The Strong Decays of Orbitally Excited $B^{*}_{sJ}$ Mesons by Improved Bethe-Salpeter Method

Abstract

We calculate the masses and the strong decays of orbitally excited states $B_{s0}$, $B'_{s1}$, $B_{s1}$ and $B_{s2}$ by the improved Bethe-Salpeter method. The predicted masses of $B_{s0}$ and $B'_{s1}$ are $M_{B_{s0}}=5.723\pm0.280 {\rm GeV}$, $M_{B'_{s1}}=5.774\pm0.330 {\rm GeV}$. We calculate the isospin symmetry violating decay processes $B_{s0}\to B_s \pi$ and $B'_{s1}\to B_s^* \pi$ through $\pi^0-\eta$ mixing and get small widths. Considering the uncertainties of the masses, for $B_{s0}$ and $B'_{s1}$, we also calculate the OZI allowed decay channels: $B_{s0}\to B\bar K$ and $B'_{s1}\to B^*\bar K$. For $B_{s1}$ and $B_{s2}$, the OZI allowed decay channels $B_{s1}\to B^{*}\bar K$, $B_{s2}\to B\bar K$ and $B_{s2}\to B^{*}\bar K$ are studied. In all the decay channels, the reduction formula, PCAC relation and low energy theorem are used to estimate the decay widths. We also obtain the strong coupling constants $G_{B_{s0}B_s\pi}$, $G_{B_{s0}B\bar K}$, $G_{B'_{s1}B_s^*\pi}$, $F_{B'_{s1}B_s^*\pi}$, $G_{B'_{s1}B^*\bar K}$, $F_{B'_{s1}B^*\bar K}$, $G_{B_{s1}B^{*}\bar K}$, $F_{B_{s1}B^{*}\bar K}$, $G_{B_{s2}B\bar K}$ and $G_{B_{s2}B^{*}\bar K}$.