We report on a calculation of the light hadron spectrum and quark masses in
three-flavor dynamical QCD using the non-perturbatively O(a)-improved Wilson
quark action and a renormalization-group improved gauge action. Simulations are
carried out on a 16^3 \times 32 lattice at \beta=1.9, where a^{-1} \simeq 2GeV,
with 6 ud quark masses corresponding to m_{pi}/m_{rho} \simeq 0.64-0.77 and 2 s
quark masses close to the physical value. We observe that the inclusion of
dynamical strange quark brings the lattice QCD meson spectrum to good agreement
with experiment. Dynamical strange quarks also lead to a reduction of the uds
quark masses by about 15%.Comment: 3 pages, 4 figures, Lattice2003(spectrum), Fig.1 correcte

Aoki, S.

Collaboration, JLQCD

CP-PACS

Fukugita, M.

Hashimoto, S.

Ishikawa, K-I.

Ishikawa, T.

Ishizuka, N.

Iwasaki, Y.

Kanaya, K.

Kaneko, T.

Kuramashi, Y.

Okawa, M.

Taniguchi, N.

Tsutsui, N.

Ukawa, A.

Yoshie, T.

English

arXiv

We report on a calculation of the light hadron spectrum and quark masses in three-flavor dynamical QCD using the non-perturbatively O(a)-improved Wilson quark action and a renormalization-group improved gauge action. Simulations are carried out on a 163 × 32 lattice at β = 1.9, where a-1 2 GeV, with 6 ud quark masses corresponding to mπ/m 0.64–0.77 and 2 s quark masses close to the physical value. We observe that the inclusion of dynamical strange quark brings the lattice QCD meson spectrum to good agreement with experiment. Dynamical strange quarks also lead to a reduction of the uds quark masses by about 15%.

CP-PACS Collaboration

JLQCD Collaboration

Kaneko, T

Aoki, S

Fukugita, M

Hashimoto, S

Ishikawa, Kenichi

Ishikawa, T

Ishizuka, N

Iwasaki, Y

Kanaya, K

Kuramashi, Y

Okawa, Masanori

Taniguchi, N

Tsutsui, N

Ukawa, A

Yoshié, T

Hiroshima University Institutional Repository

arXiv:hep-lat/0309137 v2   24 Sep 2003KEK-CP-144UT-CCP-P140UTHEP-474Light hadron spectrum in three-flavor QCD with O(a)-improved Wilsonquark action ∗CP-PACS and JLQCD Collaborations: T. Kanekoa, S. Aokib, M. Fukugitac, S. HashimotoaK-I. Ishikawad, T. Ishikawad, N. Ishizukab,d, Y. Iwasakib,d, K. Kanayab,d, Y. Kuramashia, M. OkawaeN. Taniguchib, N. Tsutsuia, A. Ukawab,d, T. Yoshie´b,daHigh Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, JapanbInstitute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, JapancInstitute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582, JapandCenter for Computational Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8577, JapaneDepartment of Physics, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, JapanWe report on a calculation of the light hadron spectrum and quark masses in three-flavor dynamical QCDusing the non-perturbatively O(a)-improved Wilson quark action and a renormalization-group improved gaugeaction. Simulations are carried out on a 163 × 32 lattice at β = 1.9, where a−1 ≃ 2 GeV, with 6 ud quark massescorresponding to mpi/mρ ≃ 0.64 – 0.77 and 2 s quark masses close to the physical value. We observe that theinclusion of dynamical strange quark brings the lattice QCD meson spectrum to good agreement with experiment.Dynamical strange quarks also lead to a reduction of the uds quark masses by about 15%.1. IntroductionAs a joint collaboration of CP-PACS andJLQCD, we have initiated a project for the pre-cise measurement of the light hadron spectrumand the quark mass with three-flavor full QCD.The systematic deviation of the quenched latticespectrum from experiment found in [1] is signif-icantly reduced with the inclusion of dynamicalup and down quarks [2,3]. We now extend thework to three flavors.We adopt the renormalization-group improvedgauge action and the O(a)-improved Wilsonquark action with the non-perturbatively im-proved clover coefficient cSW obtained in [4]. Sim-ulations are carried out at β = 1.9, at the scalea−1 = 2.05(5) GeV, on a 163 × 32 lattice us-ing a Polynomial Hybrid Monte Carlo algorithmdeveloped in [5]. Six values of the ud quarkmass, corresponding to mPS,LL/mV,LL ≃ 0.64 –0.771, are used to extrapolate to the physical∗Talk presented by T. Kaneko1In this report, subscripts LL, LS and SS represent thelight-light, light-strange and strange-strange mesons, re-valuempi/mρ≃0.18. Two values are taken for thes quark mass, corresponding to mPS,SS/mV,SS≃0.72 and 0.77. They are close to the semi-empirical value mηs/mφ = 0.68 from chiral per-turbation theory, so that a short extrapolation isenough to get to the physical value. 3000 HMCtrajectories are accumulated at each simulationparameter.2. meson massesWe focus on the meson spectrum since our lat-tice size of La≃ 1.6 fm is too small for baryons[3].Fig. 1 shows the J parameter [6] defined byJ = mV,LSmV,LS −mV,LLm2PS,LS −m2PS,LL. (1)This is compared with the previous results in two-flavor and quenched QCD [2], which are evaluatedfor the physical kaons mPS/mV = mK/mK∗ asJ=mV(dmV/dm2PS) after taking the chiral limitspectively.0.0 2.0 4.0 6.0(r0mPS,LL)20.350.400.450.500.55JNf=3, mPS,SS/mV,SS=0.77Nf=3, mPS,SS/mV,SS=0.72Nf=2experimentNf=0Figure 1. The J parameter in two- and three-flavor QCD (left panel) and in quenched QCD(right panel).for sea quarks2. We see that J in three-flavorQCD stays at values systematically higher than inquenched and two-flavor QCD, and is consistentwith experiment.Our lattice size La ≃ 1.6 fm is significantlysmaller than that used in quenched or two-flavorQCD. Because finite-size effects generally lowerthe J parameter [3], we conclude that the consis-tency of J between three-flavor QCD and exper-iment is not an artifact of finite-size effects.Chiral extrapolations are carried out usingpolynomial forms. We fix the lattice spacing andthe ud quark mass with mpi and mρ. The strangequark mass is fixed with either mK (K-input) ormφ (φ-input).In Fig. 2, mK∗ is plotted as a function of thelattice spacing. The three-flavor result is higherthan that in two-flavor QCD at comparable lat-tice spacings. The consistency of the three-flavorvalue with experiment seen already at a finitelattice spacing lends us hope that scaling viola-tion with the use of the non-perturbatively O(a)-improved action is indeed small and the consis-tency with experiment holds in the continuumlimit. This should be verified in a future study.Similar consistency with experiment can alsobe seen in other meson masses as shown in Fig. 3,where deviations from experiment are plotted.Improvement over the quenched results of [1] is2We now prefer the definition of J by Eq. (1), as it ismore straightforward, using the hadron masses measuredin the simulation without resorting to any extrapolationprocedures.0.00 0.05 0.10 0.15 0.20 0.25a [fm]0.850.90mK* [GeV]Nf=3,  RG + cloverNf=2,  RG + cloverNf=0,  plaq + WilsonNf=2,  plaq + cloverNf=0,  plaq + cloverexperimentFigure 2. K∗ meson mass as a function of latticespacing.-10-50510(m-mexp)/mexp [%]Nf=3Nf=0mK* (K-input) mφ (K-input) mK (φ-input) mK* (φ-input)Figure 3. Deviation of meson spectrum fromexperiment in three-flavor (filled symbols) andquenched QCD (open symbols).evident, as anticipated from the agreement of theJ with experiment.3. Quark massesThe physical quark masses, mud and ms, arecalculated through the axial-vector Ward identity(AWI): mq = 〈∆4A4P 〉/(2 〈PP 〉). The matchingto the MS scheme is carried out at µ=a−1 usingthe one-loop Z factor [7] with the tadpole im-provement. The renormalized mass is evolved toµ=2 GeV using the 4-loop β function.The vector Ward identity (VWI) may offer anindependent determination of mud and ms. Thecritical hopping parameter Kc for ud quarks, de-fined where the light-light PS meson mass van-ishes, depends on ms due to the lack of chiralsymmetry. The two natural choices, Kc(ms =0), i.e., Kc in degenerate three-flavor QCD, andKc(ms = mphyss ) with the physical ms, however,lead to mud with the sign opposite to each other,indicating a large uncertainty from chiral symme-try breaking at a−1≃2 GeV. The determinationof the VWI mud requires a careful study of scal-ing violation; we focus on the AWI quark mass inthis report.Fig. 4 compares mud and ms in three-flavorQCD with our previous results in two-flavor andquenched QCD [1,2]. The discrepancy in ms be-tween K- and φ-inputs in quenched QCD disap-pears in two- and three-flavor QCD. Note thatmud and ms decrease with an increasing numberof flavors of dynamical quarks.Taking the AWI mass with the K-input as thecentral value and including the deviation betweenthe K- and φ-inputs into the error, we obtainmMSud = 2.89(6) MeV, (2)mMSs = 75.6(3.4) MeV, (3)ms/mud = 26.2(1.0) (4)in three-flavor QCD. Dynamical strange quarksdecrease both mud and ms by about 15%. Theratio ms/mud is consistent with the one-loop es-timate of chiral perturbation theory 24.4(1.5) [8].4. ConclusionOur simulation for three-flavor QCD showsthat the inclusion of dynamical strange quarksbrings the lattice QCD meson spectrum to goodagreement with experiment. A non-negligible re-duction is also found for quark masses. Thesepreliminary results are sufficiently encouragingto warrant further detailed and careful investiga-tions with time-consuming three-flavor full QCD.This work is supported by Large Scale Simu-lation Program No. 98 (FY2003) of High EnergyAccelerator Research Organization (KEK), andalso in part by the Grants-in-Aid of the Min-istry of Education (Nos. 12740133, 13135204,13640259, 13640260, 14046202, 14540289,14740173, 15204015, 15540251, 15540279). NT issupported by JSPS.2.03.04.05.06.0mudMS (µ=2GeV)RG+clover, K-inputRG+clover, φ-inputNf=3  (a=0.1fm)RG + cloverNf=2  (a=0)RG + cloverplaq + WilsonNf=0  (a=0)6080100120140160msMS (µ=2GeV)RG+clover, K-inputRG+clover, φ-inputNf=3  (a=0.1fm)RG+clover, K-inputRG+clover, φ-inputNf=2  (a=0)RG+clover, K-inputRG+clover, φ-inputplaq+Wilson, K-inputplaq+Wilson, φ-inputNf=0  (a=0)Figure 4. Comparison of mud (top figure) andms (bottom figure) between full and quenchedQCD. The left, middle and right panels in eachfigure show results in three- and two-flavor andquenched QCD, respectively.REFERENCES1. S. Aoki et al. (CP-PACS Collaboration),Phys. Rev. Lett. 84 (2000) 238; Phys. Rev.D67 (2003) 034503.2. A. Ali Khan et al. (CP-PACS Collaboration),Phys. Rev. Lett. 85, 4674 (2000); Phys. Rev.D 65, 054505 (2002).3. S. Aoki et al. (JLQCD Collaboration),hep-lat/0212039.4. K-I. Ishikawa (CP-PACS and JLQCD Collab-orations), in these proceedings.5. JLQCD Collaboration, Phys. Rev. D65(2002) 094507.6. P. Lacock and C. Michael, Phys. Rev. D52(1995) 5213.7. S. Aoki, et al, Phys. Rev. D58 (1998) 074505.8. H. Leutwyler, Phys. Lett. B378 (1996) 313.

Light hadron spectrum in three-flavor QCD with O(a)-improved Wilson quark action

CP-PACS Collaboration,

JLQCD Collaboration,

Name not available

Nuclear Physics B - Proceedings Supplements

Light hadron spectrum in three-flavor QCD with O(a)-improved Wilson
  quark action

Light hadron spectrum in three-flavor QCD with O(a)-improved Wilson quark action

Abstract

Similar works

Full text

Available Versions

Hiroshima University Institutional Repository

Name not available