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One-Loop Renormalization of the Nonlinear σ Model

1972; American Physical Society; Volume: 5; Issue: 6 Linguagem: Inglês

10.1103/physrevd.5.1313

1538-4500

D. Bessis, Jean Zinn‐Justin,

Black Holes and Theoretical Physics

We propose a method for regularizing and renormalizing the nonlinear $\ensuremath{\sigma}$ model based on the limit of the linear $\ensuremath{\sigma}$ model when the $\ensuremath{\sigma}$ mass tends to infinity. The linear $\ensuremath{\sigma}$ model being renormalized using Ward identities, this procedure ensures automatically the soft-pion theorems. It also retains the properties of transformations of the Green's functions under the chiral group. In the one-loop approximation, we show that the pion propagator has a finite limit when the $\ensuremath{\sigma}$ mass tends to infinity, while the four-pion Green's function diverges only logarithmically with the $\ensuremath{\sigma}$ mass.