Order α_s^2 Contributions to charm production in charged-current deep-inelastic lepton-hadron scattering

TL;DR

This work addresses the ${\cal O}(\alpha_s^2)$ corrections to charm production in charged-current deep-inelastic scattering by deriving asymptotic heavy-quark coefficient functions in the limit $Q^2 \gg m^2$ and applying them to both fixed-flavour and variable-flavour-number schemes. The authors relate CC heavy-quark coefficients to their electromagnetic counterparts via heavy-quark operator matrix elements, enabling practical NNLO-like estimates in kinematic regions where exact results are unavailable. They find that the corrections are modest for $F_{2,c}$ but sizable for $F_{3,c}$ at small $x$ and large $Q^2$ due to logarithmic enhancements, highlighting the necessity of resumming these terms in VFNS for reliable predictions. The results have important implications for interpreting charm data and for the extraction of the strange-quark density from CC and EM processes, especially at small $x$.

Abstract

The most important part of the order $α_s^2$ corrections to the charm component of the charged-current structure functions $F_2(x,Q^2)$ and $F_3(x,Q^2)$ have been calculated. This calculation is based on the asymptotic form of the heavy-quark coefficient functions corresponding to the higher order corrections to the W-boson-gluon fusion process. These coefficient functions which are in principle only valid for $Q^2 \gg m^2$ can be also used to estimate the order $α_s^2$ contributions at lower $Q^2$ values provided $x < 0.1$. It turns out that the above corrections are appreciable in the large $Q^2$-region and they explain the discrepancy found for the structure functions between the fixed-flavour scheme (FFS) and the variable-flavour-number scheme (VFNS). These corrections also hamper the extraction of the strange-quark density from the data obtained for the charged-current and the electromagnetic-current processes.

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