Effective Field Theory of the Linear $O(N)$ Sigma Model
  The low energy structure of a theory containing light and heavy particle species which are separated by a mass gap can adequately be described by an effective theory which contains only the light particles. In this work we present a thorough analysis of the effective field theory of the linear $O(N)$ sigma model in the spontaneously broken phase. In particular, we present a detailed discussion of two techniques, a short-distance expansion and a method based on loop-integrals, which can be used to explicitly evaluate the functional relationships between the low energy constants of the effective theory and the parameters of the underlying theory. We furthermore provide a detailed analysis of the matching relation between the linear sigma model and its effective theory, in order to clarify some discrepancies which can be found in the literature. 
A. Nyffeler and A. Schenk