Eur. Phys. J. A 13, 461-469 (2002)
DOI: 10.1140/epja/iepja1245

Validity of the one-body current for the calculation of form factors in the point form of relativistic quantum mechanics

B. Desplanques and L. Theußl

Institut des Sciences Nucléaires (UMR CNRS/IN2P3-UJF), F-38026 Grenoble Cedex, France

desplanq@isn.in2p3.fr
Lukas.Theussl@uv.es

(Received: 11 July 2001 / Revised version: 9 November 2001 Communicated by V. Vento)

Abstract
Form factors are calculated in the point form of relativistic quantum mechanics for the lowest energy states of a system made of two scalar particles interacting via the exchange of a massless boson. They are compared to the exact results obtained by using solutions of the Bethe-Salpeter equation which are well known in this case (Wick-Cutkosky model). The relevance of the comparison is examined by considering other relativistic quantum-mechanics approaches where results are known or have been obtained recently. Deficiencies of the point-form approach together with the single-particle current are emphasized. They point to quite sizeable contributions of two-body currents. These ones are required to fulfil current conservation in any case and to reproduce the high momentum transfer behaviour expected from the Born amplitude.

PACS
11.10.St - Bound and unstable states; Bethe-Salpeter equations.
11.30.Cp - Lorentz and Poincaré invariance.
13.40.Gp - Electromagnetic form factors.

© Società Italiana di Fisica, Springer-Verlag 2002