Effective Field Theory of the Linear $O(N)$ Sigma Model

Details Effective Field Theory of the Linear $O(N)$ Sigma Model Effective Field Theory of the Linear $O(N)$ Sigma Model

1994-09-29

arxiv.org/abs/hep-ph/9409436v1

Ann.Phys.241:301-336,1995

Physics

High Energy Physics

High Energy Physics - Phenomenology

42 pages, LaTeX, BUTP-94/12, HUTP-94/A012, to appear in Ann. Phys

Scientific paper

10.1006/aphy.1995.1065

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.

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