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

Quark mass dependence of light resonances and phase shifts in elastic π π and π к scattering

We study the light quark mass dependence of the π π scattering phase shifts in standard one and two-loop SU(2) Chiral Perturbation Theory (ChPT). We then repeat the study with unitarized ChPT and; furthermore, we extend the analysis to SU(3) and generate the elastic f_0(600), к(800) ρ(770) and K*(892) resonances from unitarization. The quark masses are varied up to values of interest for lattice studies. We find that the SU(2) π π phase shifts both in standard and unitarized ChPT depend very softly on the pion mass and that our results are in fair agreement with lattice results in the I=2, J=0 channel. In the SU(3) amplitudes, the mass and width of the ρ (770) and K*(892) present an analogous and smooth quark mass dependence. In contrast, both scalars present a similar non-analyticity at high quark masses. We also confirm the lattice assumption of independence of the vector two-meson coupling on the quark mass, that is, nevertheless, violated for scalars

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

The non-ordinary Regge behavior of the K_(0)^(*)(800) or κ-meson versus the ordinary K_(0)^(*) (1430)

The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the K_(0)^(*)(1430) Regge trajectory, finding the ordinary almost real and linear behavior, typical of q (q) over bar resonances. In contrast, for the K_(0)^(*)(800) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the f_(0)(500) or σ meson. The slope of these unusual Regge trajectories seems to scale with themeson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non- ordinary, predominantly meson-meson- like, interpretation for the lightest strange and non-strange resonances

Meson-meson scattering within one-loop chiral perturbation theory and its unitarization

We present a complete one-loop calculation of all the two-meson scattering amplitudes within the framework of SU(3) chiral perturbation theory, which includes pions, kaons, and the eta. In addition, we have unitarized these amplitudes with the coupled channel inverse amplitude method, which simultaneously ensures the good low energy properties of chiral perturbation theory and unitarity. We show how this method provides a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and the generation of seven light resonances, which is consistent with previous determinations of the chiral parameters. Particular attention is paid to discussing the differences and similarities of this work with previous analyses in the literature

m_π and N_c dependence of rho and σ mesons from unitarized chiral perturbation theory

We review the N_c and m_π dependence of the rho(770) and σ (or f_0(600) resonances generated with the Inverse Amplitude Method. The σ N_c behavior is at odds with being dominantly a q̅q̅ state, but there is a hint of a subdominant q̅q̅o component with a mass above 1 GeV. We find fair agreement with lattice results for the chiral extrapolation of the ρ mass, and that the ρ π π coupling is almost m_π independent whereas the σ π π depends strongly on m_π

The equivalence theorem for gauge boson scattering in a five-dimensional Standard Model

We present an equivalence theorem for the longitudinal components of the gauge bosons in a compactified five-dimensional extension of the Standard Model, whose spontaneous symmetry breaking is driven either by one Higgs in the bulk or by one on a brane or by both together. We also show some implications for the unitarity bounds on Higgs masses

Erratum: On the equivalence theorem in he XPT description of the symmetry-breaking sector of the standard model (vol b425, pg 110, 1994)

Depto. de Física TeóricaFac. de Ciencias FísicasTRUEpu

Dispersive calculation of complex Regge trajectories for the lightest f_2 resonances and the K^∗(892)

We apply a recently developed dispersive formalism to calculate the Regge trajectories of the f_2(1270), f´_ 2(1525) and K^∗(892) mesons. Trajectories are calculated, not fitted to a family of resonances. Assuming that these resonances can be treated in the elastic approximation, the only input are the pole position and residue of a resonance. In all three cases, the predicted Regge trajectories are almost real and linear, with slopes in agreement with the universal value of order 1 GeV_(−2). We also show how these results barely change when considering more than two subtractions in the dispersive formalism

Strange resonance poles from K π scattering below 1.8 GeV

In this work we present a determination of the mass, width, and coupling of the resonances that appear in kaon-pion scattering below 1.8 GeV. These are: the much debated scalar ĸ- meson, nowadays known as K(_1)(*) (800), the scalar K(_1)(*) (1430), the K*(892) and K(_1)(*) (1410) vectors, the spin-two K(_1)(*) (1430) as well as the spin-three K(_1)(*) (1780). The parameters will be determined from the pole associated to each resonance by means of an analytic continuation of the Kπ scattering amplitudes obtained in a recent and precise data analysis constrained with dispersion relations, which were not well satisfied in previous analyses. This analytic continuation will be performed by means of Pade approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties