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April 30, 2026Open Access

Erratum: Time-like heavy-flavour thresholds for fragmentation functions: the light-quark matching condition at NNLO

Key Points

This erratum corrects a specific term in the NNLO matching condition for light-quark fragmentation functions, addressing scheme dependency issues.
Identified a scheme-dependent term in the double-real contribution of light-quark fragmentation functions at NNLO.
Described necessary changes to the equations to enable correct matching to MS conventions.
Proposed adjustments to the fragmentation antenna definition to resolve the discrepancies.
Corrected scheme-dependent term aligns with correct MS conventions in fragmentation functions.
Confirmed that the antenna function remains finite in four dimensions despite previous issues in scheme adaptation.

Abstract

We provide a correction to the coefficient proportional to (1z) in the NNLO time-like matching condition for lightquark fragmentation functions.Although the antenna function containing the double-real correction to the massive contribution is finite in four dimensions, it inheritances a scheme dependency when promoted to a distribution, due to the end-point soft regularisation.Therefore, Eq. ( 39) of the paper introduced a scheme-dependent terms proportional to (1-z) in the double-real contribution.A scheme transformation is needed to match the MS conventions of all the other ingredients entering the calculation.In order to be able to perform a scheme transformation to MS, for the fragmentation antenna B0,id.iih h (z, ), the prescription of Eq. ( 39) must be replaced as follows

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