Longitudinal and Transverse Scaling Functions within the Coherent Density Fluctuation Model

TL;DR

This paper introduces a modified Coherent Density Fluctuation Model (CDFM) to better describe superscaling in inclusive electron scattering and extends its application to neutrino scattering, showing improved agreement with experimental data.

Contribution

A new modified CDFM approach is developed for calculating scaling functions, enhancing the description of electron and neutrino scattering in nuclei.

Findings

The modified CDFM accurately reproduces electron scattering cross sections.

The model successfully extends to neutrino scattering at 1 GeV.

Superscaling behavior is validated against experimental data.

Abstract

We extend our previous description of the superscaling phenomenon in inclusive electron scattering within the Coherent Density Fluctuation Model (CDFM). This model is a natural extension to finite nuclei of the Relativistic Fermi Gas Model (RFG) within which the scaling variable $\psi^{\prime}$ was introduced. In this work we propose a new modified CDFM approach to calculate the total, longitudinal and transverse scaling functions built up from the hadronic tensor and the longitudinal and transverse response functions in the RFG. We test the superscaling behavior of the new CDFM scaling functions by calculating the cross sections of electron scattering (in QE- and $\Delta$-region for nuclei with $12\leq A\leq208$ at different energies and angles) and comparing to available experimental data. The new modified CDFM approach is extended to calculate charge-changing neutrino and antineutrino scattering on $^{12}$C at 1 GeV incident energy.