Theoretical Status of the $B_{c}$ Meson in the Shifted l-Expansion Technique

Abstract

In the framework of phenomenological static and QCD-motivated model potentials for heavy quarkonium, we compute the $\bar{b}c$ mass spectrum as well as its $\QTR{rm}{1S}$ hyperfine splitting using the recently introduced shifted $l$- expansion technique. We also predict the leptonic constant \ $f_{B_{c}}$ of the lightest pseudoscalar $B_{c}$ and $f_{B_{c}^{\ast}}$ of the vector $B_{c}^{\ast}$ states taking into account the one-loop and two-loop QCD corrections. Further, we use the scaling relation to predict the leptonic constant of the R{rm}{nS}$-states of the $\bar{b}c$ system. For the sake of comparison, we use the same fitting parameters of our previous model potentials. From our results we conclude that shifted $l$-expansion method has the same accuracy, convergence and status as our previous work.