Scaling violation and relativistic effective mass from quasielastic electron scattering: implications for neutrino reactions

TL;DR

This paper reanalyzes quasielastic electron scattering data from carbon using a new scaling variable linked to relativistic effective mass, identifying a universal behavior and improving predictions for neutrino scattering cross sections.

Contribution

It introduces a novel scaling analysis based on relativistic effective mass, enabling better data selection and more accurate neutrino reaction predictions.

Findings

Most data fall within a universal scaling region around the relativistic Fermi gas function.

The spread of data indicates fluctuations in the effective mass around 0.8 ± 0.1.

The method improves the accuracy of neutrino scattering cross section predictions.

Abstract

The experimental data from quasielastic electron scattering from $^{12}$C are reanalyzed in terms of a new scaling variable suggested by the interacting relativistic Fermi gas with scalar and vector interactions, which is known to generate a relativistic effective mass for the interacting nucleons. By choosing a mean value of this relativistic effective mass $m_N^* =0.8 m_N$, we observe that most of the data fall inside a region around the inverse parabola-shaped universal scaling function of the relativistic Fermi gas. This suggests a method to select the subset of data that highlight the quasielastic region, about two thirds of the total 2,500 data. Regardless of the momentum and energy transfer, this method automatically excludes the data that are not dominated by the quasielastic process. The resulting band of data reflects deviations from the perfect universality, and can be used to characterize experimentally the quasielastic peak, despite the manifest scaling violation. Moreover we show that the spread of the data around the scaling function can be interpreted as genuine fluctuations of the effective mass $M^* \equiv m^*_N/m_N \sim 0.8 \pm 0.1$. Applying the same procedure we transport the scaling quasielastic band into a theoretical prediction band for neutrino scattering cross section that is compatible with the recent measurements and slightly more accurate.