Search Results (5 total)

We demonstrate that near the threshold, the ππ scattering amplitude contains a pole with the quantum numbers of the vacuum—commonly referred to as the σ—and determine its mass and width within small uncertainties. Our derivation does not involve models or parametrizations but relies on a straightforward calculation based on the Roy equation for the isoscalar S wave.

In a recent paper, Peláez and Ynduráin evaluate some of the low energy observables of ππ scattering and obtain flat disagreement with our earlier results. The authors work with unsubtracted dispersion relations, so that their results are very sensitive to the poorly known high energy behavior of the scattering amplitude. They claim that the asymptotic representation we used is incorrect and propose an alternative one. We repeat their calculations on the basis of the standard, subtracted fixed-t dispersion relations, using their asymptotics. The outcome fully confirms our earlier findings. Moreover, we show that the Regge parametrization proposed by these authors for the region above 1.4 GeV violates crossing symmetry: Their ansatz is not consistent with the behavior observed at low energies.

We show that, independently of the size of the quark condensate, chiral symmetry correlates the two S-wave ππ scattering lengths. In view of this constraint, the new precision data on K_e4 decay allow a remarkably accurate determination of these quantities. The result confirms the hypothesis that the quark condensate is the leading order parameter.

In a small window of phase space, chiral perturbation theory can be used to make standard model predictions for τ decays into two and three pions. For τ→2πν_τ, we give the analytical result for the relevant form factor F_V up to two loops, then calculate the differential spectrum and compare with available data. For τ→3πν_τ, we have calculated the hadronic matrix element to one loop. We discuss the decomposition of the three pion states into partition states and we give detailed predictions for the decay in terms of structure functions. We also compare with low energy predictions of meson dominance models. Overall, we find good agreement, but also some interesting discrepancies, which might have consequences beyond the limit of validity of chiral perturbation theory.

We consider the O(p⁴) predictions of chiral perturbation theory (χPT) in the process γγ→π⁰π⁰, together with the study of the existing experimental measurements and the planned new ones. At the Frascati Φ factory DAΦNE the rate of the events e⁺e^-→e⁺e^-π⁰π⁰ is large enough to allow for a measurement of the cross section with a good statistical sensitivity. However, a quantitative analysis of the commonly used approximation of considering only real photons for the detection of the γγ→π⁰π⁰ signal is still lacking. This motivates us to compute the cross section in χPT for the production of π⁰ pairs due to off-shell photons. A measurement of the azimuthal correlations would test the higher order χPT corrections independently from the measurement of the cross section. We approximate these corrections by including the contribution of the low-lying vector resonances in the scattering amplitude.