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 calculate the radiative corrections to the decays τ → Mν τ and π → lν l , where the meson M is M = π or K and the lepton l is l = e or µ. We perform a complete calculation, which includes internal bremsstrahlung and structure dependent radiation in the radiative decays and point meson, hadronic structure dependent and short distance contributions in the virtual corrections. Our result for the radiative correction to the ratio Γ(τ → πν τ (γ))/Γ(π → µν µ (γ)) is δR τ /π = 0.16 +0.09 −0.14 %. For the ratio Γ(τ → Kν τ (γ))/Γ(K → µν µ (γ)), we obtain δR τ /K = 0.90 +0.17 −0.26 %. For completeness we have also calculated the ratio of the electronic and muonic decay modes of the pion.

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We reexamine radiative corrections to π l2 and K l2 decays. We perform a matching calculation, including vector and axial vector resonances as explicit degrees of freedom in the long distance part. By considering the dependence on the matching scale and on the hadronic parameters, and by comparing with model independent estimates, we scrutinize the model dependence of the results. For the pseudoscalar meson decay constants, we extract the values f π = (92.1±0.3) MeV and f K = (112.4±0.9) MeV. For the ratios R π and R K of the electronic and muonic decay modes, we predict R π = (1.2354 ± 0.0002) · 10 −4 and R K = (2.472 ± 0.001) · 10 −5 .

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