On qualitative aspects of the choice of factorization schemes at NLO

TL;DR

This paper investigates how the choice of factorization schemes at NLO affects theoretical predictions, highlighting the challenges and restrictions in selecting optimal schemes for Monte Carlo event generators.

Contribution

It provides a detailed analysis of the dependence of NLO predictions on factorization schemes and examines the practical limitations of the ZERO scheme.

Findings

The dependence on factorization schemes at NLO is significant.

The ZERO scheme is practically inapplicable despite initial appeal.

Restrictions on factorization schemes depend on properties of NLO splitting functions.

Abstract

Although the choice of a factorization scheme is as important as the choice of a factorization scale, the dependence of theoretical predictions (at finite order) on the choice of a factorization scheme has been little investigated. This is due to the fact that the freedom in the choice of a factorization scheme is enormous, even at NLO. One of the reason why to study factorization schemes is the possible exploitation of the freedom in their choice in the construction of NLO Monte Carlo event generators with NLO initial state parton showers. However, the ZERO factorization scheme, which should be optimal for such Monte Carlo event generators, has turned out to be practically inapplicable although it appears at first sight as reasonable. A detailed analysis has then shown that if some given NLO splitting functions do not satisfy a certain nontrivial condition, then the corresponding factorization scheme has some restrictions on its practical applicability. Relevant technical details of the discussed issues are the content of this short contribution.