Fragmentation Functions Beyond Fixed Order Accuracy

TL;DR

This paper develops a comprehensive formalism for all-order resummation of logarithmic contributions in parton-to-hadron fragmentation functions, including their phenomenological extraction from data and comparison with fixed-order results.

Contribution

It provides the first detailed derivation of resummation expressions up to NNLL order for fragmentation functions and implements a numerical framework for their phenomenological analysis.

Findings

Resummed results show reduced scale dependence compared to fixed-order calculations.

First extractions of pion fragmentation functions using resummed formalism.

Comparison indicates the importance of resummation at small momentum fractions.

Abstract

We give a detailed account of the phenomenology of all-order resummations of logarithmically enhanced contributions at small momentum fraction of the observed hadron in semi-inclusive electron-positron annihilation and the time-like scale evolution of parton-to-hadron fragmentation functions. The formalism to perform resummations in Mellin moment space is briefly reviewed, and all relevant expressions up to next-to-next-to-leading logarithmic order are derived, including their explicit dependence on the factorization and renormalization scales. We discuss the details pertinent to a proper numerical implementation of the resummed results comprising an iterative solution to the time-like evolution equations, the matching to known fixed-order expressions, and the choice of the contour in the Mellin inverse transformation. First extractions of parton-to-pion fragmentation functions from semi-inclusive annihilation data are performed at different logarithmic orders of the resummations in order to estimate their phenomenological relevance. To this end, we compare our results to corresponding fits up to fixed, next-to-next-to-leading order accuracy and study the residual dependence on the factorization scale in each case.