Comparison between variable flavor number schemes for charm quark electroproduction

TL;DR

The paper compares two NNLO variable-flavor-number schemes (CSN and BMSN) for charm quark electroproduction, focusing on mass factorization, matching across three- and four-flavor schemes, and threshold behavior. It develops a four-flavor PDF set from a three-flavor input and analyzes how heavy-quark contributions to structure functions behave in each scheme, including a soft-hard separation controlled by a Δ cut. The study finds that the charm component F_{2,c} is largely insensitive to the scheme, while F_{L,c} exhibits significant threshold-related differences, with CSN potentially producing unphysical negative results near threshold. Based on simplicity and threshold behavior, the authors advocate the BMSN approach as preferable for practical NNLO charm production modeling in deep inelastic scattering.

Abstract

Where appropriate, the abbreviation 'VFNS' is replaced by 'CSN' to indicate the scheme using massive heavy quark coefficient functions proposed in this paper. The text below Eq. (2.13) and between Eqs. (2.33) and (2.36) has been considerably changed.

Figures (7)

• Figure 1: Lowest-order photon-gluon fusion process $\gamma^* + g \rightarrow Q + \bar{Q}$ contributing to the coefficient functions $H_{i,g}^{\rm S,(1)}$.
• Figure 2: Virtual gluon corrections to the process $\gamma^* + g \rightarrow Q + \bar{Q}$ contributing to the coefficient functions $H_{i,g}^{\rm S,(2)}$.
• Figure 3: The bremsstrahlung process $\gamma^* + g \rightarrow Q + \bar{Q} + g$ contributing to the coefficient functions $H_{i,g}^{\rm S,(2)}$.
• Figure 4: Bethe-Heitler process $\gamma^* + q(\bar{q}) \rightarrow Q + \bar{Q} + q(\bar{q})$ contributing to the coefficient functions $H_{i,q}^{\rm PS,(2)}$. The light quarks $q$ and the heavy quarks $Q$ are indicated by dashed and solid lines respectively.
• Figure 5: Compton process $\gamma^*(q) + q(p) \rightarrow Q(p_1) + \bar{Q}(p_2) + q(p')$ contributing to the coefficient functions $L_{i,q}^{\rm NS,(2)}$. The light quarks $q$ and the heavy quarks $Q$ are indicated by dashed and solid lines respectively ($s=(p+q)^2$, $s_{Q\bar{Q}}=(p_1+p_2)^2$ see text).