Reversors and Symmetries for Polynomial Automorphisms of the Plane

We obtain normal forms for symmetric and for reversible polynomial automorphisms (polynomial maps that have polynomial inverses) of the plane. Our normal forms are based on the generalized \Henon normal form of Friedland and Milnor. We restrict to the case that the symmetries and reversors are also polynomial automorphisms. We show that each such reversor has finite-order, and that for nontrivial, real maps, the reversor has order 2 or 4. The normal forms are shown to be unique up to finitely many choices. We investigate some of the dynamical consequences of reversibility, especially for the case that the reversor is not an involution.Comment: laTeX with 5 figures. Added new sections dealing with symmetries and an extensive discussion of the reversing symmetry group

Light meson resonances from unitarized Chiral Perturbation Theory

We report on our recent progress in the generation of resonant behavior in unitarized meson-meson scattering amplitudes obtained from Chiral Perturbation Theory. These amplitudes provide simultaneously a remarkable description of the resonance region up to 1.2 GeV as well as the low energy region, since they respect the chiral symmetry expansion. By studying the position of the poles in these amplitudes it is possible to determine the mass and width of the associated resonances, as well as to get a hint on possible classification schemes, that could be of interest for the spectroscopy of the scalar sector.Comment: Invited talk to the II International Workshop on Hadron Physics & Effective Theories of Low Energy QCD. 25-29 September 2002. Coimbra. Portuga

Meson resonances from unitarized meson scattering at one loop in Chiral Perturbation Theory

We show the results for the scattering poles associated to the rho, f0, a0, K*, sigma and kappa resonances in meson-meson scattering. Our amplitudes are obtained from the complete one-loop meson-meson scattering amplitudes from Chiral Perturbation Theory. Once unitarized with the Inverse Amplitude Method, they describe remarkably well the data simultaneously in the low energy and resonance regions up to 1.2 GeV, using low energy parameters compatible with present determinations.Comment: To appear in the proceedings of the 5th International Conference on ``Quark confinement and the hadron spectrum'', held in Gargnano, Garda Lake, Italy. 10-14th September 2002. 3 page

Unitarization of the complete meson-meson scattering at one loop in Chiral Perturbation Theory

We report on our one-loop calculation of all the two meson scattering amplitudes within SU(3) Chiral Perturbation Theory, i.e. with pions, kaons and etas. Once the amplitudes are unitarized with the coupled channel Inverse Amplitude Method, they satisfy simultaneously the correct low-energy chiral constraints and unitarity. We obtain a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and seven light resonances.Comment: To appear in the proceedings of QCD@work: International Workshop on QCD: Theory and Experiment. Martina Franca (Italy) June 16-20. 200

Complete meson-meson scattering within one loop in Chiral Perturbation Theory: Unitarization and resonances

We review our recent one-loop calculation of all the two meson scattering amplitudes within SU(3) Chiral Perturbation Theory, i.e. with pions, kaons and etas. By unitarizing these amplitudes we are able to generate dynamically the lightest resonances in meson-meson scattering. We thus obtain a remarkable description of the meson-meson scattering data right from threshold up to 1.2 GeV, in terms of chiral parameters in good agreement with previous determinations.Comment: 4 pages, To appear in the Proceedings of the IX International Conference on Hadron Spectroscopy, HADRON2001, IHEP, Protvino, Russia, August 200