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 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.