Form factors of the $\rho$ meson from effective field theory and the lattice

TL;DR

This paper introduces a novel method combining background fields and the Feynman-Hellmann theorem to calculate the electromagnetic form factors of the rho meson, providing initial estimates and outlining lattice computation procedures.

Contribution

It applies a new approach to rho meson form factors, matching results to Chiral Perturbation Theory and outlining lattice calculation procedures.

Findings

Substantial contact contributions to rho meson form factors.

First crude estimates of all three rho meson form factors.

A procedure for lattice calculations is proposed.

Abstract

The calculation of resonance form factors in effective field theory as well as on the lattice is a highly challenging task. In a recent paper, we proposed a novel method based on the introduction of a background field and the Feynman-Hellmann theorem to address the problem, and applied it to a toy model. In the present work we use this method for the electromagnetic form factors of the $\rho$-meson. By matching the results to Chiral Perturbation Theory, we provide a first, crude estimate of all three form factors of the $\rho$-meson within the effective field theory. Contact contributions to these form factors turn out to be substantial. A procedure for lattice calculations is outlined, paving the way for an ab initio approach to the problem.