# Computing one-loop corrections to effective vertices with two scales in the EFT for Multi-Regge processes in QCD

## TL;DR

This paper calculates one-loop corrections to effective vertices in QCD's Multi-Regge processes using a gauge-invariant EFT, addressing rapidity divergences with tilted Wilson lines and confirming results with known scattering amplitudes.

## Contribution

It introduces a method to compute one-loop effective vertices with two scales in QCD's EFT, including a novel regulation of rapidity divergences and explicit scalar integral calculations.

## Key findings

- Rapidity divergences are regulated by tilted Wilson lines.
- Explicit scalar integrals with two scales are computed.
- Results reproduce the Regge limit of one-loop QCD amplitudes.

## Abstract

The computation of one-loop corrections to Reggeon-Particle-Particle effective vertices with two scales of virtuality is considered in the framework of gauge-invariant effective field theory for Multi-Regge processes in QCD. Rapidity divergences arising in loop integrals are regulated by "tilted Wilson lines" prescription. General analysis of rapidity divergences at one loop is given and necessary scalar integrals with one and two scales of virtuality are computed. Two examples of effective vertices at one loop are considered: the effective vertex of interaction of (space-like) virtual photon with one Reggeized and one Yang-Mills quark and the effective vertex of Reggeized gluon to Yang-Mills gluon transition with an insertion of the operator ${\rm tr}\left[G_{\mu\nu}G^{\mu\nu} \right]$ carrying the (space-like) off-shell momentum. All terms $\sim r^{\pm\epsilon}$ in the rapidity-regulator variable $r$ cancel between diagrams and only $\log r$-divergence is left. It is checked on several examples, that obtained results indeed allow one to reproduce Regge limit of one-loop QCD scattering amplitudes.