Effect of changes of variable flavor number scheme on parton distribution functions and predicted cross sections

TL;DR

This paper examines how different definitions of the variable flavor number scheme at NLO and NNLO affect parton distribution functions and cross section predictions, introducing an optimal scheme for smoother transitions and assessing the associated uncertainties.

Contribution

It introduces a new 'optimal' GM-VFNS scheme and analyzes the impact of scheme variations on PDFs and collider predictions at NLO and NNLO.

Findings

At NLO, PDFs and predictions vary by 2-3% due to scheme choice.

At NNLO, variations are less than 1%, especially at small x.

Mass-scheme uncertainty decreases with higher perturbative order.

Abstract

I consider variations in the definitions, at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO), of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions. I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the PDFs when a new MSTW2008-type global fit to data is performed for each GM-VFNS. At NLO the parton distributions, and predictions using them at hadron colliders, can vary by 2-3% from the mean value. At NNLO there is far more stability with varying GM-VFNS definition, and changes in PDFs and predictions are less than 1%, with most variation at very small x values. Hence, mass-scheme variation is an additional and significant source of uncertainty when considering parton distributions, but as with all perturbative uncertainties, it diminishes quickly as higher orders are included.