Effective Spectral Function for Quasielastic Scattering on Nuclei

TL;DR

The paper introduces an effective spectral function (ESF) that better models quasielastic scattering on nuclei by incorporating final state interactions, improving agreement with electron scattering data compared to traditional spectral functions.

Contribution

It proposes a modified effective spectral function (ESF) that accurately describes QE scattering kinematics and aligns with electron scattering data, addressing limitations of existing spectral functions.

Findings

ESF matches electron QE scattering data.

Traditional spectral functions disagree with superscaling predictions.

ESF combined with transverse enhancement predicts cross sections accurately.

Abstract

Spectral functions that are used in neutrino event generators to model quasielastic (QE) scattering from nuclear targets include Fermi gas, Local Thomas Fermi gas (LTF), Bodek-Ritchie Fermi gas with high momentum tail, and the Benhar-Fantoni two dimensional spectral function. We find that the $\nu$ dependence of predictions of these spectral functions for the QE differential cross sections (${d^2\sigma}/{dQ^2 d\nu}$) are in disagreement with the prediction of the $\psi'$ superscaling function which is extracted from fits to quasielastic electron scattering data on nuclear targets. It is known that spectral functions do not fully describe quasielastic scattering because they only model the initial state. Final state interactions distort the shape of the differential cross section at the peak and increase the cross section at the tails of the distribution. We show that the kinematic distributions predicted by the $\psi'$ superscaling formalism can be well described with a modified {\it {effective spectral function}} (ESF). By construction, models using ESF in combination with the transverse enhancement contribution correctly predict electron QE scattering data.