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Register a new userImpact of the heavy quark matching scales in PDF fits
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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.
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xFitter is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton for many different kinds of analyses in Quantum Chromodynamics (QCD). It incorporates experimental data from a wide range of experiments including fixed-target, Tevatron, HERA, and LHC. xFitter version 2.0.0 has recently been released, and offers an expanded set of tools and options. The new xFitter 2.0.0 program links to the APFEL code which has implemented generalized matching conditions that enable the switch from $N_F$ to $N_F+1$ active flavors at an arbitrary matching scale $mu_m$. This enables us to generalize the transition between a FFNS and a VFNS and essentially vary continuously between the two schemes; in this sense the matching scale $mu_m$ allows us to unify the FFNS and VFNS in a common framework. This paper provides a brief overview of xFitter with emphasis of these new features.
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