NNLO classical solution for Lipatov's effective action for reggeized gluons

TL;DR

This paper develops a NNLO classical solution for Lipatov's effective action for reggeized gluons, incorporating fermion loops, and demonstrates a recursive scheme for constructing solutions ensuring self-consistency.

Contribution

It introduces a NNLO classical gluon field solution with fermion loops in Lipatov's small-x effective action, using a recursive approach based on transversality conditions.

Findings

Classical gluon field calculated to NNLO with fermion loops.

Self-consistency of equations linked to transversality conditions.

Recursive scheme for constructing solutions at each perturbative order.

Abstract

We consider the formalism of small-x effective action for reggeized gluons, Gribov (Sov Phys JETP 26:414, 1968), Lipatov (Nucl Phys B 452:369, 1995; Phys Rep 286:131, 1997; Subnucl Ser 49:131, 2013, Int J Mod Phys Conf Ser 39:1560082, 2015; Int J Mod Phys A 31(28/29):1645011, 2016; EPJ Web Conf 125:01010, 2016) and Lipatov et al. (Sov J Nucl Phys 23:338, 1976; Sov Phys JETP 45:199, 1977; Sov J Nucl Phys 28:822, 1978), and, following to the approach developed in Bondarenko et al. (Eur Phys J C 77(8):527, 2017, Eur Phys J C 77(9):630, 2017), calculate the classical gluon field to NNLO precision with fermion loops included. It is demonstrated, that the the self-consistency of the equations of motion in each perturbatie order in the approach is equivalent to the transversality conditions applied to the solutions of the equations in the lower orders, that allows to construct the solutions with the help of some recursive scheme. Applications of the obtained results are also discussed.