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

TL;DR

The paper proposes a new hybrid scheme, H-VFNS, that combines advantages of FFNS and VFNS for heavy flavor analysis, allowing flexible and accurate data fitting across different energy scales.

Contribution

A novel Hybrid Variable Flavor Number Scheme (H-VFNS) that explicitly incorporates $N_F$ dependence in PDFs and $ abla_S$, enabling optimized data analysis across energy scales.

Findings

H-VFNS generates coexisting PDFs for multiple $N_F$ values.

It allows fitting HERA data in FFNS while analyzing LHC data with VFNS benefits.

The scheme is demonstrated with combined HERA and LHC data analysis.

Abstract

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 $\alpha_S$, 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 $\overline{\text{MS}}$ 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.