BFKL equation for an integrated gluon density

TL;DR

This paper derives a modified BFKL equation incorporating next-to-leading log terms and kinematic constraints, aiming to unify BFKL and DGLAP evolution for high-energy processes at the LHC.

Contribution

It presents a reformulation of the BFKL equation in terms of integrated gluons, including key higher-order corrections and constraints for improved accuracy.

Findings

Inclusion of next-to-leading log terms enhances the BFKL equation.

The unified approach addresses both small-x and large-Q^2 regimes.

Potential application to LHC processes with simultaneous large logs.

Abstract

We show how it is possible to rewrite the BFKL equation for the unintegrated gluon distribution, in terms of integrated gluons, similar to that used in DGLAP. We add to our equation the next-to-leading log terms which provide exact energy-momentum conservation and account for the kinematic constraint in real gluon emission. In this way the equation includes the major part of the higher-order corrections to BFKL evolution. We discuss the possibility to obtain a unified BFKL-DGLAP evolution equation relevant to processes at the LHC where both log(1/x) and logQ^2 are large simultaneously.