On the one-loop calculations with Reggeized quarks

TL;DR

This paper develops a gauge-invariant method for one-loop calculations involving Reggeized quarks in QCD, addressing rapidity divergences and demonstrating consistency with full QCD results.

Contribution

It introduces a covariant regularization procedure for rapidity divergences in Reggeized quark calculations within an effective field theory framework.

Findings

Successful regularization of rapidity divergences while preserving gauge invariance

Calculation of one-loop corrections to Reggeized quark propagator and scattering vertices

Validation of the effective theory predictions against full QCD results

Abstract

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.