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

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.