Balitsky-Kovchegov equation

Abstract

In high-energy particle physics the energy evolution of various quantities can be calculated from the Balitsky-Kovchegov (BK) equation. Depending on the frame that is used to describe the process, the BK equation can be seen to describe either the energy evolution of the virtual photon wave function or the gluon distribution function of a hadron.

In this work the BK equation is derived at leading logarithm accuracy from QCD and solved analytically in some special cases. In order to derive it the quantum field theory on the light cone is introduced. Part of the higher order corrections to the BK equation, namely the running strong coupling constant and the kinematical constraint effects, are studied numerically.

As a result it is shown that the running coupling slows down the evolution significantly compared with the evolution obtained with a fixed coupling constant. The different running coupling prescriptions used in the literature also cause significantly different evolution speeds. In addition the running coupling changes the asymptotical shape of the solution. On the other hand the kinematical constraint effects are shown to affect mainly the evolution speed while leaving the shape of the solution intact.

The numerical codes developed in this work can be used when studying the phenomenology of high-energy QCD.