Form Factors of Few-Body Systems: Point Form Versus Front Form

TL;DR

This paper develops a relativistic point-form approach for calculating electroweak form factors of few-body systems, aligning with covariant light-front results, and addresses unphysical contributions inherent in the Bakamjian-Thomas framework.

Contribution

It introduces a point-form formalism that reproduces covariant light-front results and provides a method to separate unphysical contributions in form factor calculations.

Findings

Form factors agree with covariant light-front results.

Unphysical contributions can be separated and corrected.

Results for heavy-light systems and Isgur-Wise function discussed.

Abstract

We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states that leads to results which resemble those obtained within the covariant light-front formalism of Carbonell et al. Our starting points are the physical processes in which such form factors are measured, i.e. electron scattering off the bound state, or the semileptonic weak decay of the bound state. These processes are treated by means of a coupled-channel framework for a Bakamjian-Thomas type mass operator. A current with the correct covariance properties is then derived from the pertinent leading-order electroweak scattering or decay amplitude. As it turns out, the electromagnetic current is affected by unphysical contributions which can be traced back to wrong cluster properties inherent in the Bakamjian-Thomas construction. These spurious contributions, however, can be separated uniquely, as in the covariant light-front approach. In this way we end up with form factors which agree with those obtained from the covariant light-front approach. As an example we will present results for electroweak form factors of heavy-light systems and discuss the heavy-quark limit which leads to the famous Isgur-Wise function.