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

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.

arXiv commentLatex, 41 pages, corrected typos, final version accepted by IJTP

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Cited by in corpus (8)

• A Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group
• The SU(2) X U(1) Electroweak Model based on the Nonlinearly Realized Gauge Group
• Further Comments on the Symmetric Subtraction of the Nonlinear Sigma Model
• On the Renormalization of the Complex Scalar Free Field Theory
• The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories
• Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
• A Symmetric Approach to the Massive Nonlinear Sigma Model
• Of Higgs, Unitarity and other Questions