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We introduce a Hybrid Variable Flavor Number Scheme (H-VFNS) for heavyflavors, which incorporates the advantages of both the traditional VariableFlavor Number Scheme (VFNS) as well as the Fixed Flavor Number Scheme (FFNS).We include an explicit dependence on number of active flavors $N_F$ in both theParton Distribution Functions (PDFs) and the strong coupling constant$\alpha_{S}$. This results in sets of coexisting PDFs and $\alpha_{S}$ for$N_F=\{3,4,5,6\}$, that are related analytically by the $\overline{\rm MS}$matching conditions. The H-VFNS resums the heavy quark contributions andprovides 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 thebenefits of the VFNS to analyze LHC data at high scales. We illustrate how sucha fit can be implemented for the case of both HERA and LHC data.

A $N_F$-Dependent VFNS for Heavy Flavors: Merging the FFNS and VFNS