Light front Bethe-Salpeter equation applied to form factors, generalized parton distributions and generalized distribution amplitudes

Abstract

We present an intuitive, light front reduction scheme for the Bethe-Salpeter equation that consists of iterations of the (light front) energy dependent covariant equation followed by an instantaneous approximation. This scheme is equivalent to and motivates the form of a standard reduction that reproduces light front, time ordered perturbation theory for bound states. We use this three-dimensional light front formalism to compute electromagnetic form factors between bound states to show how higher, light front Fock components arise from the covariant Bethe-Salpeter wave function. Moreover, we show that non-wave function vertices, which arise after integration over the minus momenta, are completely removed in favor of higher Fock states when one correctly takes into account all contributions at a given order in perturbation theory. Such non-wave function vertices are shown only to occur in models in which the interactions are instantaneous. These models lack true higher Fock states. The normalization of the reduced wave function is derived from the covariant framework and related to nonvalence probabilities using familiar Fock space projection operators. Using a simple model, we obtain expressions for generalized parton distributions that are continuous. The nonvanishing of these distributions at the crossover between kinematic regimes (where the plus component of the struck quark's momentum is equal to the plus component of the momentum transfer) is tied to higher Fock components. Lastly we apply the light front reduction to timelike form factors and derive expressions for the generalized distribution amplitudes in this model.