We explore skewed parton distributions for two-body, light-front wave functions. In order to access all kinematical régimes, we adopt a covariant Bethe-Salpeter approach, which makes use of the underlying equation of motion (here the Weinberg equation) and its Green’s function. Such an approach allows for the consistent treatment of the non-wave-function vertex (but rules out the case of phenomenological wave functions derived from ad hoc potentials). Our investigation centers around checking internal consistency by demonstrating time-reversal invariance and continuity between valence and nonvalence régimes. We derive our expressions by assuming the effective $\mathrm{qq}$ potential is independent of the mass squared, and verify the sum rule in a nonrelativistic approximation in which the potential is energy independent. We consider bare-coupling as well as interacting skewed parton distributions and develop approximations for the Green’s function which preserve the general properties of these distributions. Lastly, we apply our approach to timelike form factors and find similar expressions for the related generalized distribution amplitudes.

• Received 26 September 2001

DOI:https://doi.org/10.1103/PhysRevD.65.074009