A consistent resummation of mass and soft logarithms in processes with heavy flavours

TL;DR

This paper develops a formalism to consistently combine resummed massless and massive calculations, capturing both mass and soft logarithms at next-to-leading accuracy, improving predictions for processes involving heavy flavors.

Contribution

It introduces an all-order formalism that unifies resummation of mass and soft logarithms, addressing the non-commutativity issue between soft and massless limits.

Findings

Successfully resums both mass and soft logarithms at next-to-leading order.

Provides detailed calculations for Higgs decay into heavy quarks.

Demonstrates applications to various processes involving heavy flavors.

Abstract

Perturbative calculations for processes that involve heavy flavours can be performed in two approaches: the massive scheme and the massless one. The former enables one to fully account for the heavy-quark kinematics, while the latter allows one to resum potentially-large mass logarithms. Furthermore, the two schemes can be combined to take advantage of the virtues of each of them. Both massive and massless calculations can be supplemented by soft-gluon resummation. However matching between massive and massless resummed calculations is difficult, essentially because of the non-commutativity of the soft and massless limits. In this paper, we develop a formalism to combine resummed massless and massive calculations. We obtain an all-order expression that consistently resums both mass and soft logarithms to next-to-leading logarithmic accuracy. We perform detailed calculations for the decay of the Higgs into a heavy-quark pair and discuss the applications of this formalism to different processes.