Impact of the heavy quark matching scales in PDF fits

TL;DR

This paper examines how varying the heavy quark matching scales affects global PDF fits, revealing significant dependence at NLO that diminishes at NNLO, and implements these findings in the xFitter framework.

Contribution

It introduces an analysis of heavy quark matching scale variations in PDF fits and incorporates this into the xFitter software, highlighting the scheme dependence and its reduction at higher orders.

Findings

Large charm matching scale dependence at NLO reduces at NNLO.

Bottom quark matching scale dependence is smaller than charm at both NLO and NNLO.

Implementation of the scheme dependence analysis in xFitter 2.0.0.

Abstract

We investigate the impact of displaced heavy quark matching scales in a global fit. The heavy quark matching scale $\mu_{m}$ determines at which energy scale $\mu$ the QCD theory transitions from $N_{F}$ to $N_{F}+1$ in the Variable Flavor Number Scheme (VFNS) for the evolution of the Parton Distribution Functions (PDFs) and strong coupling $\alpha_S(\mu)$. We study the variation of the matching scales, and their impact on a global PDF fit of the combined HERA data. As the choice of the matching scale $\mu_{m}$ effectively is a choice of scheme, this represents a theoretical uncertainty; ideally, we would like to see minimal dependence on this parameter. For the transition across the charm quark (from $N_{F}=3$ to $4$), we find a large $\mu_m=\mu_{c}$ dependence of the global fit $\chi^2$ at NLO, but this is significantly reduced at NNLO. For the transition across the bottom quark (from $N_{F}=4$ to $5$), we have a reduced $\mu_{m}=\mu_b$ dependence of the $\chi^2$ at both NLO and NNLO as compared to the charm. This feature is now implemented in xFitter 2.0.0, an open source QCD fit framework.