Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities

We explore some of the constraints imposed by positivity of the QCD measure (Weingarten's inequalities) on the parameters defining chiral perturbation theory. We find, in particular, that $2 m_q (\mu)\leq B_0(\mu) Z(\mu)$. The use of further properties of the exact fermion propagator yields information on some higher order parameters.