We give a review and present a comprehensive calculation for the leptonic constant fBc of the low-lying pseudoscalar and vector states of Bc-meson in the framework of static and QCD-motivated nonrelativistic potential models taking into account the one-loop and two-loop QCD corrections in the short distance coefficient that governs the leptonic constant of Bc quarkonium system. Further, we use the scaling relation to predict the leptonic constant of the nS-states of the system. Our results are compared with other models to gauge the reliability of the predictions and point out differences.
We present bound state masses of the self-conjugate and non-self-conjugate mesons in the context of the Schrödinger equation taking into account the relativistic kinematics and the quark spins. We apply the usual interaction by adding the spin dependent correction. The hyperfine splittings for the 2S charmonium and 1S bottomonium are calculated. The pseudoscalar and vector decay constants of the Bc meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar-β+κrβ+V0, with β = 1, 1/2, 3/4 which can also be decomposed into scalar and vector parts in the form VV(r) = -Ar-β+(1-ɛ)κrβ and VS(r) = ɛκrβ+V0 where 0≤ɛ≤1. The energy eigenvalues are carried out up to the third order approximation using the shifted large-N-expansion technique.
In the framework of potential models for heavy quarkonium, we compute the mass spectrum of the bottom-charmed Bc meson system and spin-dependent splittings from the Schrödinger equation using the shifted-large-N expansion technique. The masses of the lightest vector Bc* and pseudoscalar Bc states as well as the higher states below the threshold are estimated. Our predicted result for the ground state energy is 6253-6+15 MeV and are generally in exact agreement with earlier calculations. Calculations of the Schrödinger energy eigenvalues are carried out up to the third order of the energy series. The parameters of each potential are adjusted to obtain best agreement with the experimental spin-averaged data (SAD). Our findings are compared with the observed data and with the numerical results obtained by other numerical methods.