  In perturbation theory we study the matching in four dimensions between the
linear sigma model in the large mass limit and the renormalized nonlinear sigma
model in the recently proposed flat connection formalism. We consider both the
chiral limit and the strong coupling limit of the linear sigma model. Our
formalism extends to Green functions with an arbitrary number of pion legs,at
one loop level,on the basis of the hierarchy as an efficient unifying principle
that governs both limits. While the chiral limit is straightforward, the
matching in the strong coupling limit requires careful use of the normalization
conditions of the linear theory, in order to exploit the functional equation
and the complete set of local solutions of its linearized form.
