$N\pi$-state contamination in lattice calculations of the nucleon electromagnetic form factors

TL;DR

This paper uses chiral perturbation theory to estimate the nucleon-pion-state contamination in lattice calculations of nucleon electromagnetic form factors, revealing a +5% effect on electric and a -5% effect on magnetic form factors at typical source-sink separations.

Contribution

It provides the first leading-order estimate of nucleon-pion-state contamination in lattice form factors using chiral perturbation theory, depending on few known constants.

Findings

Nucleon-pion-state contamination causes about +5% deviation in electric form factor at 2 fm separation.

Magnetic form factor underestimates by approximately 5%, decreasing with higher Q^2.

Results align reasonably with existing lattice data at 1.6 fm separation.

Abstract

The nucleon-pion-state contribution to QCD two-point and three-point functions relevant for lattice calculations of the nucleon electromagnetic form factors are studied in chiral perturbation theory. To leading order the results depend on a few experimentally known low-energy constants only, and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the electric form factor $G_{\rm E}(Q^2)$ is at the +5 percent level for a source-sink separation of 2 fm, and it increases with increasing momentum transfer $Q^2$. For the magnetic form factor the nucleon-pion-state contribution leads to an underestimation of $G_{\rm M}(Q^2)$ by about 5 percent that decreases with increasing $Q^2$. For smaller source-sink separations that are accessible in present-day lattice simulations the impact is larger, although the ChPT results may not be applicable for such small time separations. Still, a comparison with lattice data at $t\approx 1.6$ fm works reasonably well.