Eur. Phys. J. C (2022) 82: 737
https://doi.org/10.1140/epjc/s10052-022-10677-3

Regular Article - Theoretical Physics

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

¹ Department of Physics and Technology, Hebei University, 071002, Baoding, China
² Key Laboratory of High-Precision Computation and Application of Quantum Field Theory of Hebei Province, Baoding, China

^e wgl@hbu.edu.cn

Received: 26 July 2022
Accepted: 3 August 2022
Published online: 23 August 2022

Abstract

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 $B^{\ast }$, 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 $\mathrm{\Gamma }(B_2^{\ast }{(5747)}^0)=25.9$ MeV and the branching fraction $\mathrm{\Gamma }(B_2^{\ast }{(5747)}^0\to B^{\ast }\pi )$ / $\mathrm{\Gamma }(B_2^{\ast }{(5747)}^0\to B\pi )=0.96$ 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 $B_2^{\ast }{(5747)}^0\to B\pi$ and $B_2^{\ast }{(5747)}^0\to B^{\ast }\pi$, respectively, which are much smaller than our expected effects, showing that the relativistic corrections cancel each other in these decays.