Analytic results for heavy-quark contributions to charged-current DIS at NNLO

Abstract

We present analytic results for the next-to-next-to-leading-order QCD corrections to heavy-quark production in charged-current deep-inelastic scattering, retaining the exact dependence on the charm quark mass. We compute the complete partonic coefficient functions for the structure functions $F_2$, $F_L$, and $F_3$ in the quark and gluon channels, including contributions with up to three heavy quarks in the final state. Working within the reverse-unitarity framework, we use integration-by-parts and canonical differential-equations techniques to express all contributions with at most two final-state heavy quarks in terms of manifestly real Goncharov polylogarithms which allow for a robust and efficient numerical evaluation. The three-heavy-quark contribution involves elliptic structures for which we give a general representation in terms of Chen iterated integrals, as well as expressions in terms of rapidly convergent expansions that are valid in the perturbative $Q\gtrsim 5~{\rm GeV}$ region and also allow for a flexible and fast numerical evaluation. We validate our results against known exact results at lower orders, massless NNLO coefficient functions, and existing leading-power expansions in the asymptotic limit where the virtuality $Q$ is much larger than the charm mass.