ar X iv : n uc l - th / 0 50 90 22 v 2 1 2 Se p 20 05 Superscaling and Charge - changing Neutrino Cross Sections
چکیده
High-quality predictions for neutrino-nucleus cross sections are needed for use in ongoing experimental studies of neutrino oscillations at GeV energies, where a fully relativistic treatment of the neutrino-nucleus scattering is mandatory, but hard to achieve. Of course any reliable calculation for neutrino scattering should first be tested against electron scattering in the same kinemati-cal conditions. In fact, while relativistic modeling of the nuclear dynamics is capable of getting the basic size and shape of the inclusive cross section, it can hardly account for important details of the response. Specifically, the data display a long tail which is largely absent in most modeling, possibly due to the absence of classes of short-range correlation effects and to the treatment of final-state interactions. In order to overcome these difficulties, instead of using a specific nuclear model, we propose here a method for extracting informations on the nuclear dynamics from electron scattering experiments and use them to predict the neutrino-nucleus cross section. The approach is based on the superscaling behavior of the electron-nucleus cross section in both the quasi-elastic (QE) and ∆ peaks. Detailed studies of superscaling can be found in Refs. [1,2]; here we simply recall the basic idea. By dividing the experimental inclusive cross section for various momentum transfers q and nuclei (or, equivalently, Fermi momentum k F) by an appropriate single-nucleon cross section, a reduced cross section f , called the superscaling function, is obtained, which embodies the nuclear dynamics. This can be plotted versus a well-chosen scaling variable: if no dependence of f upon q is observed , we call this behavior scaling of the first kind, whereas if no dependence occurs on the specific nucleus, we call it scaling of the second kind; if both types of scaling behavior are found we say that superscaling occurs. Several choices for the appropriate scaling variable have been proposed in the literature. Here we choose that which naturally emerges from the relativistic Fermi gas (RFG) model. In this framework the nuclear response functions in both the quasi-elastic (X = QE) and ∆-resonance (X = ∆) regions have the general structure