Searching for signals of an exotic $I=1,J^P=2^{+}$ state of $D^{\ast }{K}^{\ast }$ nature and the structure of the $P_c(4312)$ in the ${\mathrm{\Lambda }}_b\to {\mathrm{\Sigma }}_c^{++}{D}^{-}{K}^{-}$ reaction

This paper investigates the decay process ${\mathrm{\Lambda }}_b\to {\mathrm{\Sigma }}_c^{++}{D}^{-}{K}^{-}$ with the objective of finding a predicted molecular state with isospin $I=1$, $J^P=2^{+}$ of $D^{\ast }{K}^{\ast }$ nature, plus finding support for the $P_c(4312)$ state as made out of ${\mathrm{\Sigma }}_c\bar{D}$. The mass distribution of the $D^{-}{K}^{-}$ system shows distinct features as a consequence of the existing of this $2^{+}$ state, while the ${\mathrm{\Sigma }}_c\bar{D}$ distribution exhibits a significant peak near the threshold, much bigger than phase space expectations, which is linked to our assumed ${\mathrm{\Sigma }}_c\bar{D}$ nature of the $P_c(4312)$ state below the ${\mathrm{\Sigma }}_c\bar{D}$ threshold. The reaction has been measured at LHCb Collaboration, but only the branching ratio is measured. The present study shows that much valuable information can be obtained about the predicted $2^{+}$ $T_{c\bar{s}}(2834)$ of $D^{\ast }{K}^{\ast }$ nature and the $P_c(4312)$ states from the measurements of the mass distributions in this reaction, which will be accessible in the planned updates of LHCb.