Analysis of photoproduction data on $\gamma p\to pf_1(1285)$ and $\gamma p\to p\eta(958)$ from the reaction $\gamma p\to p\eta\pi^+\pi^-$
We investigate the reaction $\gamma p\to pf_1(1285)\to p\eta\pi^+\pi^-$ in a simple $\rho+\omega$ Reggeon exchanges. As the decay mode $\eta(1295)\to \eta\pi^+\pi^-$ is potentially overlapped with the former reaction, a combined analysis of $\gamma p\to p\eta'\to p\eta\pi^+\pi^-$ reaction including $\eta(1295)$ is performed to find that the measured cross sections for $\eta'$ and $f_1$ are well explained by the vector meson exchanges with a correction by the branching fraction to $\eta'\to\eta\pi^+\pi^-$ and $f_1\to\eta\pi^+\pi^-$, respectively. The numerical consequences show that $\eta(1295)$ cross section is negligible in the reconstruction of $f_1$ cross section from $\gamma p\to p\eta\pi^+\pi^-$.