Study of the threshold behavior of the $\eta$N scattering amplitude through the associated photoproduction of $\varphi$- and $\eta$-mesons

Abstract

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

Comments: 8 pages, 6 figures, Invited talk at MESON 2006, June 9th-13th, 2006, Cracow (Poland)