# Impact of the heavy-quark matching scales in PDF fits

The European Physical Journal C, Dec 2017

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.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-017-5407-3.pdf

V. Bertone, D. Britzger, S. Camarda, A. Cooper-Sarkar, A. Geiser, F. Giuli, A. Glazov, E. Godat, A. Kusina, A. Luszczak, F. Lyonnet, F. Olness, R. Plačakytė, V. Radescu, I. Schienbein, O. Zenaiev, The xFitter Developers’ Team:. Impact of the heavy-quark matching scales in PDF fits, The European Physical Journal C, 2017, 837, DOI: 10.1140/epjc/s10052-017-5407-3