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 $D_s^{+}(2^1{S}_0)$. 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, $B_q\to D_q^{(\ast )}{D}_{s0}(2590{)}^{+}$ ($q=u,d$), followed by $D_{s0}(2590{)}^{+}\to D^{\ast }K$. We find $Br(B_q\to D_q^{(\ast )}{D}_{s0}(2590{)}^{+})\times Br(D_{s0}(2590{)}^{+}\to D^{\ast }K)=(2.16\sim 2.82)\times 10^{-3}$ 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.

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