Strong decays of $D_3^{\ast }(2760)$, $D_{s3}^{\ast }(2860)$, $B_3^{\ast }$, and $B_{s3}^{\ast }$

Abstract

In this paper, we study the OZI-allowed two-body strong decays of $3^{-}$ heavy-light mesons. Experimentally the charmed $D_3^{\ast }(2760)$ and the charm-strange $D_{s3}^{\ast }(2860)$ states with these quantum numbers have been discovered. For the bottomed $B(5970)$ state, which was found by the CDF Collaboration recently, its quantum number has not been decided yet and we assume its a $3^{-}$ meson in this paper. The theoretical prediction for the strong decays of bottom-strange state $B_{s3}^{\ast }$ is also given. The relativistic wave functions of $3^{-}$ heavy mesons are constructed and their numerical values are obtained by solving the corresponding Bethe-Salpeter equation with instantaneous approximation. The transition matrix is calculated by using the PCAC and low energy theorem, following which, the decay widths are obtained. For $D_3^{\ast }(2760)$ and $D_{s3}^{\ast }(2860)$, the total strong decay widths are 72.6 MeV and 47.6 MeV, respectively. For $B_3^{\ast }$ with $M=5978$ MeV and $B_{s3}^{\ast }$ with $M=6178$ MeV, their strong decay widths are 22.9 MeV and 40.8 MeV, respectively.

16 pages, 4 figures