Improved superscaling description of electron and charged-current neutrino quasielastic scattering using effective mass dynamics

We present an improved version of the Superscaling Analysis with Relativistic Effective Mass, denoted as SuSAM-v2. In the original SuSAM model, a universal scaling function was fitted to a selected set of quasielastic electron scattering <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">(</a:mo><a:mi>e</a:mi><a:mo>,</a:mo><a:msup><a:mi>e</a:mi><a:mo>′</a:mo></a:msup><a:mo stretchy="false">)</a:mo></a:math> cross section data, using a phenomenological ansatz inspired by the relativistic mean field model of nuclear matter. In this work, we refine the procedure by first fitting a longitudinal scaling function directly to experimental longitudinal response data. Subsequently, a separate transverse scaling function is extracted from purely transverse data, after subtracting the longitudinal contribution already determined. We find that the resulting transverse scaling function must exhibit an explicit dependence on the momentum transfer <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>q</e:mi></e:math> in order to reproduce all kinematics consistently. The resulting SuSAM-v2 model simultaneously describes inclusive quasielastic cross sections and both longitudinal and transverse response functions in electron scattering. The model is then applied to neutrino-nucleus scattering, showing an improved prediction compared to the previous SuSAM-v1 version, due to a more accurate treatment of the relative contributions of the longitudinal and transverse weak nuclear responses.