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 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 ${\alpha }_S$, we generate coexisting sets of PDFs and ${\alpha }_S$ for $N_F=\{3,4,5,6\}$ at any scale $\mu$ that are related analytically by the $\overline{\mathrm{MS}}$ 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.

• Received 1 July 2013

DOI:https://doi.org/10.1103/PhysRevD.88.074032