A Relativistic Coupled-Channel Formalism for the Pion Form Factor

¹ Institut für Physik, Universität Graz, A-8010 Graz, Austria
² BE-OP Division, CERN, CH-1211 Geneve 23, Switzerland
³ Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa, USA

^a e-mail: elmar.biernat@uni-graz.at

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 the exchanged photon is explicitly taken into account by treating the electromagnetic 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 su?ciently large invariant mass of the electron-meson system. In the limit of an in?nitely large invariant mass, an equivalence with form-factor calculations done in front-form relativistic quantum mechanics is established analytically.