The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model |
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Authors: | D Bettinelli R Ferrari A Quadri |
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Institution: | (1) Dipartimento di Fisica, Università degli Studi di Milano and INFN, Sezione di Milano, via Celoria 16, 20133 Milano, Italy |
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Abstract: | 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. |
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Keywords: | |
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