  The recently proposed hard-pion chiral perturbation theory predicts that the
leading chiral logarithms factorize with respect to the energy dependence in
the chiral limit. This claim has been successfully tested in the pion form
factors up to two loops in chiral perturbation theory. In the present paper we
explain this factorization property at two loops and even show that it is valid
to all orders for a subclass of diagrams. We also demonstrate that
factorization is violated starting at three loops.
