Theoretical aspects of heavy-flavour electroproduction

TL;DR

This work addresses reliable descriptions of charm quark electroproduction across different momentum transfer scales by comparing TFNS (finite charm mass) and FFNS (massless charm density after matching) approaches and introducing a variable-flavor-number scheme (VFNS) to interpolate between them. It develops ACOT-type and VFNS frameworks, providing two-loop matching conditions for alpha_s and parton densities and explicit heavy-quark coefficient functions with their asymptotic behavior. The VFNS formulation yields reduced scale sensitivity and a smooth transition between regimes, showing compatibility with EMC, H1, and ZEUS data and enabling more accurate global proton PDFs with heavy flavors. Overall, the paper emphasizes precise matching across thresholds as essential for faithful heavy-quark contributions to F_2 and the proton's parton content.

Abstract

We discuss three theoretical schemes to describe charm quark electroproduction.

Figures (5)

• Figure 1: Scale dependence of $F_{2,c}(x=0.05,Q=10 \,{\rm GeV}/c)$.
• Figure 2: $F_{2,c}(x=0.01)$ as a function of $Q$.
• Figure 3: Scale dependence of $F_{2,c}(x=0.05,Q=10 \,{\rm GeV}/c)$.
• Figure 4: $F_{2,c}(x=0.01)$ as functions of $Q$.
• Figure 5: The functions $F_{2,c}^{\rm PDF,(2)}(4,x,Q^2)$ dashed line, $F_{2,c}^{\rm VFNS,(2)}(x,Q^2,m^2)$ solid line and $F_{2,c}^{\rm EXACT,(2)}(3,x,Q^2,m^2)$ dotted line, plotted as a functions of $Q^2$ for fixed $x$. The data points are from the EMC, H1 and ZEUS experiments.