Decay Constants of Heavy–light Mesons in the Relativistic Quark Model

Abstract

The decay constants of pseudoscalar and vector heavy-light mesons are calculated in the framework of the relativistic quark model with the completely relativistic treatment of the light quark. It is argued that relativistic effects play a significant role. Good agreement of the model predictions with recent lattice and QCD sum rule calculations as well as available experimental data is found.The pseudoscalar and vector decay constants of the heavy-light mesons are important hadronic characteristics of these mesons. They determine such quantities as the weak decay rates of mesons to lepton pairs and the magnitude of B d −B d and B s −B s mixings. These constants also enter the nonleptonic decay rates, considered in the factorization approximation. In this brief note we consider them in the framework of the relativistic quark model.The decay constants f P and f V of the pseudoscalar (P ) and vector (V ) mesons parameterize the matrix elements of the weak current between the corresponding meson and the vacuum. In the case of a meson, composed from a heavy antiquark Q and a light quark q, they are defined by1

Properties of heavy quarkonia andBcmesons in the relativistic quark model

“…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.…”

“…In the relativistic quark model the decay constants can be expressed through the meson wave function Φ P,V (p) in the momentum space and are given by [39] f P,V = 12…”

“…(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)…”

Relativistic treatment of the decay constants of light and heavy mesons

“…The weak decay constants of pseudoscalar and vector mesons belong to their most important characteristics, which enter in various decay rates. Many efforts were undertaken to calculate these constants within lattice QCD (both quenched and unquenched) [1,2,3,4,5,6], QCD sum rules [7,8,9], and constituent quark models [10,11,12,13,14,15,16]. At present, the decay constants of light mesons are measured with high precision, while in the heavy-light meson sector only D and D s meson decay constants are available with rather large errors [17].…”

“…(14). In the literature [10,14] usually only the first term is taken into account, since it provides the nonrelativistic limit, while other terms give only relativistic corrections and thus vanish in this limit. Such approximation can be justified for mesons containing only heavy quarks.…”