The $\\gamma p \\rightarrow \\phi \\eta p$
reaction is studied in the kinematic region where the $\\eta p$ 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 $E_\\gamma^{Lab}$=3 GeV.
We will discuss it somewhat above threshold, at $E_\\gamma^{Lab}\\gtrsim 4$ GeV,
in order to reach lower (absolute) values of the squared 4-momentum transfer from the initial photon
to the final $\\phi$-meson. In these conditions, we expect the t-channel $\\pi$-
and $\\eta$-meson exchanges to contribute to the $\\gamma p \\rightarrow \\phi \\eta p$
cross section according to the following dynamics.
The initial photon dissociates into the final $\\phi$-meson and a virtual pseudoscalar
meson ($\\pi$ or $\\eta$). The strength of this dissociation
is determined by the coupling constant appearing in the
corresponding anomalous interaction Lagrangian. The virtual pseudoscalar meson
scatters from the proton target to produce the final $\\eta p$ state.
The $\\pi^0 p \\rightarrow \\eta p$ and $\\eta p \\rightarrow \\eta p$
amplitudes are calculated in the framework of a coupled-channel
effective field theory of meson-baryon scattering. They
reflect the dominance of the N*(1535) in the $\\eta p$ channel.
We have calculated the t-channel $\\pi$-
and $\\eta$-meson exchanges and found the
$\\eta$-meson exchange to be largely dominant.
We computed the full double pole term of the $\\eta$-exchange process in a gauge-invariant manner.
Our result suggest that
accurate data on the $\\gamma p \\rightarrow \\phi \\eta p$ reaction in the specific
kinematics under consideration could be most helpful in clarifying our understanding of the
$\\eta$-nucleon scattering amplitude in the N*(1535) resonance region.
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