Time-Like Heavy-Flavour Thresholds for Fragmentation Functions: the Light-Quark Matching Condition at NNLO

TL;DR

This paper derives the analytical NNLO matching condition for light-flavour fragmentation functions at heavy-flavour thresholds, crucial for precise QCD predictions involving identified hadrons.

Contribution

It provides the first NNLO analytical form of the matching condition for light-quark fragmentation functions, extending previous formalism to higher order accuracy.

Findings

First non-trivial heavy-quark effect in light-quark fragmentation functions

Analytical NNLO matching condition derived and expressed in Mellin space

Enhances precision in QCD predictions for identified hadron observables

Abstract

Matching conditions are universal ingredients that describe how fragmentation functions change when heavy-flavour thresholds are crossed during the factorisation scale evolution. They are the last missing piece for a consistent description of observables with identified final-state hadrons at next-to-next-to leading order accuracy in quantum chromodynamics. We present an analytical form of the matching condition for light-flavour to hadron fragmentation function at next-to-next-to leading order. The derivation is performed by extending the formalism employed in the extraction of the next-to leading order matching conditions to the subsequent order, making use of $e^+e^-$ annihilation cross sections. We obtain the first non-trivial heavy-quark effect in the light-quark fragmentation functions and provide results in Mellin space.