Searching for a $P_{cs}(4200)$ state in the ${\mathrm{\Lambda }}_b\to \phi {\eta }_c\mathrm{\Lambda }$ reaction

We propose the ${\mathrm{\Lambda }}_b\to \phi {\eta }_c\mathrm{\Lambda }$ reaction to observe a $P_{cs}$ state around $4200$ MeV, predicted at lower masses than expected from comparison with the $P_c$ states, stemming as a consequence of the important role played by coupled channels in the $P_{cs}$ case, which does not appear in the $P_c$ case. That state decays to ${\eta }_c\mathrm{\Lambda }$ with a width of about $200$ keV. The reaction is related to ${\mathrm{\Lambda }}_b^0\to \phi D_s^{-}{\mathrm{\Lambda }}_c^{+}$, which has already been observed. We predict a branching fraction for ${\mathrm{\Lambda }}_b\to \phi P_{cs}(4200)$; $P_{cs}\to {\eta }_c\mathrm{\Lambda }$ of the order of ${10}^{-5}$, which is within present capabilities of the LHCb collaboration. The observation of this state would bring valuable light on the nature of the $P_c$ and $P_{cs}$ states and the role played by coupled channels in hadron structure and hadron reactions.