Bridging massive and massless schemes for soft gluon resummation in heavy-flavour production in $e^+e^-$ collisions

TL;DR

This paper develops a unified framework for soft gluon resummation in heavy-flavour production in electron-positron collisions, combining massive and massless schemes at NLL' accuracy to include finite soft terms.

Contribution

It extends existing resummation methods to achieve NLL' accuracy, enabling consistent treatment of finite mass effects in heavy-quark fragmentation functions.

Findings

Achieved NLL' resummation accuracy for heavy-quark fragmentation.

Provided a method to match massive and massless schemes in soft gluon resummation.

Enhanced precision in theoretical predictions for heavy-flavour production.

Abstract

Perturbative calculations for processes involving heavy flavours can be carried out using two approaches: the massive and the massless schemes. These schemes can also be combined to leverage their respective strengths. Additionally, both massive and massless frameworks can be supplemented by soft-gluon resummation. However, matching resummed calculations across the two schemes presents significant challenges, primarily due to the non-commutativity of the soft and small mass limits. The consistent resummation of mass and soft logarithms has been recently achieved at next-to-leading logarithmic (NLL) accuracy. In this paper, we consider heavy-quark fragmentation functions in electron-positron collisions and we extend this framework to achieve the so-called NLL$^\prime$ accuracy, which accounts for finite terms in the soft limit.