Improving the description of dimuon production in neutrino-nucleus collisions using the SACOT-$\chi$ scheme

Dimuon production in deeply inelastic scattering between neutrinos and nuclei plays an important role in constraining the strange-quark parton distribution functions (PDFs). Here, we present a self-contained calculation of this process consisting of a next-to-leading order semi-inclusive charmed-hadron production in the SACOT-$\chi$ general-mass variable-flavor-number scheme, followed by a semi-leptonic decay of the charmed hadron. We find that invoking the SACOT-$\chi$ scheme introduces modifications up to $20 \, \%$ in comparison to our previous esimates, where only kinematic mass effects were considered through the slow-rescaling variable. We reiterate our earlier observation that the effective acceptance correction - typically used in global PDF fits as a simplifying approximation - depends on the perturbative order, PDFs, scales, and also on the treatment of heavy-quark effects. We find good agreement with the corresponding data from the NuTeV experiment.