Analysis of the data for $\gamma p \to f_1(1285) p$ photoproduction

The photoproduction of $f_1(1285)$ meson off proton is investigated within an effective Lagrangian approach. The $t$-channel $\rho$- and $\omega$-exchange diagrams, $u$-channel nucleon-exchange diagram, generalized contact term, and $s$-channel pole diagrams of nucleon and a minimal number of nucleon resonances are taken into account in constructing the reaction amplitudes to describe the experimental data. Three different models, i.e., the Feynman model, the Regge model, and the interpolated Regge model, are employed where the $t$-channel reaction amplitudes are constructed in Feynman type, Regge type, and interpolated Regge type, respectively. The results show that in neither Feynman model with two nucleon resonances introduced nor interpolated Regge model with one nucleon resonances included, can the available data for $\gamma p \to f_1(1285) p$ be satisfactorily reproduced. Nevertheless, in the Regge model, when any one of the $N(1990){7/2}^+$, $N(2000){5/2}^+$, $N(2040){3/2}^+$, $N(2060){5/2}^-$, $N(2100){1/2}^+$, $N(2120){3/2}^-$, $N(2190){7/2}^-$, $N(2300){1/2}^+$, and $N(2570){5/2}^-$ resonances is considered, the data can be well described. The resulted resonance parameters are consistent with those advocated in Particle Data Group (PDG) review. Further analysis shows that in high-energy region, the peaks of $\gamma p \to f_1(1285) p$ differential cross sections at forward angles are dominated by the contributions from $t$-channel $\rho$- and $\omega$-exchange diagrams, while in low-energy region, the $s$-channel pole diagrams of resonances also provide significant contributions to the $\gamma p \to f_1(1285) p$ cross sections.