Non commutativity between massless and soft limit in processes with heavy quarks

TL;DR

This paper investigates the differences in soft logarithmic structures when computing processes with heavy quarks using massless versus massive schemes, highlighting non-commutativity issues and performing threshold resummation for Higgs decay.

Contribution

It analyzes the non-commutativity between massless and massive limits in heavy quark processes and performs NLL threshold resummation in the massive scheme for Higgs decay.

Findings

Identifies non-commutativity between soft and massless limits.

Performs NLL threshold resummation for Higgs decay into b anti-b.

Highlights differences in soft logarithmic structures.

Abstract

Processes involving heavy quarks can be computed in perturbation theory in two different ways: we can adopt a scheme in which the mass of the quark is considered only as a regulator of the collinear divergences because of the fact that the hard scale of the process is far bigger or we can consider the quark as a massive particle. Each picture has its own advantages and drawbacks: we investigate the differences between the two approaches with particular attention to the soft logarithmic structure. We examine the origin of this difference, focusing on different processes involving the Higgs boson . Finally we perform the threshold resummation of the Higgs boson decay rate into a $b\bar{b}$ pair at NLL accuracy in the massive scheme.