Scaling violation and relativistic effective mass from quasi-elastic electron scattering: Implications for neutrino reactions

Abstract

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 ${m}_{N}^{*}=0.8{m}_{N}$, 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 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 ${M}^{*}\ensuremath{\equiv}{m}_{N}^{*}/{m}_{N}\ensuremath{\sim}0.8\ifmmode\pm\else\textpm\fi{}0.1$. 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.