EPJ

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EPJ C - Particles and Fields
Particles and Fields
Eur. Phys. J. C 1, 669-710

Effective linear meson model

D.-U. Jungnickel - C. Wetterich

Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany
(e-mail: D.Jungnickel@thphys.uni-heidelberg.de, C.Wetterich@thphys.uni-heidelberg.de)

Received: 8 July 1996

Abstract
The effective action of the linear meson model generates the mesonic n-point functions with all quantum effects included. Based on chiral symmetry and a systematic quark mass expansion we derive relations between meson masses and decay constants. The model ``predicts'' values for $f_\eta$ and $f_{\eta^\prime}$ which are compatible with observation. This involves a large momentum dependent $\eta$-$\eta^\prime$ mixing angle which is different for the on-shell decays of the $\eta$ and the $\eta^\prime$. We also present relations for the masses of the 0++ octet. The parameters of the linear meson model are computed and related to cubic and quartic couplings among pseudoscalar and scalar mesons. We also discuss extensions for vector and axialvector fields. In a good approximation the exchange of these fields is responsible for the important nonminimal kinetic terms and the $\eta$-$\eta^\prime$ mixing encountered in the linear meson model.

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