Chiral Limit of Nucleon Lattice Electromagnetic Form Factors

TL;DR

This study computes nucleon electromagnetic form factors using quenched lattice QCD, extrapolates to the chiral limit, and compares results with experimental data, revealing some discrepancies and methodological insights.

Contribution

It introduces a zero-momentum technique for magnetic moments and provides lattice QCD calculations of nucleon form factors near the chiral limit.

Findings

Proton and neutron magnetic moments are 10-15% lower than experimental values.

The dipole to nucleon mass ratio is about 7% lower than experimental data.

Positive neutron electric form factors are obtained but poorly fit by phenomenological models.

Abstract

We calculate electric and magnetic form factors of protons and neutrons in quenched Monte Carlo lattice QCD on a $16^3\times 24$ lattice at $\beta = 6.0$ using Wilson fermions. We employ a method which characterizes one of the nucleon fields as a fixed zero-momentum secondary source. Extrapolating the overall data set to the chiral limit, we find acceptable fits for either dipole or monopole forms and extract proton and neutron magnetic moments, the magnitude of which are $10$ to $15\%$ low compared to experiment. In the extrapolation of the dipole fit of the form factors, we find that the dipole to nucleon mass ratio is about $7\%$ low compared to experiment. In addition, we obtain positive values of the neutron electric form factor, which, however, are poorly represented by a popular phenomenological form at intermediate to small $\kappa$ values. A zero-momentum technique for extracting hadron magnetic moments is briefly discussed and shown to yield unrealistically small magnetic moment values.