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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 have calculated the O(α) radiative corrections to the tau decay τ → π(K)ν, taking into account both the point meson contribution and the structure dependent radiation. We find for the ratio Γ(τ → πν(γ))/Γ(π → µν(γ)) a radiative correction of +1.2% and for Γ(τ → Kν(γ))/Γ(K → µν(γ)) one of +2.0%. We compare our results with an earlier estimation and with experimental data.

We compute branching ratios and invariant mass distributions of the tau decays into four pions. The hadronic matrix elements are obtained by starting from the structure of the hadronic current i n c hiral limit and then implementing low-lying resonances in the dierent c hannels with slowly varying coupling constants. Reasonable agreement with experiment is obtained both for the ! + (4) decay rates and the e + e ! (4) cross sections. We derive a new prediction for the decay rate of ! 2 + 0 which i s signicantly lower than a previous one. Furthermore we supply an interface to use our matrix elements within the Tauola Monte-Carlo program.

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We calculate the dominant three body Higgs decays,), in the Standard Model. We find that the branching ratios of these decays are of the order of few percent for large Higgs masses. We comment on the behaviour of the partial decay width Γ(H → tbW − ) below the tt threshold. Numerical results of the following three body top decays, t → W + b(γ, g, Z 0 ) and t → W + bH, are also given. We discuss the feasibility of observing these Higgs and top decays at future high energy colliders.