Heavy Quark mass effects in charged-current Deep-Inelastic Scattering at NNLO in the ACOT scheme

The approximate SACOT-$\chi$ scheme for heavy quark production in deep-inelastic scattering was initially formulated for the neutral current structure functions $F_2$ and $F_L$. We extend this approach to the charged current case (also including $F_3$), and thereby complete the definitions for the most relevant inclusive structure functions. Furthermore, we implement these structure functions in the open-source code $\texttt{APFEL++}$ which provides fast numerical evaluations over a wide kinematic range; this addition to the $\texttt{APFEL++}$ code is publicly available, with details provided in the appendix. This SACOT-$\chi$ implementation enables, for the first time, detailed numerical insights on the mass dependence of the structure functions and cross sections in the $(x,Q^2)$-plane for both neutral and charged current processes. We consider kinematic regions relevant for the experimental measurements from fixed-target $\nu$DIS experiments (NuTeV, CCFR and Chorus) and HERA, and also projections for the upcoming EIC. In particular, the $\nu$DIS experiments reveal a surprisingly strong dependence on the mass effects, offering valuable insights that may help resolve long-standing challenges in accurately describing these datasets.