Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory
M. Buza, Y. Matiounine, J. Smith, W. L. van Neerven
TL;DR
The paper analyzes charm electroproduction in deep-inelastic scattering by comparing fixed-order perturbation theory (FOPT) with the variable-flavour number scheme (VFNS). It derives a VFNS representation of the structure functions from FOPT through mass factorization and heavy-quark operator-matrix elements, establishing how n_f and n_f+1 parton densities are related. The study finds that at Q^2 ≳ 20 GeV^2 the exact and asymptotic heavy-quark contributions to F2 coincide, while VFNS generally yields larger charm contributions and improved perturbative stability (smaller higher-order corrections) for Q^2 ≳ 10 GeV^2, with threshold effects mitigated in VFNS. The results have implications for PDF parametrizations and underline the VFNS as a robust framework for predicting charm structure functions at high Q^2, while recognizing FOPT near threshold. Overall, the work clarifies the regime of validity for each approach and demonstrates how resumming heavy-quark logarithms via VFNS enhances predictive power in DIS charm production.
Abstract
Starting from fixed-order perturbation theory (FOPT) we derive expressions for the heavy-flavour components of the deep-inelastic structure functions FL and F2 in the variable-flavour number scheme (VFNS). These expressions are valid in all orders of perturbation theory. This derivation establishes a relation between the parton densities parametrized at N and N light flavours. The consequences for the existing parametrizations of the parton densities are discussed. Further we show that in charm electroproduction the exact and asymptotic expressions for the heavy-quark coefficient functions yield identical results for F2 when Q^2>20 (GeV/c)^2. We also study the differences between the FOPT and the VFNS descriptions for F2. It turns out that the charm structure function in the VFNS is larger than the one obtained in FOPT over the whole Q^2-range. Furthermore inspection of the perturbation series reveals that the higher order corrections in the VFNS are smaller than those present in FOPT for Q^2>10 (GeV/c)^2. Therefore the VFNS gives a better prediction for the charm structure function at large Q^2-values than FOPT.