A model for the pion structure function

The pion structure function is investigated in a simple model, where pion and constituent quark fields are coupled through the simplest pseudoscalar coupling. The imaginary part of the forward γ★π→γ★π scattering amplitude is evaluated and related to the structure functions. It is shown that the introduction of non-perturbative effects, linked to the size of the pion and preserving gauge invariance, allows a connection with the quark distribution. It is predicted that higher-twist terms become negligible for Q2 larger than ∼2 GeV2 and that quarks in the pion have a momentum fraction smaller than in the proton case.