Impact of the heavy quark matching scales in PDF fits

Abstract

We investigate the impact of displaced heavy quark matching scales in a global fit. The heavy quark matching scale $μ_{m}$ determines at which energy scale $μ$ 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 $α_S(μ)$. 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 $μ_{m}$ 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 $μ_m=μ_{c}$ dependence of the global fit $χ^2$ 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 $μ_{m}=μ_b$ dependence of the $χ^2$ 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.

18 pages, 12 figures. Updated to match published version