On the Next-to-Next-to-Leading Order Evolution of Flavour-Singlet Fragmentation Functions

TL;DR

This paper computes third-order corrections to timelike splitting functions in perturbative QCD, improving the precision of fragmentation function evolution with implications for high-energy particle physics.

Contribution

It presents the first calculation of third-order contributions to quark-gluon and gluon-quark splitting functions, using physical evolution kernels and sum rule constraints.

Findings

Third-order corrections are numerically significant for fragmentation functions.

Compact parametrizations of the new splitting functions are provided.

Uncertainty remains small for the quark-gluon splitting function.

Abstract

We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top limit. A numerically tolerable uncertainty remains for the quark-gluon splitting function, which does not affect the endpoint logarithms for small and large momentum fractions. We briefly discuss these limits and illustrate the numerical impact of the third-order corrections. Compact and accurate parametrizations are provided for all third-order timelike splitting functions.