Searching for signals of an exotic I = 1,JP = 2+ state of D⁎K⁎ nature and the structure of the Pc(4312) in the Λb→Σc++D−K− reaction

Abstract

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 $P_c\left(4312\right)$ state as made out of ${\Sigma }_c\overline{D}$. The mass distribution of the $D^{-}{K}^{-}$ system shows distinct features as a consequence of the existence of this $2^{+}$ state, while the ${\Sigma }_c\overline{D}$ distribution exhibits a significant peak near the threshold, much bigger than phase space expectations, which is linked to our assumed ${\Sigma }_c\overline{D}$ nature of the $P_c\left(4312\right)$ state below the ${\Sigma }_c\overline{D}$ 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 $2^{+}$ $T_{c\overline{s}}\left(2834\right)$ of $D^{⁎}{K}^{⁎}$ nature and the $P_c\left(4312\right)$ states from the measurements of the mass distributions in this reaction, which will be accessible in the planned updates of LHCb.