  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.
