Analysis of the kinematic boundaries of the quasi-elastic neutrino-nucleus cross section in the superscaling model with a relativistic effective mass

TL;DR

This paper derives analytical boundaries for the CCQE neutrino-nucleus cross section in the superscaling model with relativistic effective mass, highlighting its suitability for Monte Carlo event generators and analyzing total cross section enhancements.

Contribution

It provides analytical expressions for the cross section boundaries within the SuSAM* model and demonstrates its advantages for neutrino event simulation over traditional models.

Findings

SuSAM* cross section peaks are nearly flat across neutrino energies.

Enhanced total cross section in SuSAM* is due to high-momentum components.

Analytical boundaries improve Monte Carlo neutrino event generation.

Abstract

In this work we obtain the analytical expressions for the boundaries of the charged current quasi-elastic double differential cross section in terms of dimensionless energy and momentum transfers, for the Relativistic Fermi Gas (RFG) and the Super-Scaling approach with relativistic effective mass (SuSAM*) models, within the scaling formalism. In addition, we show that this double differential cross section in the scaling formalism has very good properties to be implemented in the Monte Carlo (MC) neutrino event generators, particularly because its peak is almost flat with the (anti)neutrino energy. This makes it especially well-suited for the event generation by the acceptance-rejection method usually used in the neutrino generators. Finally, we analyze the total charged current quasi-elastic (CCQE) cross section $\sigma(E_{\nu})$ for both models and attribute the enhancement observed in the SuSAM* total cross section to the high-momentum components which are present, in a phenomenological way, in its scaling function, while these are absent in the RFG model.