A Hybrid Scheme for Heavy Flavors: Merging the FFNS and VFNS

We introduce a Hybrid Variable Flavor Number Scheme for heavy flavors, denoted H-VFNS, which incorporates the advantages of both the traditional Variable Flavor Number Scheme (VFNS) as well as the Fixed Flavor Number Scheme (FFNS). By including an explicit $N_F$-dependence in both the Parton Distribution Functions (PDFs) and the strong coupling constant $α_S$, we generate coexisting sets of PDFs and $α_S$ for $N_F=\{3,4,5,6\}$ at any scale $μ$, that are related analytically by the $\overline{\text{MS}}$ matching conditions. The H-VFNS resums the heavy quark contributions and provides the freedom to choose the optimal $N_F$ for each particular data set. Thus, we can fit selected HERA data in a FFNS framework, while retaining the benefits of the VFNS to analyze LHC data at high scales. We illustrate how such a fit can be implemented for the case of both HERA and LHC data.

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