Abstract
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.
Highlights
We investigate the impact of displaced heavyquark matching scales in a global fit
The heavy-quark matching scale μm determines at which energy scale μ the QCD theory transitions from NF to NF + 1 in the variable flavor number scheme (VFNS) for the evolution of the parton distribution functions (PDFs) and strong coupling αS(μ)
For the transition across the charm quark, we find a large μm = μc dependence of the global fit χ 2 at NLO, but this is significantly reduced at NNLO
Summary
A generalized formulation of the VFNS factorization is based on the Collins–Wilczek–Zee (CWZ) renormalization scheme which involves a sequence of sub-schemes parameterized by the number of active quark flavors (NF ) [20,21]. For each sub-scheme, the NF (active) flavors are renormalized using the MS scheme while the heavy (inactive) flavors are renormalized using zero-momentum subtraction This ensures that to all orders in perturbation theory (i) the results are gauge invariant, (ii) the results for the active NF flavors match the standard MS results, and (iii) the heavy (inactive) flavors manifestly decouple.. This ensures that to all orders in perturbation theory (i) the results are gauge invariant, (ii) the results for the active NF flavors match the standard MS results, and (iii) the heavy (inactive) flavors manifestly decouple.3 Both the DGLAP evolution kernels for the NF active PDFs and the renormalization group equation for. The freedom to arbitrarily choose the matching scale μm (and decide where to place the discontinuities) will have a number of advantages, as the subsection will demonstrate
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