The partial waves of B${}_2^{\ast }$(5747) and their contributions in strong decays

The relativistic Bethe-Salpeter method is adopted to study the OZI-allowed strong decays of the 2${}^{+}$ state B${}_2^{\ast }$(5747)${}^0$, with emphasis on the relativistic corrections. We first study the partial waves in the wave functions used and find that there are P, D, and F partial waves in the B${}_2^{\ast }$(5747)${}^0$ meson, with ratios of P/D/F = 1 : 0.421 : 0.051. We also find that S/P/D = 1 : 0.354 : 0.046 for B*, and S/P=1:0.343 for the B meson. The large components of the D wave in B${}_2^{\ast }$(5747)${}^0$ and the P wave in B${}^{(\ast )}$ mean that large relativistic effects exist in these states. Second, we calculate the strong decays, and the total decay width Γ(B${}_2^{\ast }$(5747)${}^0$) = 25.9 MeV and the branching fraction Γ(B${}_2^{\ast }$(5747)${}^0$ → B*π) / Γ(B${}_2^{\ast }$(5747)${}^0$ → Bπ) = 0.96 obtained are consistent with experimental data. Third, we study the contributions of different partial waves in the initial and final wave functions, and find that the relativistic effects are about 15% and 11% for B${}_2^{\ast }$(5747)${}^0$ → Bπ and B${}_2^{\ast }$(5747)${}^0$ → B*π, respectively, which are much smaller than our expected effects, showing that the relativistic corrections cancel each other in these decays.