A relativistic coupled-channel formalism for the pion form factor

TL;DR

This paper develops a relativistic formalism using point-form quantum mechanics to accurately calculate the pion's electromagnetic form factor, ensuring Poincare invariance and addressing cluster-separability issues.

Contribution

It introduces a coupled-channel approach with a Bakamjian-Thomas mass operator to compute the pion form factor within a relativistic framework, establishing equivalence with front-form calculations.

Findings

The formalism guarantees Poincare invariance.

Cluster-separability violations diminish at high invariant mass.

Analytic equivalence with front-form calculations is demonstrated.

Abstract

The electromagnetic form factor of a confined quark-antiquark pair is calculated within the framework of point-form relativistic quantum mechanics. The dynamics of theexchanged photon is explicitly taken into account by treating theelectromagnetic scattering of an electron by a meson as a relativistic two-channel problem for a Bakamjian-Thomas type mass operator. This approach guarantees Poincare invariance. Using a Feshbach reduction the coupled-channel problem can be converted into a one-channel problem for the elastic electron-meson channel. By comparing the one-photon-exchange optical potential at the constituent and hadronic levels, we are able to unambiguously identify the electromagnetic meson form factor. Violations of cluster-separability properties, which are inherent in the Bakamjian-Thomas approach, become negligible for sufficiently large invariant mass of the electron-meson system. In the limit of an infinitely large invariant mass, an equivalence with form-factor calculations done in front-form relativistic quantum mechanics is established analytically.