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 $\text{QTR}rm1S$ 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}$-statesofthe$\bar{b}c$system.Forthesakeofcomparison,weusethesamefittingparametersofourpreviousmodelpotentials.Fromourresultsweconcludethatshifted$l$-expansion method has the same accuracy, convergence and status as our previous work.

Comments: 33 pages, 1 figure