Searching for a P(4200) state in the Λ  → ϕηΛ reaction

We propose the $Λ_b\toϕη_c Λ$ 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 $η_c Λ$ with a width of about $200$ keV. The reaction is related to $Λ_b^0\toϕD_s^- Λ_c^+$, which has already been observed. We predict a branching fraction for $Λ_b\toϕP_{cs}(4200)$; $P_{cs}\toη_c Λ$ 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.