Resummation of Singlet Parton Evolution at Small x

TL;DR

This paper introduces an improved small-x splitting function approach that stabilizes the evolution equations, respects momentum conservation, and accurately describes parton distribution scaling violations across the entire x range.

Contribution

It presents a novel method to improve singlet parton evolution at small x by incorporating higher-order anomalous dimensions, ensuring stability and better convergence.

Findings

Stable expansion for chi(M) near M=0

Effective parameterization of small x behavior with lambda

Accurate description of scaling violations at all x

Abstract

We propose an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach. We obtain a stable expansion for the x-evolution function chi(M) near M=0 by including in it a sequence of terms derived from the one- and two-loop anomalous dimension gamma. The requirement of momentum conservation is always satisfied. The residual ambiguity on the splitting functions is effectively parameterized in terms of the value of lambda, which fixes the small x asymptotic behaviour x^-lambda of the singlet parton distributions. We derive from this improved evolution function an expansion of the splitting function which leads to good apparent convergence, and to a description of scaling violations valid both at large and small x.