Electromagnetic form factors in the light-front formalism and the Feynman triangle diagram: Spin-0 and spin-1 two-fermion systems

Abstract

The connection between the Feynman triangle diagram and the light-front formalism for spin-0 and spin-1 two-fermion systems is analyzed. It is shown that in the limit ${q}^{+}=0$ the form factors for both spin-0 and spin-1 systems can be uniquely determined using only the good amplitudes, which are not affected by spurious effects related to the loss of rotational covariance present in the light-front formalism. At the same time, the unique feature of the suppression of the pair creation process is maintained. Therefore, a physically meaningful one-body approximation, in which all the constituents are on their mass shells, can be consistently formulated in the limit ${q}^{+}=0.$ Moreover, it is shown that the effects of the contact term arising from the instantaneous propagation of the active constituent can be canceled out from the triangle diagram by means of an appropriate choice of the off-shell behavior of the bound state vertices; this implies that in the case of good amplitudes the Feynman triangle diagram and the one-body light-front result match exactly. For illustrative purposes our covariant light-front approach is applied to the evaluation of the $\ensuremath{\rho}$-meson elastic form factors.