Finding $B_c(3S)$ States via Their Strong Decays

Abstract

The experimentally known $B_c$ states are all below open bottom-charm threshold, which experience three main decay modes, and all induced by weak interaction. In this work, we investigate the mass spectrum and strong decays of the $B_c(3S)$ states, which just above the threshold, in the Bethe-Salpeter formalism and ${}^3{P}_0$ model. The numerical estimation gives $M(B_c(3^1{S}_0))=7273\mathrm{MeV}$, $M(B_c^{\ast }(3^3{S}_1))=7304\mathrm{MeV}$, $\hat{I}“\left(B_c(3^1{S}_0)\to B^{\ast }D\right)=26.02_{-2.21}^{+2.33}\mathrm{MeV}$, $\hat{I}“\left(B_c^{\ast }(3^3{S}_1)\to BD\right)=3.39_{-0.26}^{+0.27}\mathrm{MeV}$, $\hat{I}“\left(B_c^{\ast }(3^3{S}_1)\to B^{\ast }D\right)=14.77_{-1.33}^{+1.40}\mathrm{MeV}$ and $\hat{I}“\left(B_c^{\ast }(3^3{S}_1)\to B{D}^{\ast }\right)=6.14_{-0.54}^{+0.58}\mathrm{MeV}$. Compared with previous studies in non-relativistic approximation, our results indicate that the relativistic effects are notable in $B_c(3S)$ exclusive strong decays. According to the results, we suggest to find the $B_c(3S)$ states in their hadronic decays to $B$ and $D$ mesons in experiment, like the LHCb.

10 pages, 1 figure, to appear in PLB