[Paper Review] Modeling Quasi-elastic Form Factors for Electron and Neutrino Scattering

H. S. Budd, A. Bodek+1 more|ArXiv.org|Aug 2, 2003

Particle Accelerators and Free-Electron Lasers13 citations

TL;DR

This paper re-evaluates quasi-elastic neutrino and electron scattering cross sections using updated nucleon electromagnetic form factors, showing that the non-zero neutron electric form factor $G_E^n$ reduces the extracted axial mass $M_A$ by 0.025 GeV. The study demonstrates that incorrect form factor assumptions can cause >10% errors in cross-section energy dependence, even when $Q^2$ shapes are matched.

ABSTRACT

We calculate the total and differential quasielastic cross sections for neutrino and antineutrino scattering on nucleons using up to date fits to the nucleon elastic electromagnetic form factors $G_E^p$, $G_E^n$, $G_M^p$, $G_M^n$, and weak and pseudoscalar form factors. We find that using the updated non-zero value of $G_E^n$ has a significant effect on both the total and differential neutrino and antineutrino quasielastic cross sections. Previous extractions of the weak axial form factor from neutrino scattering data are sensitive to the assumptions that were used for the vector form factors. We perform a re-analysis of previous neutrino data using updated form factors and obtain updated value of the axial vector mass.

Motivation & Objective

• To improve predictions of quasi-elastic neutrino and electron scattering cross sections by incorporating the latest nucleon electromagnetic form factors.
• To re-evaluate the extracted axial vector mass $M_A$ from neutrino scattering data using updated form factors and $g_A = -1.267$.
• To quantify the impact of form factor uncertainties on neutrino cross-section energy dependence and $Q^2$-dependence.
• To assess the limitations of the Fermi gas model in describing nuclear effects in heavy targets and identify the need for refined nuclear corrections.

Proposed method

• Uses the conserved vector current (CVC) hypothesis to relate electron scattering form factors $G_E^p$, $G_E^n$, $G_M^p$, $G_M^n$ to neutrino scattering vector form factors.
• Applies updated fits to $G_E^p$ and $G_E^n$ from SLAC and Jefferson Lab data, replacing the traditional dipole approximation.
• Calculates total and differential cross sections for neutrino and antineutrino scattering using the hadronic current formalism with $F_A(q^2)$, $F_V^1(q^2)$, and $\xi F_V^2(q^2)$ form factors.
• Performs a re-analysis of historical neutrino scattering data using the BBA-2003 form factors to extract a revised $M_A$ value.
• Compares predictions using BBA-2003 form factors against dipole form factors and experimental data, including $Q^2$-dependence and energy-dependent cross sections.
• Evaluates nuclear effects using a Fermi gas model with 25 MeV binding energy and 220 MeV Fermi momentum, and considers modifications like high-momentum tails.

Experimental results

Research questions

• RQ1 How do updated nucleon electromagnetic form factors affect the predicted quasi-elastic neutrino and antineutrino cross sections?
• RQ2 What is the impact of a non-zero $G_E^n$ on the extracted axial mass $M_A$ from neutrino scattering data?
• RQ3 To what extent do incorrect form factor assumptions introduce systematic errors in the energy dependence of neutrino cross sections?
• RQ4 Why do calculations with updated form factors still show discrepancies with data from heavy targets, and what nuclear effects may be missing?

Key findings

• The inclusion of a non-zero $G_E^n$ significantly affects both total and differential neutrino and antineutrino quasi-elastic cross sections.
• The re-analysis of previous neutrino data using updated form factors and $g_A = -1.267$ reduces the extracted axial mass $M_A$ by 0.025 GeV compared to earlier extractions.
• Even when $Q^2$-dependence is matched, using incorrect form factors can lead to cross-section errors of up to 7.5% due to differences in energy dependence.
• The discrepancy between calculations and data on heavy targets persists, with anti-neutrino data on heavy nuclei systematically below predictions, suggesting limitations of the Fermi gas model.
• The ratio of cross sections using BBA-2003 form factors with $M_A = 1.00$ GeV to dipole form factors with $M_A = 1.11$ GeV shows differences as large as 12% at high energies.
• Accurate determination of quasi-elastic cross sections requires precise measurement of both the normalized cross section versus energy and the $Q^2$-distribution shape.