Heavy quark mass effects in charged-current deep-inelastic scattering at approximate NNLO in the Aivazis-Collins-Olness-Tung scheme

The approximate SACOT- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>χ</a:mi> </a:math> scheme for heavy quark production in deep-inelastic scattering was initially formulated for the neutral current structure functions <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>F</c:mi> <c:mn>2</c:mn> </c:msub> </c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>F</e:mi> <e:mi>L</e:mi> </e:msub> </e:math> . We extend this approach to the charged current case (also including <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>F</g:mi> <g:mn>3</g:mn> </g:msub> </g:math> ), and thereby complete the definitions for the most relevant inclusive structure functions. Furthermore, we implement these structure functions in the open-source code ++ which provides fast numerical evaluations over a wide kinematic range; this addition to the ++ code is publicly available, with details provided in the Appendix. This SACOT- <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>χ</i:mi> </i:math> implementation enables detailed numerical insights on the mass dependence of the structure functions and cross sections in the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo stretchy="false">(</k:mo> <k:mi>x</k:mi> <k:mo>,</k:mo> <k:msup> <k:mi>Q</k:mi> <k:mn>2</k:mn> </k:msup> <k:mo stretchy="false">)</k:mo> </k:math> -plane for both neutral and charged current processes. We consider kinematic regions relevant for the experimental measurements from fixed-target <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>ν</o:mi> <o:mi>DIS</o:mi> </o:math> experiments (NuTeV, CCFR, and Chorus) and HERA, and also projections for the upcoming EIC. In particular, the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>ν</q:mi> <q:mi>DIS</q:mi> </q:math> 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.