Quark part of the non-forward BFKL kernel and the "bootstrap" for the gluon Reggeization

We calculate the quark part of the kernel of the generalized nonforward BFKL equation at nonzero momentum transfer t in the next-to-leading logarithmic approximation. Along with the quark contribution to the gluon Regge trajectory, this part includes pieces coming from the quark-antiquark production and from the quark contribution to the radiative corrections in one-gluon production in Reggeon-Reggeon collisions. The results obtained can be used for an arbitrary representation of the color group in the t channel. Using the results for the adjoint representation, we demonstrate explicitly the fulfillment of the ‘‘bootstrap’’ condition for the gluon Reggeization in the next-to-leading logarithmic approximation in the part concerning the quark contribution.