The partial waves of $B_2^{\ast }(5747)$ and their contributions in strong decays

By adopting the relativistic Bethe-Salpeter method, the OZI allowed strong decays of the $2^{+}$ state $B_2^{\ast }(5747{)}^0$ 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 $B_2^{\ast }(5747{)}^0$ meson, and the ratios $P:D:F=1:0.421:0.051$. We also find $S:P:D=1:0.354:0.046$ for $B^{\ast }$, and $S:P=1:0.343$ for $B$ meson. The large components of the $D$ wave in $B_2^{\ast }(5747{)}^0$ and $P$ wave in $B^{(\ast )}$ means that large relativistic effects existing in these states. Second, we calculate the strong decays, the obtained total decay width $\mathrm{\Gamma }(B_2^{\ast }(5747{)}^0)=25.9$ MeV and the branching fraction $\mathrm{\Gamma }(B_2^{\ast }(5747{)}^0\to B^{\ast }\pi )$ / $\mathrm{\Gamma }(B_2^{\ast }(5747{)}^0\to B\pi )=0.96$ 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 $15\mathrm{\%}$ and $11\mathrm{\%}$ for $B_2^{\ast }(5747{)}^0\to B\pi$ and $B_2^{\ast }(5747{)}^0\to B^{\ast }\pi$, respectively, which are much smaller than our expected, showing that the relativistic corrections are cancelled to each other in these decays.