On the one-loop calculations with Reggeized quarks

The technique of one-loop calculations for the processes involving Reggeized quarks is described in the framework of gauge invariant effective field theory for the Multi-Regge limit of QCD, which has been introduced by Lipatov and Vyazovsky. The rapidity divergences, associated with the terms enhanced by $\log (s)$, appear in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and $\gamma Q q$-scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop $\gamma\gamma\to q\bar q$ amplitude. The cancellation of rapidity divergences and consistency of the effective field theory prediction with the full QCD result is demonstrated. The rapidity renormalization group within the effective field theory is discussed.