# Effective action for reggeized gluons, classical gluon field of relativistic color charge and color glass condensate approach

## TL;DR

This paper applies the small-$x$ effective action formalism for reggeized gluons to calculate classical gluon fields of relativistic color charges, comparing results with the CGC approach and exploring NLO solutions.

## Contribution

It introduces new solutions for the classical gluon field using reggeized gluon formalism at LO and NLO, bridging effective action and CGC frameworks.

## Key findings

- LO CGC results are reproduced in the reggeized gluon formalism.
- New NLO solutions for the classical gluon field are found.
- Comparison shows consistency between approaches.

## Abstract

We discuss application of formalism of small-$x$ effective action for reggeized gluons, \cite{Gribov,LipatovEff,BFKL}, for the calculation of classical gluon field of relativistic color charge, similarly to that done in CGC approach of \cite{Venug,Kovner}. The equations of motion with the reggeon fields are solved in LO and NLO approximations and new solutions are found. The results are compared to the calculations performed in the CGC framework and it is demonstrated that the LO CGC results for the classical field are reproduced in our calculations. Possible applications of the NLO solution in the effective action and CGC frameworks are discussed as well.