Using Electron Scattering Superscaling to predict Charge-changing Neutrino Cross Sections in Nuclei

Superscaling analyses of few-GeV inclusive electron scattering from nuclei are extended to include not only quasielastic processes, but now also into the region where $\Delta$-excitation dominates. It is shown that, with reasonable assumptions about the basic nuclear scaling function extracted from data and information from other studies of the relative roles played by correlation and MEC effects, the residual strength in the resonance region can be accounted for through an extended scaling analysis. One observes scaling upon assuming that the elementary cross section by which one divides the residual to obtain a new scaling function is dominated by the $N\to\Delta$ transition and employing a new scaling variable which is suited to the resonance region. This yields a good representation of the electromagnetic response in both the quasielastic and $\Delta$ regions. The scaling approach is then inverted and predictions are made for charge-changing neutrino reactions at energies of a few GeV, with focus placed on nuclei which are relevant for neutrino oscillation measurements. For this a relativistic treatment of the required weak interaction vector and axial-vector currents for both quasielastic and $\Delta$-excitation processes is presented.