The experimental data from quasi-elastic electron scattering from ${}^{12}\mathrm{C}$ 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 $m_N^{*}=0.8m_N$, 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 quasi-elastic region, about two thirds of the total 2500 data. Regardless of the momentum and energy transfer, this method automatically excludes the data that are not dominated by the quasi-elastic process. The resulting band of data reflects deviations from perfect universality and can be used to characterize experimentally the quasi-elastic 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 quasi-elastic band into a theoretical prediction band for the neutrino-scattering cross section that is compatible with the recent measurements and slightly more accurate.

• Received 20 May 2015
• Revised 29 June 2015

DOI:https://doi.org/10.1103/PhysRevC.92.054607