Searching for a P_{cs}(4200) state in the Λ_btoφη_cΛ reaction

We propose the $\Lambda_b\to\phi \eta_c \Lambda$ 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 $\eta_c \Lambda$ with a width of about $200$ keV. The reaction is related to $\Lambda_b^0\to\phi D_s^- \Lambda_c^+$, which has already been observed. We predict a branching fraction for $\Lambda_b\to\phi P_{cs}(4200)$; $P_{cs}\to\eta_c \Lambda$ 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.