Short and Long Distance Effects in the Decay $τ\to πν_τ (γ)$

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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39 pages, Latex [19 figures, not included]: A complete postscript file, including figures, is available via anonymous ftp at

Scientific paper

10.1016/0550-3213(95)00597-L

We calculate the radiative corrections to the decays $\tau\to M \nu_\tau$ and $\pi \to l \nu_\l$, where the meson $M$ is $M=\pi$ or $K$ and the lepton $l$ is $l = e$ or $\mu$. 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 $\Gamma(\tau\to\pi\nu_\tau(\gamma))/ \Gamma(\pi\to\mu\nu_\mu(\gamma))$ is $\delta R_{\tau/\pi} = \left(0.16_{\T - 0.14}^{\T+0.09}\right) \%$. For the ratio $\Gamma(\tau\to K\nu_\tau(\gamma)) / \Gamma(K\to \mu\nu_\mu(\gamma))$, we obtain $\delta R_{\tau/K } = \left(0.90_{\T - 0.26}^{\T + 0.17}\right) \%$. For completeness we have also calculated the ratio of the electronic and muonic decay modes of the pion.

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