No abstract

The low energy scattering of pions is investigated in the presence of electromagnetic interactions at leading order and at next-to-leading order for the amplitudes involving at most one pair of charged pions. The size of the electromagnetic corrections to the S-wave scattering lengths is found to be comparable to the size of the two loop strong interaction corrections.

In a small window of phase space, chiral perturbation theory can be used to make standard model predictions for tau 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 construct an effective Lagrangian for the hadronic decays of a heavy excited s-wave-spin-one quarkonium into its ground state. We show that reasonable fits to the measured invariant mass spectra in the J/ψ and Υ systems can be obtained working in the chiral limit. The mass dependence of the various terms in the Lagrangian is discussed on the basis of a quark model.

The electromagnetic corrections to the masses of the pseudoscalar mesons π and K are considered. We calculate in chiral perturbation theory the contributions which arise from resonances within a photon loop at order O(e 2 m q ). Within this approach we find rather moderate deviations to Dashen's theorem.