Strong decays of $2^+$ charm and charm-strange mesons

TL;DR

This paper calculates the strong decay widths and branching ratios of specific 2+ charm and charm-strange mesons using a Bethe-Salpeter approach, providing theoretical estimates consistent with experimental data.

Contribution

It introduces a method combining the reduction formula, PCAC, and Bethe-Salpeter wave functions to compute decay properties of heavy-light mesons.

Findings

Decay width of D*_2(2460)^0 is 51.3 MeV.

Decay width of D*_{s2}(2573)^+ is 19.6 MeV.

Branching ratio of D*_2(2460)^0 to D+π− over D*+π− is 2.13.

Abstract

In this paper, we calculate the strong decays of $2^+$ heavy-light states, namely, the charmed $D^*_2(2460)^0$ meson and the charm-strange $D^*_{s2}(2573)^+$ meson. The method we adopt is the reduction formula, PCAC relation and low energy theorem, following which, the transition amplitudes are calculated. The wave functions of the heavy mesons involved are achieved by solving the instantaneous Bethe-Salpeter equation. As the OZI-allowed two-body strong decays give the dominant contribution, they can be used to estimate to total widths of mesons. Our results are: $\Gamma[D^*_2(2460)^0]=51.3$ MeV and $\Gamma[D^*_{s2}(2573)^+]=19.6$ MeV. The ratios of branching ratios of two main channels are $Br[D^*_2(2460)^0\rightarrow D^+\pi^-]/Br[D^*_2(2460)^0\rightarrow D^{\ast+}\pi^-]=2.13$ and $Br[D^*_{s2}(2573)^+\rightarrow D^{\ast 0} K^+]/Br[D^*_{s2}(2573)^+\rightarrow D^0K^+]=0.08$, respectively.