Check of the gluon-reggeization condition in the next-to-leading order: Quark part

The bootstrap condition for gluon production in multi-Regge kinematics is considered in the next-to-leading order. Bootstrap conditions follow fromthe requirement that the Regge formof amplitudes in QCD be consistent with s -channel unitarity and are nonlinear relations between the Reggeized-gluon trajectory and vertex functions. Their fulfillment ensures the Reggeization of gluons—that is, the Regge form of both elastic and inelastic amplitudes. This condition is the only one that has not yet been verified. The demonstration of its fulfillment is the ultimate step in proving the Reggeization of gluons in the next-to-leading logarithmic approximation. In the present article, this is done for the quark part of the bootstrap condition.