Searching for signals of an exotic $I=1,J^P=2^+$ state of $D^*K^*$ nature and the structure of the $P_c(4312)$ in the $\Lambda_b\to \Sigma_c^{++} D^- K^-$ reaction

This paper investigates the decay process $\Lambda_b \to \Sigma_c^{++} D^- K^-$ with the objective of finding a predicted molecular state with isospin $I=1$, $J^P=2^+$ of $D^* K^*$ nature, plus finding support for the $P_c(4312)$ state as made out of $\Sigma_c \bar{D}$. The mass distribution of the $D^- K^-$ system shows distinct features as a consequence of the existing of this $2^+$ state, while the $\Sigma_c \bar{D}$ distribution exhibits a significant peak near the threshold, much bigger than phase space expectations, which is linked to our assumed $\Sigma_c \bar{D}$ nature of the $P_c(4312)$ state below the $\Sigma_c \bar{D}$ 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 $D^* K^*$ 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.