40,664 research outputs found
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
The hadronic off-shell width of meson resonances
Within the resonance chiral effective theory we study the dressed propagators
of the spin-1 fields, as arise from a Dyson-Schwinger resummation
perturbatively constructed from loop diagrams with absorptive contributions in
the s-channel. We apply the procedure to the vector pion form factor and the
elastic pion-pion scattering to obtain the off-shell width of the rho_0 meson.
We adopt a definition of the off-shell width of spin-1 meson resonances that
satisfies the requirements of analyticity, unitarity, chiral symmetry and
asymptotic behaviour ruled by QCD. To fulfil these constraints the resummation
procedure cannot consist only of self-energy diagrams. Our width definition is
shown to be independent of the formulation used to describe the spin-1 meson
resonances.Comment: 1+12 pages, 4 figures. Minor changes in text. Conclusions unchanged.
Version accepted for publication in Phys. Rev.
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