Global superscaling analysis of quasielastic electron scattering with relativistic effective mass

Abstract

We present a global analysis of the inclusive quasielastic electron scattering data with a superscaling approach with relativistic effective mass. The SuSAM* model exploits the approximation of factorization of the scaling function $f^*(\psi^*)$ out of the cross section under quasifree conditions. Our approach is based on the relativistic mean field theory of nuclear matter where a relativistic effective mass for the nucleon encodes the dynamics of nucleons moving in presence of scalar and vector potentials. Both the scaling variable $\psi^*$ and the single nucleon cross sections include the effective mass as a parameter to be fitted to the data alongside the Fermi momentum $k_F$. Several methods to extract the scaling function and its uncertainty from the data are proposed and compared. The model predictions for the quasielastic cross section and the theoretical error bands are presented and discussed for nuclei along the periodic table from $A=2$ to $A=238$: $^2$H, $^3$H, $^3$He, $^4$He, $^{12}$C, $^{6}$Li, $^{9}$Be, $^{24}$Mg, $^{59}$Ni, $^{89}$Y, $^{119}$Sn, $^{181}$Ta, $^{186}$W, $^{197}$Au, $^{16}$O, $^{27}$Al, $^{40}$Ca, $^{48}$Ca, $^{56}$Fe, $^{208}$Pb, and $^{238}$U. We find that more than 9000 of the total $\sim 20000$ data fall within the quasielastic theoretical bands. Predictions for $^{48}$Ti and $^{40}$Ar are also provided for the kinematics of interest to neutrino experiments.