Excited bottom-charmed mesons in a nonrelativistic quark model

Abstract

Using the newly measured masses of ${B}_{c}(1S)$ and ${B}_{c}(2S)$ from the CMS Collaboration and the $1S$ hyperfine splitting determined from the lattice QCD as constraints, we calculate the ${B}_{c}$ mass spectrum up to the $6S$ multiplet with a nonrelativistic linear potential model. Furthermore, using the wave functions from this model we calculate the radiative transitions between the ${B}_{c}$ states within a constituent quark model. For the higher mass ${B}_{c}$ states lying above $DB$ threshold, we also evaluate the Okubo-Zweig-Iizuka (OZI) allowed two-body strong decays with the $^{3}{P}_{0}$ model. Our study indicates that there is large potential for the observations of the low-lying ${B}_{c}$ states below the $DB$ threshold via their radiative transitions; in addition, some higher mass ${B}_{c}$ states, such as ${B}_{c}({2}^{3}{P}_{2})$, ${B}_{c}(2^{3}{D}_{1})$, ${B}_{c}({3}^{3}{D}_{1})$, ${B}_{c}(4^{3}{P}_{0})$, and the $1F$-wave ${B}_{c}$ states, might be first observed in their dominant strong decay channels $DB$, $D{B}^{*}$, or ${D}^{*}B$ at the LHC for their relatively narrow widths.