Renormalization Group Improved Small-x Equation

TL;DR

This paper develops an improved small-x evolution equation that combines BFKL kernels with renormalization group constraints, providing stable, scheme-independent predictions for gluon dynamics and pomeron intercepts.

Contribution

It introduces a novel small-x equation incorporating exact BFKL kernels and renormalization group constraints, with detailed analysis of solutions and pomeron properties.

Findings

Resummed results are stable and scheme-independent.

Provides bounds on pomeron intercepts.

Smoothly connects with fixed-order perturbative results.

Abstract

We propose and analyze an improved small-x equation which incorporates exact leading and next-to-leading BFKL kernels on one hand and renormalization group constraints in the relevant collinear limits on the other. We work out in detail the recently proposed omega-expansion of the solution, derive the Green's function factorization properties and discuss both the gluon anomalous dimension and the hard pomeron. The resummed results are stable, nearly renormalization-scheme independent, and join smoothly with the fixed order perturbative regime. Two critical hard pomeron exponents are provided, which - for reasonable strong-coupling extrapolations - are argued to provide bounds on the pomeron intercept.