Study of the $η$N scattering amplitude through the associated photoproduction of $ϕ$- and $η$-mesons in the region of the N*(1535) resonance

Abstract

The $γp \to ϕηp$ reaction is studied in the kinematic region where the $ηp$ final state originates dominantly from the decay of the N*(1535) resonance. The threshold laboratory photon energy for this reaction (at the peak of the S11 resonance) is $E_γ^{Lab} = $3 GeV. We will discuss it somewhat above threshold, at $E_γ^{Lab}\simeq 4-5$ GeV, in order to reach lower (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. The initial photon dissociates into the final $ϕ$-meson and a virtual pseudoscalar meson ($π^0$ or $η$). The virtual pseudoscalar meson scatters from the proton target to produce the final $ηp$ state. The $π^0 p \to ηp$ and $ηp \to ηp$ amplitudes are derived in the framework of a coupled-channel effective field theory of meson-baryon scattering. We found the $η$-meson exchange to be largely dominant. The $η$-$π^0$ interference is of the order of $20 - 30 %$. The sign of this term is not known and has a significant influence on the results. The $πN\to ηN$ amplitude being largely determined by data on the $π^- p \to ηn$ reaction, we found that the $γp \to ϕηp$ reaction cross section is rather directly related to the $η$-nucleon scattering amplitude in the N*(1535) resonance region. Accurate data on the $γp \to ϕηp$ process would therefore put additional constraints on this still poorly known amplitude.