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

Abstract

Abstract The relativistic Bethe–Salpeter method is adopted to study the OZI-allowed strong decays of the $$2^+$$ 2 + state $$B^{*}_{2}(5747)^{0}$$ B 2 ∗ ( 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 $$B^{*}_{2}(5747)^{0}$$ B 2 ∗ ( 5747 ) 0 meson, with ratios of $$P/D/F=1:0.421:0.051$$ P / D / F = 1 : 0.421 : 0.051 . We also find that $$S/P/D=1:0.354:0.046$$ S / P / D = 1 : 0.354 : 0.046 for $$B^*$$ B ∗ , and $$S/P=1:0.343$$ S / P = 1 : 0.343 for the B meson. The large components of the D wave in $$B^{*}_{2}(5747)^{0}$$ B 2 ∗ ( 5747 ) 0 and the P wave in $$B^{(*)}$$ B ( ∗ ) mean that large relativistic effects exist in these states. Second, we calculate the strong decays, and the total decay width $$\Gamma (B^{*}_{2}(5747)^{0})=25.9$$ Γ ( B 2 ∗ ( 5747 ) 0 ) = 25.9 MeV and the branching fraction $$\Gamma (B^{*}_{2}(5747)^{0} \rightarrow B^{*}\pi )$$ Γ ( B 2 ∗ ( 5747 ) 0 → B ∗ π ) / $$\Gamma (B^{*}_{2}(5747)^{0} \rightarrow B\pi )=0.96$$ Γ ( B 2 ∗ ( 5747 ) 0 → B π ) = 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 $$15\%$$ 15 % and $$11\%$$ 11 % for $$B^{*}_{2}(5747)^{0} \rightarrow B\pi $$ B 2 ∗ ( 5747 ) 0 → B π and $$B^{*}_{2}(5747)^{0} \rightarrow B^{*}\pi $$ B 2 ∗ ( 5747 ) 0 → B ∗ π , respectively, which are much smaller than our expected effects, showing that the relativistic corrections cancel each other in these decays.