Generalized parton distributions for $q\bar{q}$ pions

We use a two-body, light-cone pion wave function (which vanishes when one of the constituents carries all of the plus-momentum) to construct a double distribution. We show that the resulting generalized parton distribution has incorrect behavior at the crossover between kinematic regions. Furthermore the positivity constraints are not respected. On the other hand, the field-theoretic, two-body double distribution gives generalized parton distributions that have physically correct crossover behavior and respect the positivity constraints independent of the model wave function used. However, the sum rule and polynomiality conditions cannot be satisfied with a two-body wave function alone since Lorentz symmetry is not maintained.