Status of Lattice QCD Determination of Nucleon Form Factors and their Relevance for the Few-GeV Neutrino Program

TL;DR

This paper reviews the progress of lattice QCD in calculating nucleon form factors, highlighting recent results, current uncertainties, and their significance for neutrino oscillation experiments, along with future research directions.

Contribution

It provides a comprehensive overview of lattice QCD results for nucleon form factors and outlines a roadmap to improve their reliability for neutrino physics applications.

Findings

LQCD results for $g_A$ agree with experimental data.

Discrepancies exist between LQCD results and existing models for form factors.

A future roadmap is proposed to enhance confidence in LQCD calculations.

Abstract

Calculations of neutrino-nucleus cross sections begin with the neutrino-nucleon interaction, making the latter critically important to flagship neutrino oscillation experiments, despite limited measurements with poor statistics. Alternatively, lattice QCD (LQCD) can be used to determine these interactions from the Standard Model with quantifiable theoretical uncertainties. Recent LQCD results of $g_{\mathrm{A}}$ are in excellent agreement with data, and results for the (quasi-)elastic nucleon form factors with full uncertainty budgets are expected within a few years. We review the status of the field and LQCD results for the nucleon axial form factor, $F_{\mathrm{A}}(Q^2)$, a major source of uncertainty in modeling sub-GeV neutrino-nucleon interactions. Results from different LQCD calculations are consistent, but collectively disagree with existing models, with potential implications for current and future neutrino oscillation experiments. We describe a road map to solidify confidence in the LQCD results and discuss future calculations of more complicated processes, important to few-GeV neutrino oscillation experiments.