Impact of the heavy-quark matching scales in PDF fits

We investigate the impact of displaced heavy-quark matching scales in a global fit. The heavy-quark matching scale $$ determines at which energy scale $$ the QCD theory transitions from $$ to $$ in the variable flavor number scheme (VFNS) for the evolution of the parton distribution functions (PDFs) and strong coupling $$ . We study the variation of the matching scales, and their impact on a global PDF fit of the combined HERA data. As the choice of the matching scale $$ 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 $$ to 4), we find a large $$ dependence of the global fit $$ at NLO, but this is significantly reduced at NNLO. For the transition across the bottom quark (from $$ to 5), we have a reduced $$ dependence of the $$ 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.