Strong decays of $D_{3}^{\ast}(2760)$, $D_{s3}^{\ast}(2860)$, $B_{3}^{\ast}$, and $B_{s3}^{\ast}$

TL;DR

This paper investigates the strong decay properties of various 3^- heavy-light mesons, providing theoretical decay width predictions for experimentally observed and hypothesized states using relativistic wave functions and decay models.

Contribution

The study constructs relativistic wave functions for 3^- heavy mesons and predicts their strong decay widths, including for recently observed and hypothesized states, using Bethe-Salpeter equations and decay models.

Findings

Decay widths for $D_{3}^ ext{*}(2760)$ and $D_{s3}^ ext{*}(2860)$ are 72.6 MeV and 47.6 MeV.

Predicted decay widths for $B_3^ ext{*}$ and $B_{s3}^ ext{*}$ are 22.9 MeV and 40.8 MeV.

Theoretical framework successfully describes decay properties of 3^- heavy-light mesons.

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.