Pion Mass Effects in the Large $N$ Limit of $\chiPT$

Details Pion Mass Effects in the Large $N$ Limit of $\chiPT$ Pion Mass Effects in the Large $N$ Limit of $\chiPT$

1994-07-18

arxiv.org/abs/hep-ph/9407321v1

Phys.Rev.D52:2878-2890,1995

Physics

High Energy Physics

High Energy Physics - Phenomenology

FT/UCM/18/94

Scientific paper

10.1103/PhysRevD.52.2878

We compute the large $N$ effective action of the $O(N+1)/O(N)$ non-linear sigma model including the effect of the pion mass to order $m^2_{\pi}/f_{\pi}^2$. This action is more complex than the one corresponding to the chiral limit not only because of the pion propagators but also because chiral symmetry produce new interactions proportional to $m^2_{\pi}/f_{\pi}^2$. We renormalize the action by including the appropriate counter terms and find the renormalization group equations for the corresponding couplings. Then we estudy the unitarity propierties of the scattering amplitudes. Finally our results are applied to the particular case of the linear sigma model and also are used to fit the pion scattering phase shifts.

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