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 \(\mu _{m}\) 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 HERAdata. 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.