Study of the threshold behavior of the $η$N scattering amplitude through the associated photoproduction of $ϕ$- and $η$-mesons

Abstract

We suggest that the $γp \to ϕηp$ reaction cross section, in the kinematics where the $ηp$ invariant mass in the final state lies between the threshold value (m$_p$+m$_η$) and the N*(1535) resonance mass, is largely determined by the $ηN$ scattering amplitude close to threshold. The initial photon energy is chosen in the range $4 < E_γ^{Lab} < 5$ GeV, in order to reach low (absolute) values of the squared 4-momentum transfer from the initial photon to the final $ϕ$-meson. In these conditions, we expect the t-channel $π^0$- and $η$-meson exchanges to drive the dynamics underlying the $γp \to ϕηp$ process. We show that the $η$-exchange is the dominating contribution to the cross section while the $π^0$-exchange is negligible. The $η$-$π^0$ interference is of the order of $20 - 30 %$. The sign of this term is not known and alters significantly our results. Data on the $γp \to ϕηp$ process would be therefore very useful to help unravelling the behavior of the $ηp$ scattering amplitude close to threshold and assessing the possibility of producing $η$-nucleus bound states.