The 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 constrains, 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 besides there are large potentials for the observations of the low-lying $B_c$ states below the $DB$ threshold via their radiative transitions, 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 $DB$, $D{B}^{\ast }$ or $D^{\ast }B$ at the LHC for their relatively narrow widths.

Comments: 19 pages, 15 tables