Heavy-quark initiated charged-current deep-inelastic scattering coefficient functions through $\mathcal{O}(\alpha_s^2)$

TL;DR

This paper calculates the heavy-quark initiated charged-current deep-inelastic scattering coefficient functions up to second order in the strong coupling, including full mass dependence, to improve theoretical predictions in particle physics.

Contribution

It provides the first complete analytical computation of these coefficient functions at $ ext{O}(oldsymbol{ ext{alpha}_s^2})$ with full mass dependence, suitable for implementation in variable-flavor schemes.

Findings

Analytical expressions derived in terms of generalized polylogarithms.

Results compatible with decoupling scheme for $n_L$ light flavors.

Facilitates more accurate theoretical predictions in QCD analyses.

Abstract

We compute the coefficient functions for heavy-quark initiated charged-current deep-inelastic scattering through $\mathcal{O}(\alpha_s^2)$, retaining full mass dependence for a single heavy-quark flavor. The calculation employs a cut-based approach to isolate individual diagram contributions and to derive differential equations for the relevant master integrals, which are solved analytically in terms of generalized polylogarithms. The results are presented in the decoupling scheme for $n_L$ light active flavors, facilitating their direct implementation in variable-flavor number schemes such as ACOT and FONLL.