1 r 0 = A + B ( 2 κ ud + 1 κ s ) 1/r data fit line β = 1.90 Continuum limit of using the lattice spacing from m ρ R 0 = 0.516(21) fm R (2/Kud+1/Ks)/ Nf=2+1 (K-input) Nf=2 quenched Nf=2+1 (MILC) consistent with 0.5 fm (preliminary) a r 0 [fm] 0.5 ( R0 = fm (MILC) Υ spectrum ) a 2 [fm 2 ] (Nf=2, 0 : RG+clover(PT)) 36

37 CP-PACS/JLQCD Nf=2+1 project RG-gauge + non-pt clover (Wilson quark formalism) Gauge configuration generation has been already finished. Analysis of spectrum and quark masses Encouraging results in the continuum limit are obtained. Assuming that the scaling is a 2, Summary Meson spectrum is consistent with experiment. All definitions and inputs of quark masses gives consistent results. Quark masses in the continuum : m MS ud (µ = 2GeV) = 3.49(15) MeV (µ = 2GeV) = 90.9(3.7) MeV m MS s Baryon spectrum signal is not so good(?), large statistical error 37

38 Required task Non-perturbative determination of renormalization factor Calcurations in progress η meson mass Heavy meson quantities using a relativistic heavy quark action (Aoki,Kuramashi,Tominaga,2001) c Γ, Z Γ, b Γ 38

39 Next direction - lighter quark mass - PACS-CS collaboration clover quark with domain decomposed HMC PACS-CS (CCS, Univ. of Tsukuba) to be installed in June 2006 cluster, 2560 nodes, 14.3 TFLOPS JLQCD collaboration dynamical overlap fermion IBM Blue Gene (KEK) 10 rack (10240 node), 57.3 TFLOPS c Γ, Z Γ, b Γ ambiguity in the chiral extrapolation will be removed 39