Searching for the $2^+$ partner of the $T_{cs0}(2870)$ in the $B^- \to D^- D^0 K^0_S$ reaction

Abstract: We study the $$B^- \to D^- D⁰ K<sup>0_S$$ reaction, recently analyzed by the LHCb collaboration, where a clear signal for the exotic $T_{cs0}(2870)$ state has been reported. We call the attention to a small peak in the $D⁰ K<sup>0_S$ mass distribution that could correspond to a state of the same nature as the $T_{cs0}(2870)$ ($D^* \bar K<sup>*$ nature in the molecular picture) but with $J^P= 2<sup>+$. In order to magnify the signal for the state, we calculate the moments of the angle-mass distribution, which are linear in the resonance signal, rather than quadratic for the angle integrated mass distribution. We find spectra for the moments with a strength far bigger than that for the angle integrated mass distribution, which should encourage the evaluation of these moments from the present measurements of the reaction.