Position space method for the nucleon magnetic moment in lattice QCD

Abstract

The extraction of the magnetic form factor of the nucleon at zero momentum transfer is usually performed by adopting a parametrization for its momentum dependence and fitting the results obtained at finite momenta. We present a position space method that allows us to remove the momentum prefactor in the form factor decomposition and hence compute the magnetic form factor directly at zero momentum without the need to assume a functional form for its momentum dependence. The method is explored on one ensemble using $N_f=2+1+1$ Wilson twisted mass fermions with a light quark mass corresponding to $M_\pi\approx373\mathrm{GeV}$ and a lattice spacing of $a\approx0.082\mathrm{fm}$. We obtain results for the isovector magnetic moment and for the proton and neutron magnetic moments. The value we find for the isovector magnetic moment is larger as compared to fitting the form factor at the discrete values of the lattice momentum transfers using a dipole Ansatz, bringing it closer to the experimental value.