Nucleon form factors from quenched lattice QCD with domain wall fermions

TL;DR

This paper presents a quenched lattice QCD calculation of nucleon form factors using domain wall fermions, providing results consistent with experiments for some ratios but underestimating radii, and verifying the axial Ward-Takahashi identity.

Contribution

First quenched lattice QCD calculation of nucleon form factors with domain wall fermions across multiple lattice sizes and quark masses, analyzing q^2 dependence and verifying theoretical relations.

Findings

Form factors well described by dipole and pion-pole models.

Calculated g_A/g_V ratio matches experimental value.

Underestimation of nucleon radii by about 20%.

Abstract

We present a quenched lattice calculation of the weak nucleon form factors: vector (F_V(q^2)), induced tensor (F_T(q^2)), axial-vector (F_A(q^2)) and induced pseudo-scalar (F_P(q^2)) form factors. Our simulations are performed on three different lattice sizes L^3 x T=24^3 x 32, 16^3 x 32 and 12^3 x 32 with a lattice cutoff of 1/a = 1.3 GeV and light quark masses down to about 1/4 the strange quark mass (m_{pi} = 390 MeV) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about (3.6 fm)^3, where the finite volume effects on form factors become negligible and the lower momentum transfers (q^2 = 0.1 GeV^2) are accessible. The q^2-dependences of form factors in the low q^2 region are examined. It is found that the vector, induced tensor, axial-vector form factors are well described by the dipole form, while the induced pseudo-scalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling g_A/g_V=F_A(0)/F_V(0)=1.219(38) and the pseudo-scalar coupling g_P=m_{mu}F_P(0.88m_{mu}^2)=8.15(54), where the errors are statistical erros only. These values agree with experimental values from neutron beta decay and muon capture on the proton. However, the root mean squared radii of the vector, induced tensor and axial-vector underestimate the known experimental values by about 20%. We also calculate the pseudo-scalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.