The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model

Details The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model

2006-11-06

arxiv.org/abs/hep-th/0611063v2

Int.J.Theor.Phys.46:2560-2590,2007

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 41 pages, corrected typos, final version accepted by IJTP

Scientific paper

10.1007/s10773-007-9371-9

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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