Nucleon form factors from quenched lattice QCD with domain wall fermions

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 pseudoscalar [${F}_{P}({q}^{2})$] form factors. Our simulations are performed on three different lattice sizes ${L}^{3}\ifmmode\times\else\texttimes\fi{}T={24}^{3}\ifmmode\times\else\texttimes\fi{}32$, ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$, and ${12}^{3}\ifmmode\times\else\texttimes\fi{}32$ with a lattice cutoff of ${a}^{\ensuremath{-}1}\ensuremath{\approx}1.3\text{ }\text{ }\mathrm{GeV}$ and light quark masses down to about $1/4$ the strange quark mass (${m}_{\ensuremath{\pi}}\ensuremath{\approx}390\text{ }\text{ }\mathrm{MeV}$) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about $(3.6\text{ }\text{ }\mathrm{fm}{)}^{3}$, where the finite volume effects on form factors become negligible and the lower momentum transfers (${q}^{2}\ensuremath{\approx}0.1\text{ }\text{ }{\mathrm{GeV}}^{2}$) 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, and axial-vector form factors are well described by the dipole form, while the induced pseudoscalar 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 pseudoscalar coupling ${g}_{P}={m}_{\ensuremath{\mu}}{F}_{P}(0.88{m}_{\ensuremath{\mu}}^{2})=8.15(54)$, where the errors are statistical errors only. These values agree with experimental values from neutron $\ensuremath{\beta}$ 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 pseudoscalar 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.