External leg corrections as an origin of large logarithms

TL;DR

This paper investigates large Sudakov-like logarithmic corrections from external-leg corrections in theories with heavy and light particles, highlighting their infrared origin and implications for precise decay calculations.

Contribution

It identifies and analyzes the origin of large logarithms from external-leg corrections, emphasizing the need for specific renormalization schemes and providing explicit two-loop results.

Findings

Large logarithms arise from infrared singularities in external-leg corrections.

Two-loop corrections with large logarithms are explicitly derived.

Choosing an on-shell-like renormalization scheme mitigates issues with large logs.

Abstract

The appearance of large logarithmic corrections is a well-known phenomenon in the presence of widely separated mass scales. In this work, we point out the existence of large Sudakov-like logarithmic contributions related to external-leg corrections of heavy scalar particles which cannot be resummed straight-forwardly using renormalisation group equations. Based on a toy model, we discuss in detail how these corrections appear in theories containing at least one light and one heavy particle that couple to each other with a potentially large trilinear coupling. We show how the occurrence of the large logarithms is related to infrared singularities. In addition to a discussion at the one-loop level, we also explicitly derive the two-loop corrections containing the large logarithms. We point out in this context the importance of choosing an on-shell-like renormalisation scheme. As exemplary applications, we present results for the two-loop external-leg corrections for the decay of a gluino into a scalar top quark and a top quark in the Minimal Supersymmetric extension of the Standard Model as well as for a heavy Higgs boson decay into two tau leptons in the singlet-extended Two-Higgs-Doublet Model.