Production of $D_{s0}(2590)^+$ in $B$ nonleptonic decays

Abstract

In 2021, a new charm-strange meson, $D_{s0}(2590)^+$, has been discovered, it is believed to be the $D_s^+(2^1S_0)$. However, its low mass and wide width are challenged by theoretical results. Given the small branching ratio of the current production channel, resulting in a small number of events and large errors. We suggest to search for the $D_{s0}(2590)^+$ in the $B$ meson nonleptonic decays, $B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+$ ($q=u,d$), followed by $D_{s0}(2590)^+\to D^*K$. We find $Br(B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+)\times Br(D_{s0}(2590)^+\to D^{*}K)=(2.16\sim2.82)\times 10^{-3}$ is very large, and the result is not sensitive to the mass of $D_{s0}(2590)^+$. Due to large branching ratio, large amount of $D_{s0}(2590)^+$ events are expected. This study is based on the framework of instantaneous Bethe-Salpeter equation, and the used relativistic wave functions for mesons contain different partial waves. The contributions of different partial waves are also studied.