Mesonic decay constants in lattice NRQCD

Abstract

Lattice NRQCD with leading finite lattice spacing errors removed is used to calculate decay constants of mesons made up of heavy quarks. Quenched simulations are done with a tadpole improved gauge action containing plaquette and six-link rectangular terms. The tadpole factor is estimated using the Landau link. For each of the three values of the coupling constant considered, quarkonia are calculated for five masses spanning the range from charmonium through bottomonium, and one set of quark masses is tuned to the B c . "Perturbative" and nonperturbative meson masses are compared. One-loop perturbative matching of lattice NRQCD with continuum QCD for the heavy-heavy vector and axial vector currents is performed. The data are consistent with af V ∝ √ M V a and f Bc = 420(13) MeV. PACS number(s): 12.38

Properties of heavy quarkonia andBcmesons in the relativistic quark model

“…We see that inclusion of relativistic corrections reduces the pseudoscalar decay constant f Bc by 20% and produces the difference between vector and pseudoscalar decay constants of approximately 70 MeV. The calculated values of these decay constants are consistent with lattice [40] and QCD sum rule [34] predictions. To determine the rates of radiative decays (B → A + γ) it is necessary to calculate the matrix element of the electromagnetic current J µ between the initial (B) and final (A) meson states.…”

“…For the hindered transitions, which are strongly suppressed in the nonrelativistic limit due to orthogonality of the initial and final state wave functions, relativistic effects are decisive. Thus for their calculations we use unexpanded expressions (39) and (40). In Tables V-VII we present the photon energy ω, the decay rates calculated discarding all relativistic corrections Γ NR , as well as using relativistic expressions for purely vector Γ V , for purely scalar Γ S and for the mixture (9) of vector and scalar potentials Γ with ε = −1.…”

“…They are compared with the ones calculated using the nonrelativistic expression (30) and other predictions of the nonrelativistic quark models [33,35], QCD sum rules [34] and lattice NRQCD [40]. We see that inclusion of relativistic corrections reduces the pseudoscalar decay constant f Bc by 20% and produces the difference between vector and pseudoscalar decay constants of approximately 70 MeV.…”

“…(39), (40) in inverse powers of the heavy quark mass m Q up to the second order corrections to the leading contribution and get (a) for the purely vector potential (ε = 0)…”

“…(39), (40) result from the wave function transformation (35) from the moving reference frame to the rest one. It is easy to see that in the limit p/m → 0 the usual nonrelativistic expression for the magnetic moment follows.…”