03 01 04 9 v 1 8 J an 2 00 3 Light meson resonances from unitarized Chiral Perturbation Theory
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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. In this work we review our recent progress in determining the position of the poles [1] that appear associated to resonant behavior in meson-meson scattering amplitudes, obtained from unitarized one-loop Chiral Perturbation Theory [2]. This apparently formal interest is motivated by the spectroscopy of light mesons, whose present status is somewhat controversial. Poles in the second Riemann sheet of partial wave scattering amplitudes are of relevance because when they are close to the real, physical values of the center of mass energy √ s, we can neglect all other terms in the partial wave and simply write t(s) = R R s − s pole = R R s − (Re √ s pole) 2 − (Im √ s pole) 2 − i 2 Re √ s pole Im √ s pole (1) where R R would be some real residue that can be calculated but is irrelevant for us here. Furthermore, if by " close to the real axis " we mean that Im √ s pole ≪Re √ s pole , then, we can approximate: (2) where in order to write our equation in the familiar Breit-Wigner form, in the last step we have identified √ s pole ≃ M R − iΓ R /2. Breit-Wigner (BW) resonances yield the familiar and experimentally distinct resonant shape in the cross section and its associated fast phase movement, which increases by π in a very small energy range. The quantum
[1] Madrid,et al. Light meson resonances from unitarized Chiral Perturbation Theory , 2003, hep-ph/0301049.