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

We study the $B^{-}\to D^{-}{D}^0{K}_S^0$ 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 $D^0{K}_S^0$ mass distribution that could correspond to a state of the same nature as the $T_{cs0}(2870)$ ($D^{\ast }{\bar{K}}^{\ast }$ nature in the molecular picture) but with $J^P=2^{+}$. 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.