Abstract
We derive a modified Balitskii-Fadin-Kuraev-Lipatov equation with the rapidity veto that originates from external kinematic constraint. Though it is a formally subleading power contribution, such kinematic effect becomes very important in the threshold region, where there is no sufficient phase space for the small $x$ evolution to be fully developed. We also investigate the phenomenological consequences of the kinematic constraint Balitskii-Fadin-Kuraev-Lipatov equation in the forward particle production processes in pp and eA collisions. It is shown that particle yield at large transverse momentum is significantly suppressed in the threshold region.
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