Decay constants of charm and beauty pseudoscalar heavy-light mesons on fine lattices

We compute decay constants of heavy-light mesons in quenched lattice QCD with a lattice spacing of a ≃ 0.04 fm using non-perturbatively O(a) improved Wilson fermions and O(a) improved currents. We obtain fDs = 220(6)(5)(11) MeV, fD = 206(6)(3)(22) MeV, fBs = 205(7)(26)(17) MeV and fB = 190(8)(23)(25) MeV, using the Sommer parameter r0 = 0.5 fm to set the scale. The first error is statistical, the second systematic and the third from assuming a ±10% uncertainty in the experimental value of r0. A detailed discussion is given in the text. We also present results for the meson decay constants fK and fπ and the ρ meson mass. PACS: 12.38.Gc, 13.20.Fc, 13.20.He 1. Weak decays of heavy-light mesons with c and b quarks are interesting for studies of CP violation and determination of the CKM mixing angles. New experimental data on such decays are emerging (e.g. [1–4]) and their interpretation requires knowledge of hadronic matrix elements governed by the strong interaction. Lattice QCD allows one to calculate the strong matrix elements from first principles. However, if the heavy quark mass mQ is of the order of the inverse lattice spacing a, considerable discretization effects proportional to powers of amQ occur. One possibility for coping with this problem is to use an effective theory such as Heavy Quark Effective Theory (HQET) [5] or Nonrelativistic QCD (NRQCD) [6]. These formalisms start from an infinitely heavy quark and consider corrections to this limit in the form of an expansion in the inverse of mQ. However, to study the charm quark in HQET or NRQCD requires a considerable number of correction terms, and one still has to worry about the uncertainty from the truncation of the 1/mQ expansion. A formulation for relativistic quarks where masses can be of O(1) in lattice units is the Fermilab approach [7] and modifications thereof, developed in [8, 9] and [10]. One expects that the dominating discretization effects are then proportional to powers of momenta of O(ΛQCD). While within HQET non-perturbative renormalization is possible [11], in many of the calculations using effective theories the renormalization constants are calculated only in perturbation theory (e.g. in Ref. [12]), leading to further uncertainties. Another possibility is to simulate on very fine lattices, and this is the approach we have adopted in the present paper. We have performed a quenched lattice study of heavy mesons with a lattice spacing a of about 0.04 fm. On such a fine lattice a relativistic treatment of the charm quark should be justified and we expect that discretization errors are small compared to previous calculations on coarser lattices. We also make an attempt to study B mesons in our relativistic framework. Even on our fine lattice we cannot simulate B mesons directly, but the required extrapolation becomes relatively short-range. We expect that the resulting uncertainty is not much larger than the systematic error caused by the use of an effective theory. For example, recent unquenched calculations of fB and fBs [12,13] employ NRQCD for the b quark and quote a ∼ 10% error based on perturbation theory and other systematic effects. In this article we present results for the leptonic decay constants of the Ds, Bs, D and B mesons. We also evaluate light meson masses and decay constants to compare with previous quenched calculations of the light spectrum on coarser lattices and in order to be able to disentangle discretization and quenching effects. 2. Our results are based on the analysis of 114 quenched Wilson gauge configurations simulated at the coupling parameter β = 6.6 with a mixed heatbath and microcanonical overrelaxation algorithm using the publicly available MILC code [14]. The lattice volume is 40 × 80, i.e. our lattice extends over 40 points (∼ 1.59 fm) in space and 80 points in time. The lattice spacing is determined using the Sommer parameter r0 = 0.5 fm. This choice is motivated by a previous calculation [15] which used r0 to determine the lattice spacings and found that the results for fDs from a quenched lattice and a lattice with Nf = 2 agreed (a ≈ 0.1 fm in these calculations). From the interpolating formula given in [16], one finds for our lattice a = 4.97 GeV. For the quarks we use the O(a) improved clover formulation [17], with the nonperturbative value of the clover coefficient cSW = 1.467 determined in Ref. [18]. We work with seven quark masses corresponding to three “light” hopping parameters κ = 0.13519, 0.13498, 0.13472 and