Zero-mass divergences in expansions about chiral and scale symmetry

Singularities of expansions in the symmetry-breaking parameters of chiral- and scale-asymmetric theories are studied, in the tree approximation, in polynomial Lagrangian models. The singularities are related to the appearance of zero-mass scalar fields, not necessarily Goldstone particles, at the radius of convergence of the expansion. Methods of avoiding these singularities are presented.