A relativistic coupled-channel formalism for electromagnetic form factors of 2-body bound states

TL;DR

This paper develops a Poincaré invariant formalism using point-form relativistic quantum mechanics to accurately compute electromagnetic form factors of two-body bound states, addressing and removing unphysical contributions.

Contribution

It introduces a coupled-channel approach based on the Bakamjian-Thomas framework that fully accounts for retardation effects and corrects for cluster property violations.

Findings

Successfully calculated pion and deuteron form factors.

Identified and eliminated unphysical spurious contributions.

Demonstrated the formalism's consistency with physical current properties.

Abstract

We discuss a Poincar\'e invariant coupled-channel formalism which is based on the point-form of relativistic quantum mechanics. Electromagnetic scattering of an electron by a 2-body bound state is treated as a 2-channel problem for a Bakamjian-Thomas-type mass operator. In this way retardation effects in the photon-exchange interaction are fully taken into account. The electromagnetic current of the 2-body bound state is then extracted from the one-photon-exchange optical potential. As an application we calculate electromagnetic pion and deuteron form factors. Wrong cluster properties, inherent in the Bakamjian-Thomas framework, are seen to cause spurious (unphysical) contributions in the current. These are separated and eliminated in an unambiguous way such that one is left with a current that has all the desired properties.