  As with parton distributions, flexible phenomenological parameterizations of
generalized parton distributions (GPDs) are essential for their extraction from
data. The large number of constraints imposed on GPDs make simple Lorentz
covariant models viable; but, such models are often incomplete in that they
employ the impulse approximation. Using the GPD of the pion as a test case, we
show that the impulse approximation can lead to violation of the positivity
bound required of GPDs. We focus on a particular model of the pion bound-state
vertex that was recently proposed and demonstrate that satisfying the bound is
not guaranteed by Lorentz covariance. Violation of the positivity bound is tied
to a problematic mismatch between the behavior of the quark distribution at the
endpoint and the crossover value of the GPD.
