Nucleon-pion-state contamination in lattice computations of the nucleon electromagnetic form factors

TL;DR

This paper uses chiral perturbation theory to estimate nucleon-pion-state contamination in lattice calculations of nucleon electromagnetic form factors, revealing a few percent level effects that vary with momentum transfer and source-sink separation.

Contribution

It provides the first leading-order chiral perturbation theory estimates of nucleon-pion-state contamination in lattice form factor calculations, depending on experimentally known constants.

Findings

Nucleon-pion-state contribution to G_E(Q^2) is about +5% at 2 fm separation.

G_M(Q^2) is underestimated by about -5% due to nucleon-pion states.

Impact of contamination increases with larger Q^2 and smaller source-sink separations.

Abstract

The nucleon-pion-state contributions 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 these time separations a comparison with recent lattice data works reasonably well.