Impact of the heavy-quark matching scales in PDF fits

Abstract

Abstract We investigate the impact of displaced heavy-quark matching scales in a global fit. The heavy-quark matching scale $$\mu _{m}$$ μ m determines at which energy scale $$\mu $$ μ the QCD theory transitions from $$N_{F}$$ N F to $$N_{F}+1$$ N F + 1 in the variable flavor number scheme (VFNS) for the evolution of the parton distribution functions (PDFs) and strong coupling $$\alpha _S(\mu )$$ 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 $$\mu _{m}$$ 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 $$N_{F}=3$$ N F = 3 to 4), we find a large $$\mu _m=\mu _{c}$$ μ m = μ c dependence of the global fit $$\chi ^2$$ χ 2 at NLO, but this is significantly reduced at NNLO. For the transition across the bottom quark (from $$N_{F}=4$$ N F = 4 to 5), we have a reduced $$\mu _{m}=\mu _b$$ μ m = μ b dependence of the $$\chi ^2$$ 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.