Resummed small-x and first-moment evolution of fragmentation functions in perturbative QCD

TL;DR

This paper develops an all-order resummation of small-x logarithms in fragmentation functions within perturbative QCD, stabilizing their evolution and enabling reliable predictions at very small x values.

Contribution

It provides the first complete analytic resummation of double logarithms for fragmentation functions at NNLL accuracy, improving small-x behavior in perturbative QCD.

Findings

Resummation removes instabilities at small x and for first moments.

Oscillatory small-x behavior of fragmentation functions is predicted.

Framework allows extension to higher accuracy and combined all-x results.

Abstract

We study the splitting functions for the evolution of fragmentation distributions and the coefficient functions for single-hadron production in semi-inclusive electron-positron annihilation in massless perturbative QCD for small values of the momentum fraction and scaling variable x, where their fixed-order approximations are completely destabilized by huge double logarithms of the form alpha_s^n 1/x ln^(2n-a) x. Complete analytic all-order expressions in Mellin-N space are presented for the resummation of these terms at the next-to-next-to-leading logarithmic accuracy. The poles for the first moments, related to the evolution of hadron multiplicities, and the small-x instabilities of the next-to-leading order splitting and coefficient functions are removed by this resummation, which leads to an oscillatory small-x behaviour and functions that can be used at N=1 and down to extremely small values of x. First steps are presented towards extending these results to the higher accuracy required for an all-x combination with the state-of-the-art next-to-next-to-leading order large-x results.