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Charm and Strange Quark Masses and Fds from Overlap Fermions Yi-Bo Yang University of Kentucky

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Charm and Strange Quark Masses and Fds from Overlap Fermions Yi-Bo Yang University of Kentucky University of Kentucky UKnowledge Physics and Astronomy Faculty Publications Physics and Astronomy 8-1-2015 Charm and Strange Quark Masses and fDs from Overlap Fermions Yi-Bo Yang University of Kentucky Ying Chen Chinese Academy of Sciences, China Andrei Alexandru George Washington University Shao-Jing Dong University of Kentucky, [email protected] Terrence Draper University of Kentucky, [email protected] See next page for additional authors Right click to open a feedback form in a new tab to let us know how this document benefits oy u. Follow this and additional works at: https://uknowledge.uky.edu/physastron_facpub Part of the Astrophysics and Astronomy Commons, and the Physics Commons Repository Citation Yang, Yi-Bo; Chen, Ying; Alexandru, Andrei; Dong, Shao-Jing; Draper, Terrence; Gong, Ming; Lee, Frank X.; Li, Anyi; Liu, Keh-Fei; Liu, Zhaofeng; and Lujan, Michael, "Charm and Strange Quark Masses and fDs from Overlap Fermions" (2015). Physics and Astronomy Faculty Publications. 390. https://uknowledge.uky.edu/physastron_facpub/390 This Article is brought to you for free and open access by the Physics and Astronomy at UKnowledge. It has been accepted for inclusion in Physics and Astronomy Faculty Publications by an authorized administrator of UKnowledge. For more information, please contact [email protected]. Authors Yi-Bo Yang, Ying Chen, Andrei Alexandru, Shao-Jing Dong, Terrence Draper, Ming Gong, Frank X. Lee, Anyi Li, Keh-Fei Liu, Zhaofeng Liu, and Michael Lujan Charm and Strange Quark Masses and fDs from Overlap Fermions Notes/Citation Information Published in Physical Review D, v. 92, no. 3, article 034517, p. 1-19. © 2015 American Physical Society The opc yright holders have granted the permission for posting the article here. Digital Object Identifier (DOI) https://doi.org/10.1103/PhysRevD.92.034517 This article is available at UKnowledge: https://uknowledge.uky.edu/physastron_facpub/390 PHYSICAL REVIEW D 92, 034517 (2015) f Charm and strange quark masses and Ds from overlap fermions Yi-Bo Yang,1,2 Ying Chen,1 Andrei Alexandru,3 Shao-Jing Dong,2 Terrence Draper,2 Ming Gong,1,2 Frank X. Lee,3 Anyi Li,4 Keh-Fei Liu,2 Zhaofeng Liu,1 and Michael Lujan3 1Institute of High Energy Physics and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049, China 2Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA 3Department of Physics, The George Washington University, Washington, DC 20052, USA 4Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195, USA (Received 20 October 2014; published 26 August 2015) We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the 2 þ 1-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates Oða2Þ and 4 4 Oðmca Þ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses à of Ds, Ds and J=ψ as inputs, Sommer’s scale parameter r0 and the masses of charm quark and strange MS quark in the MS scheme are determined to be r0 ¼ 0.465ð4Þð9Þ fm, mc ð2 GeVÞ¼1.118ð6Þð24Þ GeV MS MS (or mc ðmcÞ¼1.304ð5Þð20Þ GeV), and ms ð2 GeVÞ¼0.101ð3Þð6Þ GeV, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine − splitting of charmonium, MJ=ψ Mηc , is determined to be 119(2)(7) MeV, which is in good agreement with 254 2 4 the experimental value. We also predict the decay constant of Ds to be fDs ¼ ð Þð Þ MeV. The masses of charmonium P-wave states χc0, χc1 and hc are also in good agreement with experiments. DOI: 10.1103/PhysRevD.92.034517 PACS numbers: 11.15.Ha, 12.38.Aw, 12.38.Gc, 14.40.Pq I. INTRODUCTION setup is a mixed action formalism where we use the overlap fermions as valence quarks and carry out the calculation on A large endeavor has been devoted by lattice QCD to the domain-wall gauge configurations generated by the determine the quark masses which are of great importance for precision tests of the standard model of particle physics RBC and UKQCD Collaborations. Both the domain-wall [1–14]. In the lattice QCD formulation, quark masses are fermion (DWF) and the overlap fermion are chiral fer- dimensionless bare parameters and their renormalized mions; as such, they do not have OðaÞ errors for the valence values at a certain scale should be determined through quark masses, and the additive renormalization for them is 10−9 physical inputs. For the light u; d quarks and the strange also negligible ( ) due to the overlap fermion imple- quark, their masses are usually set by the physical pion and mentation. It is also shown that the nonperturbative renormalization via chiral Ward identities or the regulari- kaon masses as well as the decay constants fπ and fK, where the chiral extrapolation is carried out through chiral zation independent/momentum subtraction (RI/MOM) perturbation theory [1,3,4]. For heavy quarks, the bare quark scheme can be implemented relatively easily. We have masses are first set in the vicinity of the physical region and explored this strategy and found that it is feasible for the physical point can be interpolated or extrapolated valence masses reaching even the charm quark region on through the quark mass dependence observed empirically the set of DWF configurations that we work on. from the simulation. In the above procedures, nonperturba- The RBC and UKQCD Collaborations have simulated tive quark mass renormalization is usually required to match 2 þ 1 flavor full QCD with dynamical domain-wall fer- the bare quark mass to the renormalized one at a fixed scale. mion (DWF) on several lattices in the last decade with pion For the heavy quark, the HPQCD collaboration [6] proposed masses as low as ∼300 MeV and volumes large enough for a promising scheme to obtain their masses from current- mesons (mπL>4) [3,10,12]. It turns out that the fermions current correlators of heavy quarkonium, which is free of the in this formalism with a finite fifth dimension Ls satisfy the quark mass renormalization [8]. Ginsparg-Wilson relation reasonably well and the chiral In this work we propose a global-fit strategy to determine symmetry breaking effects can be absorbed in the small the strange and charm quark masses which incorporates residual masses. As for the overlap fermion, its multimass simultaneously the Oða2Þ correction, the chiral extrapola- algorithm permits calculation of multiple quark propaga- tion, and the strange/charm quark interpolation. The lattice tors covering the range from very light quarks to the charm 1550-7998=2015=92(3)=034517(19) 034517-1 © 2015 American Physical Society YI-BO YANG et al. PHYSICAL REVIEW D 92, 034517 (2015) quark. This makes it possible to study the properties of results on quark masses and fDs are given in Sec. III, where charmonium and charmed mesons using the same fermion a thorough discussion of the statistical and systematic formulation for the charm and light quarks. Having errors is also presented. The summary and the conclusions multiple masses helps in determining the functional forms are presented in Sec. IV. for the quark mass dependence of the observables. In practice, we calculate the masses of charmonia and charm- II. NUMERICAL DETAILS strange mesons with the charm and strange quark mass 2 1 varying in a range, through which a clear observation of the Our calculation is carried out on the þ flavor domain valence quark mass dependence of meson masses can be wall fermion configurations generated by the RBC/ obtained. Similar calculations are carried out on six UKQCD Collaborations [17]. We use two lattice setups, 3 243 64 β 2 13 configuration ensembles and the results are treated as a namely, the L × T ¼ × lattice at ¼ . and the 323 64 β 2 25 β 2 13 total data set for the global fit as mentioned above. It should × lattice with ¼ . For the ¼ . lattice, the ðsÞ be noted that the quark masses in the global fit are matched mass parameter of the strange sea quark is set to ms a ¼ to the renormalized quark masses at 2 GeV in the minimal- 0.04 and that of the degenerate u=d sea quark takes the subtraction scheme (MS scheme) by the quark mass ðsÞ 0 005 0 01 values of ml a ¼ . ; . , and 0.02, which give three renormalization constant Zm calculated in Ref. [15].In different gauge ensembles. However, it is found that the order to convert the quantities on the lattice to the values in ðsÞ physical strange quark mass parameter is actually ms a ¼ physical units, we take the following prescription. First, the 0.0348 [17] as determined by the physical Ω baryon mass, ratio of the Sommer scale parameter r0 to the lattice spacing this discrepancy has been corrected by the corresponding a, namely r0=a, is measured precisely from each gauge ðsÞ reweighting factors. Similarly, the ms a of the β ¼ 2.25 ensemble. Subsequently, r0=a’s in the chiral limit are used to replace the explicit finite-a dependence. Instead of lattice is set to 0.03 in generating the three gauge ensembles ðsÞ determining the exact value of r0 by a specific physical with ml a taking values 0.004, 0.006, and 0.008, but the ðsÞ quantity, we treat it as an unknown parameter and deter- physical ms a for β ¼ 2.25 is found to be 0.0273 [17].
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