The background field method on the lattice

TL;DR

This paper investigates the impact of background electric fields on lattice QCD simulations, specifically analyzing how they influence the quark hopping matrix and calculating neutron electric polarizability at various quark masses.

Contribution

It introduces a formulation for incorporating background electric fields into lattice QCD and provides the first simulation results for neutron polarizability at low pion masses.

Findings

Neutron electric polarizability is approximately constant at ~1.5×10^{-4} fm^3 for the quark masses studied.

The polarizability is positive but smaller than experimental values due to large quark masses.

The method clarifies how to properly implement electric fields in lattice simulations.

Abstract

The background field method has been used successfully to determine hadron electromagnetic polarizabilities. Recently questions have been raised regarding the proper way to deal with the electric field on the lattice. In this paper, we show how the presence of a background electric field affects the quark hopping matrix. We use this formulation to carry out simulations on quenched configurations, and we present the results for neutron electric polarizability for pion masses as low as $500\MeV$. We find that the polarizability is roughly constant for the quark masses considered, $\alpha\sim 1.5 \times 10^{-4} \fm^3$. While the polarizability is positive, it is significantly smaller than the experimental value due to the fact that the quark masses used are too large.