The collinearly-improved Balitsky-Kovchegov equation

TL;DR

This paper introduces a resummed version of the Balitsky-Kovchegov equation that addresses convergence issues in high-energy QCD evolution by summing double and single logarithms, leading to stable solutions that fit HERA data.

Contribution

The authors develop a collinearly-improved BK equation by resumming double and single transverse logarithms, enhancing the equation's stability and predictive power.

Findings

Resummed BK equation admits stable solutions.

Successfully fits HERA small-x data.

Addresses convergence issues in high-energy QCD evolution.

Abstract

The high-energy evolution in perturbative QCD suffers from a severe lack-of-convergence problem, due to higher order corrections enhanced by double and single transverse logarithms. We resum double logarithms to all orders within the non-linear Balitsky-Kovchegov equation, by taking into account successive soft gluon emissions strongly ordered in lifetime. We further resum single logarithms generated by the first non-singular part of the splitting functions and by the one-loop running of the coupling. The resummed BK equation admits stable solutions, which are used to successfully fit the HERA data at small $x$ for physically acceptable initial conditions and reasonable values of the fit parameters.