We calculate charmed meson spectra and decay constants in lattice QCD
employing one-loop $O(a)$ improved heavy quark action and axial-vector
currents. In quenched simulations at $a \sim 0.1$ fm with the plaquette gauge
action as well as a renormalization-group improved one, it is shown that the
deviation from the continuum dispersion relation and the violation of
space-time symmetry for the pseudoscalar meson decay constants are
substantially reduced, once the $O(a)$ improvement is applied. Preliminary
results with two flavors of dynamical quarks are also presented.Comment: 3 pages, 4 figure, talk presented at Lattice2004(heavy), Fermilab,
  June 21-26, 200

Aoki, S.

CP-PACS Collaboration,

Fukugita, M.

Ishikawa, Kenichi

Iwasaki, Y.

Kanaya, K.

Kaneko, T.

Kayaba, Y.

Kuramashi, Y.

Okawa, Masanori

Ukawa, A.

Yoshie, T.

Nuclear Physics B - Proceedings Supplements

English

arXiv

We calculate charmed meson spectra and decay constants in lattice QCD employing one-loop O(a) improved heavy quark action and axial-vector currents. In quenched simulations at anot, vert, similar0.1 fm with the plaquette gauge action as well as a renormalization-group improved one, it is shown that the deviation from the continuum dispersion relation and the violation of space-time symmetry for the pseudoscalar meson decay constants are substantially reduced, once the O(a) improvement is applied. Preliminary results with two flavors of dynamical quarks are also presented

CP-PACS Collaboration

Hiroshima University Institutional Repository

arXiv:hep-lat/0409086 v1   15 Sep 2004UTHEP-497UTCCS-P-9Charmed meson spectra and decay constants with one-loop O(a)improved relativistic heavy quark action ∗CP-PACS Collaboration : Y. Kayaba,a S. Aoki,a M. Fukugita,b K-I. Ishikawa,c Y. Iwasaki,a K. Kanaya,a,T. Kaneko,d Y. Kuramashi,a, e M. Okawa,c A. Ukawa,a,e T. Yoshie´,a,ea Grad. School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japanb Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japanc Department of Physics, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japand High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japane Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, JapanWe calculate charmed meson spectra and decay constants in lattice QCD employing one-loop O(a) improvedheavy quark action and axial-vector currents. In quenched simulations at a ∼ 0.1 fm with the plaquette gaugeaction as well as a renormalization-group improved one, it is shown that the deviation from the continuumdispersion relation and the violation of space-time symmetry for the pseudoscalar meson decay constants aresubstantially reduced, once the O(a) improvement is applied. Preliminary results with two flavors of dynamicalquarks are also presented.1. IntroductionWith current computational resources it isdifficult to achieve a precise determination ofweak matrix elements associated with B andD mesons because of large mQa corrections forb- and c-quarks. Recently a relativistic heavyquark(RHQ) action was proposed to controlthese mQa corrections by applying the on-shellO(a) improvement program to massive quarks[1],and the mass-dependent improvement coefficientshave been perturbatively determined up to one-loop level[2]. The improvement of the heavy-heavy and heavy-light axial vector currents arealso carried out up to one-loop level in a massdependent way[3]. In this report we perform anumerical study of the RHQ action in quenchedQCD by investigating the effective speed of lightceff from the meson energy and the space-timeasymmetry R for the pseudoscalar decay con-stant. The deviation from ceff = 1 and R = 1measures typical systematic errors due to finitemQa corrections left in the formulation, whichshould be incorporated in the results of charmed∗Talk presented by Y. Kayabameson spectra and decay constants. Preliminaryresults with two flavors of dynamical quarks arealso presented.2. Simulation detailsWe employ the clover(CL) action with non-perturbative cNPSW [4,5] for light quarks and theRHQ action for heavy quarks combined with theplaquette and the Iwasaki gauge actions. It isworth mentioning that we replace the masslesspart of the one-loop improvement coefficients cBand cE in the RHQ action with that of the non-perturbative one ascB/E = cPTB/E(mQa)− cPTB/E(0) + cNPSW,where the superscript PT represents “perturba-tive” value. With this replacement O(a) errorsare completely removed at mQ = 0. We calculatecharmed meson spectra using 300 configurationson a 243 × 48 lattice at a ∼ 0.1fm in quenchedQCD. Three values of the lihgt quark mass cor-responding to MPS/MV ∼ 0.56 − 0.77 and fourvalues of the heavy quark mass around the charmquark mass are adopted. For comparison we per-10.850.90.9510 0.5 1 1.5 2MPSa0.80.91RHQ, H-HRHQ, H-LCL, H-HCL, H-L0 0.5 1 1.5 2 2.5MPSaDs J/ΨPlaquette IwasakiFigure 1. Effective speed of light for the PS me-son(top) and space-time asymmetry for the PSmeson decay constant(bottom) as a function ofthe meson mass in quenched QCD.form parallel calculations with the CL action forboth heavy and light quarks at the same gaugecoupling and lattice size.3. Numerical study of the RHQ actionLet us examine effectiveness of the O(a) im-provement for the RHQ action in a nonperturba-tive way. We extract the effective speed of lightceff by fitting the pesudoscalar(PS) meson energyaE as a function of spatial momentum aps:(aE)2 = (aMpole)2 + c2eff(aps)2,where Mpole denotes the pole mass. ceff is ex-pected to become unity in the continuum limit.Numerical results are plotted in Fig. 1(top) as afunction of the meson mass for heavy-heavy(H-H)and heavy-light(H-L) systems. Around charmedmeson mass the deviation from ceff = 1 is equal toor larger than about 10% for the CL heavy quarkaction, while less than 5% for the RHQ action.We also measure the space-time asymmetry interms of the PS meson decay matrix elements:R ≡ i〈0|ARk |PS〉〈0|AR4 |PS〉·E|ps|,which should become unity in the continuumlimit. Results are plotted in Fig.1(bottom) as0.060.080.10.12∆M(J/Ψ-η c) [GeV] expt.RHQ+Plq., MpoleRHQ+Plq, MkinRHQ+RG, MpoleRHQ+RG, MkinAniso, Mpole [6]0 0.02 0.04 0.06 0.08 0.1a[fm]0.20.250.3f Ds [GeV]expt.RHQ+Plq., A4RHQ+Plq., AkRHQ+RG, A4RHQ+RG, AkCL+Plq., A4 [7](a)(b)Figure 2. Charmonium S-state hyperfine split-ting(top) and Ds meson decay constant(bottom)in quenched QCD as a function of a set by Som-mer scale r0.a function of the meson mass. The asymmetryreaches 10 ∼ 20% around the charmed mesonmass for the CL action, while it is less than 8%for the RHQ action. These observations allow usto conclude that the improved action works asdesigned in reducing the mQa corrections.Figure 2(a) shows the charmonium S-state hy-perfine splitting as a function of lattice spacing,where we practice two analysis: one is based onthe pole mass of the charmed meson and anotheron the kinetic mass:aMkin = aMpole/c2eff .We find 15% discrepancy, which should be in-cluded as a systematic error. Compared to re-sults with anisotropic lattice QCD[6], our resultsare slightly larger at a ∼ 0.1fm. Both are sub-stantially lower than the experimental value.In Fig. 2(b) we plot the Ds meson decay con-stant which are obtained from the time and spa-tial components of the axial vector current. Thedifference between two definitions is less than 3%for both gauge actions. For comparison we alsoplot the results obtained by the CL heavy quarkaction with the plaquette gauge action[7]. Ourresults at a ∼ 0.1fm are much closer to the valueof the CL heavy quark action in the continuumlimit than at a similar lattice spacing. This would0.910 1 2MPSa0.80.910 2 4MPS [GeV]β=2.1, H-Hβ=2.1, H-Lβ=1.95, H-Hβ=1.95, H-LDs J/ΨFigure 3. Effective speed of light for the PS me-son(top) and space-time asymmetry for the PSmeson decay constant(bottom) as a function ofthe meson mass in lattice unit(left) and physicalunit(right) for Nf = 2 QCD.suggest that the RHQ action indeed improves thescaling behavior of the decay constant.4. Preliminary results of Nf = 2 QCDEncouraging results in quenched QCD urge usto apply the calculation to the two-flavor QCDgauge configurations[8]. We employ the mean-field improved CL light quark action and theRHQ action for the valence quraks. Up to nowtwo set of lattices have been analyzed: 400/200configurations for 163 × 32/243 × 48 at β =1.95/2.1 with four sea quark masses. Latticespacings are roughly 0.15fm and 0.11fm, respec-tively. We make a similar choice for the set ofvalence heavy and light quark masses as in thequenched case.In Fig. 3 we show the effective speed of lightand the space-time asymmetry for the PS me-son decay constant. As a decreases, the devi-ation from ceff = 1 and R = 1 is reduced atfixed mQa and mQ. These behavior are consis-tent with the expected leading scaling violation ofthe RHS action given by O(f2(mQa)(aΛQCD)2) orO(f1(mQa)g4aΛQCD), where f1 and f2 are someunkown functions. A little surprising is that, asseen from the left panels in Fig. 3, f1,2 look almostlinear in terms of mQa even beyond mQa = 1.Figure 4 illustrates the a dependence of the Dsmeson decay constant. While the scaling behav-ior from A4 with the RHQ action is only a little0 0.05 0.1 0.15 0.2a [fm]0.20.250.30.35f Ds [GeV]expt.RHQ+RG, A4RHQ+RG, AkFNAL+RG, A4 [9]Nf=0, CL+Plq., A4 [7]Figure 4. Ds meson decay constant for Nf = 2QCD as a function of a. The scale is set by r0 forour results and mρ for FNAL method.milder over the previous result obtained by theFNAL interpretation with the CL heavy quarkaction[9], the one from Ak is much improved.This result suggests that we will be able to make areliable continuum extrapolation, employing a si-multaneous fit for fDs obtained from A4 and Ak,once we have data on CP-PACS configurations atβ = 2.2 or 1.8.This work is supported in part by the Grants-in-Aid for Scientific Research from the Ministryof Education, Culture, Sports, Science and Tech-nology. (Nos. 13135204, 13640260, 14046202,14740173, 15204015, 15540251, 15540279,16028201, 16540228, 16740147, )REFERENCES1. S. Aoki, Y. Kuramashi and S. Tominaga,Prog. Theor. Phys. 109 (2003) 383.2. S. Aoki, Y. Kayaba and Y. Kuramashi,Nucl. Phys. B 697 (2004) 271.3. S. Aoki, Y. Kayaba and Y. Kuramashi,Nucl. Phys. B 689 (2004) 127.4. M. Lu¨scher, S. Sint, R. Sommer, P. Weisz andU. Wolf, Nucl. Phys. B 491 (1997) 323.5. CP-PACS Collaboration: S. Aoki et al., inpreparation.6. CP-PACS Collaboration: M .Okamoto et al.,Phys. Rev. D65 (2002) 094508.7. ALPHA Collaboration: A. Juttner et al.,Phys. Lett. B560 (2003) 598. CP-PACS Collaboration: A. Ali Khan et al.,Phys. Rev. D65 (2002) 0545059. CP-PACS Collaboration: A. Ali Khan et al.,Phys. Rev. D64 (2001) 034505

Charmed meson spectra and decay constants with one-loop O(a) improved relativistic heavy quark action

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Charmed meson spectra and decay constants with one-loop $O(a)$ improved
  relativistic heavy quark action

Charmed meson spectra and decay constants with one-loop $O(a)$ improved relativistic heavy quark action

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Charmed meson spectra and decay constants with one-loop O(a)O(a)O(a) improved relativistic heavy quark action

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Charmed meson spectra and decay constants with one-loop $O(a)$ improved relativistic heavy quark action