Relativistic treatment of the decay constants of light and heavy mesons

Abstract

Novel relativistic expressions are used to calculate the weak decay constants of pseudoscalar and vector mesons within the constituent quark model. Meson wave functions satisfy the quasipotential equation with the complete relativistic potential. New contributions, coming from the negative-energy quark states, are substantial for the light mesons, significantly decrease the values of their decay constants and, thus, bring them into agreement with experiment. For heavy-light mesons these contribution are much less pronounced, but permit to reduce uncertainties of the predicted decay constants. Their values agree with the results of lattice calculations and experimental data. 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]. Recently, a relatively precise experimental value for the D meson decay constant was presented by the CLEO Collaboration [18]. Therefore it is actual to reconsider the meson decay constants treating quarks, composing the meson, in a consistently relativistic way. Such procedure was formulated and successfully applied for light mesons in the papers [19]. In this letter we evaluate new contributions to relativistic expressions for the meson decay constants coming from the negative-energy quark states both for light and heavy-light mesons. We use the meson wave functions satisfying the quasipotential equation with the complete relativistic potential in order to obtain new, more accurate predictions for the meson decay constants.In the quasipotential approach a meson is described by the wave function of the bound quark-antiquark state [20], which satisfies the quasipotential equation of the Schrödinger

Charmless weakBsdecays in the relativistic quark model

“…The pseudoscalar f P and vector f V decay constants of light and heavy mesons were calculated within our model in Ref. [37]. Their values are in agreement with the available experimental data [2].…”

Analysis of the masses and decay constants of the heavy-light mesons with QCD sum rules

“…In Table 4, we compare the present predictions for the decay constants of the heavy vector mesons to other theoretical calculations, such as the QCD sum rules [7,24,25,32], lattice QCD [33][34][35][36], the relativistic potential model (RPM) [41], the field-correlator method (FCM) [44], and the lightfront quark model [47]. From the table, we can see that the predictions differ from each other in one way or the other.…”

“…There has been much theoretical work on the decay constants of the heavy-light mesons, such as the QCD sum rules [2][3][4][5][6][7], the lattice QCD [8][9][10][11][33][34][35][36][37][38], the BetheSalpeter equation [39,40], the relativistic potential model [41][42][43], the field-correlator method [44], the light-front quark model [45][46][47], the chiral extrapolation [48], the extended chiral-quark model [49,50], the constituent quark model [51], etc.…”

Heavy hadron spectroscopy and the bag model

“…In Tables 4 and 5 we compare our predictions for the masses of heavy mesons with the calculations in four different variants of the potential model. We have chosen for this the relativized quark model [16], the model based on the Bethe-Salpeter equation [49], the relativistic treatment using quasipotential approach [50,51], and one specific variant of nonrelativistic potential model [34] where the Goldstone-boson exchanges are considered together with the one-gluon-exchange. The experimental values are from the Particle Data Tables [42] with the exeption of the η b meson.…”