Investigation of pion-induced $f_1(1285)$ production off a nucleon target within an interpolating Reggeized approach

In this work, the pion-induced $f_1(1285)$ production off a nucleon target is investigated in an effective Lagrangian approach with an interpolating Reggeized treatment in a large range of the pion-beam momentum from threshold up to several tens of GeV. The $s$-channel, $u$-channel, and $t $-channel Born terms are included to calculate production cross sections. An interpolating Reggeized treatment is applied to the $t$ channel, which is found to be important to reproduce the behavior of the existent experimental total cross sections at both low ($\lesssim$ 8 GeV) and high pion-beam momenta ($\gtrsim$ 8 GeV). It is found that the $t$-channel contribution is dominant in the pion-induced $f_1(1285)$ production at low beam momentum and still dominant at very forward angles at high momentum. The interpolated Reggeized treatment of the $u$ channel is also discussed. The $u$-channel contribution is small and negligible at low momentum, and it becomes dominant at backward angles at momenta higher than 10 GeV. The differential cross sections are predicted with the model fixed by the fitting existent experimental data. The results are helpful to the possible experiments at J-PARC and COMPASS.