Treatment of heavy quarks in QCD

TL;DR

This paper emphasizes the importance of using the physical scheme for accurate heavy-quark effects in QCD evolution, ensuring smooth threshold transitions and simplifying NLO calculations.

Contribution

It demonstrates that accounting for heavy-quark mass effects at LO suffices for NLO accuracy and advocates for the physical scheme over MS-bar in heavy-quark treatments.

Findings

Physical scheme provides smooth heavy-quark threshold transitions.

Heavy-quark mass effects at LO are sufficient for NLO accuracy.

Explicit formulas for mass-dependent splitting functions and alpha_s are provided.

Abstract

We show that to correctly describe the effects of the heavy-quark mass, m_h, in DGLAP evolution, it is necessary to work in the so-called `physical' scheme. In this way, we automatically obtain a smooth transition through the heavy-quark thresholds. Moreover, we show that to obtain NLO accuracy, it is sufficient to account for the heavy-quark mass, m_h, just in the LO (one-loop) splitting function. The use of the MS-bar factorisation scheme is not appropriate, since at NLO we deal with a mixture of quarks and gluon (that is, the mass of the heavy parton is not well-defined). The formulae for the explicit m_h dependence of the splitting functions, and for alpha_s, are presented.