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Study of two- and three-meson decay modes of tau-lepton with Monte Carlo generator TAUOLA

The study of the $τ$-lepton decays into hadrons has contributed to a better understanding of non-perturbative QCD and light-quark meson spectroscopy, as well as to the search of new physics beyond the Standard Model. The two- and three-meson decay modes, considering only those permitted by the Standard Model, are the predominant decays and together with the one-pion mode compose more than $85\%$ of the hadronic $τ$-lepton decay width. In this note we review the theoretical results for these modes implemented in the Monte Carlo event generator TAUOLA and present at the same time a comparison with the Belle Collaboration data for the two-pion decay mode and the BaBar preliminary data for the three-pion decay mode as well for the decay mode into two-kaon and one-pion.