A solvable model for small-x physics in D > 4 dimensions

TL;DR

This paper introduces a simplified, solvable model for high-energy QCD gluon dynamics in arbitrary dimensions, providing explicit solutions and clarifying the mathematical structure of gluon densities and anomalous dimensions.

Contribution

It presents a new solvable differential equation model for the gluon Green's function in D > 4 dimensions, extending understanding of high-energy QCD in arbitrary dimensions.

Findings

Explicit solutions for gluon density and anomalous dimension in MS and Q_0 schemes.

Validation of the gamma-representation method for resummed anomalous dimensions.

Qualitative analysis of gluon density features in different factorization schemes.

Abstract

I present a simplified model for the gluon Green's function governing high-energy QCD dynamics, in arbitrary space-time dimensions. The BFKL integral equation (either with or without running coupling) reduces to a second order differential equation that can be solved in terms of Bessel and hypergeometric functions. Explicit expressions for the gluon density and its anomalous dimension are derived in MS and Q_0 factorization schemes. This analysis illustrates the qualitative features of the QCD gluon density in both factorization schemes. In addition, it clarifies the mathematical properties and validates the results of the ``gamma-representation'' method proposed by M.Ciafaloni and myself for extracting resummed next-to-leading-log x anomalous dimensions of phenomenological relevance in the two schemes.