The partial waves of $B^{*}_{2}(5747)$ and their contributions in strong decays

Abstract

By adopting the relativistic Bethe-Salpeter method, the OZI allowed strong decays of the $2^+$ state $B^{*}_{2}(5747)^{0}$ are studied, emphasis is paid to the relativistic corrections. We first study the partial waves in the wave functions used, find that there are $P$, $D$ and $F$ partial waves in $B^{*}_{2}(5747)^{0}$ meson, and the ratios $P:D:F=1:0.421:0.051$. We also find $S:P:D=1:0.354:0.046$ for $B^*$, and $S:P=1:0.343$ for $B$ meson. The large components of the $D$ wave in $B^{*}_{2}(5747)^{0}$ and $P$ wave in $B^{(*)}$ means that large relativistic effects existing in these states. Second, we calculate the strong decays, the obtained total decay width $\Gamma(B^{*}_{2}(5747)^{0})=25.9$ MeV and the branching fraction $\Gamma(B^{*}_{2}(5747)^{0} \to B^{*}\pi)$ / $\Gamma(B^{*}_{2}(5747)^{0} \to B\pi)=0.96$ are consistent well with experimental data. Third, we study the contributions of different partial waves in the initial and final wave functions, find that the relativistic effects are about $15\%$ and $11\%$ for $B^{*}_{2}(5747)^{0} \to B\pi$ and $B^{*}_{2}(5747)^{0} \to B^{*}\pi$, respectively, which are much smaller than our expected, showing that the relativistic corrections are cancelled to each other in these decays.