  We present a method to evaluate the pion structure functions from a box
diagram calculation. Pion and constituent quark fields are coupled through the
simplest pseudoscalar coupling. The gamma^* pi -> q \bar q cross-section is
evaluated and related to the structure functions. We then show that the
introduction of non-perturbative effects, related to the pion size and
preserving gauge invariance, provides us with a straighforward relation with
the quark distribution. It is predicted that higher-twist terms become
negligible for Q^2 larger than about 2 GeV^2 and that quarks in the pion have a
momentum fraction smaller than in the proton. We enlarge the discussion
concerning this violation of the momentum sum rule, emphasizing that the sum
rule is recovered in the chiral limit and also when the finite size condition
is not imposed.
