The Strong Decays of Orbitally Excited $B_{sJ}^{\ast }$ Mesons by Improved Bethe-Salpeter Method

Abstract

We calculate the masses and the strong decays of orbitally excited states $B_{s0}$, $B_{s1}^{\prime }$, $B_{s1}$ and $B_{s2}$ by the improved Bethe-Salpeter method. The predicted masses of $B_{s0}$ and $B_{s1}^{\prime }$ are $M_{B_{s0}}=5.723\pm 0.280\mathrm{GeV}$, $M_{B_{s1}^{\prime }}=5.774\pm 0.330\mathrm{GeV}$. We calculate the isospin symmetry violating decay processes $B_{s0}\to B_s\pi$ and $B_{s1}^{\prime }\to B_s^{\ast }\pi$ through ${\pi }^0-\eta$ mixing and get small widths. Considering the uncertainties of the masses, for $B_{s0}$ and $B_{s1}^{\prime }$, we also calculate the OZI allowed decay channels: $B_{s0}\to B\bar{K}$ and $B_{s1}^{\prime }\to B^{\ast }\bar{K}$. For $B_{s1}$ and $B_{s2}$, the OZI allowed decay channels $B_{s1}\to B^{\ast }\bar{K}$, $B_{s2}\to B\bar{K}$ and $B_{s2}\to B^{\ast }\bar{K}$ 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 $G_{B_{s0}{B}_s\pi }$, $G_{B_{s0}B\bar{K}}$, $G_{B_{s1}^{\prime }{B}_s^{\ast }\pi }$, $F_{B_{s1}^{\prime }{B}_s^{\ast }\pi }$, $G_{B_{s1}^{\prime }{B}^{\ast }\bar{K}}$, $F_{B_{s1}^{\prime }{B}^{\ast }\bar{K}}$, $G_{B_{s1}{B}^{\ast }\bar{K}}$, $F_{B_{s1}{B}^{\ast }\bar{K}}$, $G_{B_{s2}B\bar{K}}$ and $G_{B_{s2}{B}^{\ast }\bar{K}}$.

21 pages, 1 figure, 4 tables

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• Decay properties of $D_{s0}^{\ast }(2317{)}^{+}$ as a conventional $c\bar{s}$ meson