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

Christian Biello; Leonardo Bonino

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arXiv · 2407.07623

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

Christian Biello·Leonardo Bonino

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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.

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Christian Biello, Leonardo Bonino. 2024-07-10. Time-Like Heavy-Flavour Thresholds for Fragmentation Functions: the Light-Quark Matching Condition at NNLO. https://arxiv.org/abs/2407.07623

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