Regge description of high energy pion pion total cross sections

We have recently presented a Regge description of pion-pion total cross sections valid above 1.4 GeV, consistent with the few existing experiments, factorization and crossing symmetry. In this note we show how it also describes a further large data sample obtained from an analysis of experiments on $\pi^\pm p\to X\Delta^{++}$ and $\pi^\pm n\to Xp$.Comment: 3 pages. To appear in the proceedings of the MESON 2004 workshop, Krakow, July 2004, to be published in Int. J. Mod. Phys.

The pion-pion scattering amplitude. II: Improved analysis above KˉK\bar{K}K threshold

We improve, in the energy region between $\bar{K}K$ threshold and $\sim~1.4$ GeV, the energy-dependent phase shift analysis of $\pi\pi$ scattering presented in a previous paper. For the S0 wave we have included more data above $\bar{K}K$ threshold and we have taken into account systematically the elasticity data on the reaction $\pi\pi\to\bar{K}K$. We here made a coupled channel fit. For the D0 wave we have considered information on low energy parameters, and imposed a better fit to the $f_2$ resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for $s^{1/2}\geq1.42$ GeV, which we also carry out. We show that this more realistic input produces $\pi\pi$ scattering amplitudes that satisfy better forward dispersion relations, particularly for $\pi^0\pi^0$ scattering.Comment: Plain TeX. 12 figures. Minor anomaly in the K-matrix fit corrected by moving matching point to 932 MeV, and pole $M_1$ to 910.6 MeV. Results unaltere

Strange resonance poles from KπK\pi 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 $\kappa$-meson, nowdays known as $K_0^*(800)$, the scalar $K_0^*(1430)$, the $K^*(892)$ and $K_1^*(1410)$ vectors, the spin-two $K_2^*(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters will be determined from the pole associated to each resonance by means of an analytic continuation of the $K\pi$ 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 Pad\'e approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties.Comment: 13 pages, 12 figures. Accepted version to appear in Eur. Phys. J. C. Clarifications and references added, minor typos correcte

Forward dispersion relations and Roy equations in pi-pi scattering

We review results of an analysis of pipi interactions in S, P and D waves for two-pion effective mass from threshold to about 1.4 GeV. In particular we show a recent improvement of this analysis above the K anti-K threshold using more data for phase shifts and including the S0 wave inelasticity from pipi -> K anti-K. In addition, we have improved the fit to the f2(1270) resonance and used a more flexible P wave parametrization above the K anti-K threshold and included an estimation of the D2 wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42 GeV. We have checked that the pipi scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations.Comment: 6 pages, invited talk to the IV International Conference on Quarks and Nuclear Physics QNP06, Madrid 5th-10th June 200

The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations

We complete and improve the fits to experimental $\pi\pi$ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations below$\bar{K}K$ threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by $1.5 \sigma$. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find $a_0^{(0)}=0.223\pm0.009 M^{-1}_\pi$, $a_0^{(2)}=-0.0444\pm0.0045 M^{-1}_\pi$ and $\delta_0^{(0)}(m^2_K)-\delta_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.Comment: Plain TeX. 29 figures. Version to be published in PRD, with improved P and F wave