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.
A two-component model of the decay K L -a O y y , in which the amplitude is the sum of a pion-loop contribution and a vector-meson-mediated term, is compared with data from the NA31 and E73 1 experiments. An estimate is obtained for the parameter G characterizing the strength of the vector-meson component. The amplitude of K L + a O y y , determined in this way, is used to calculate the CPconserving amplitude of the decays KL -roe ' e -and KL TO^+^-, without neglect of lepton masses.This complex amplitude (containing both absorptive and dispersive parts) is allowed to interfere with the CP-violating amplitude expected from the short-distance interaction sd+l + Iand from the CP impurity of the KL wave function. Results are obtained for the branching ratios of KL +rO1 + 1-and for the CP-violating 1+1-asymmetry in the Dalitz plot.
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