SHORT AND LONG-DISTANCE EFFECTS IN THE DECAY TAU-]PI-NU(TAU)(GAMMA)

We calculate the radiative corrections to the decays tau --> M nu(tau) and M -->, mu nu(mu), where the meson M is M = pi or K. 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 --> pi nu(tau)(gamma))/Gamma(pi --> mu nu(mu)(gamma)) is delta R(tau/pi) = (0.16 +/- 0.14) %. For theratio Gamma(tau --> K nu(tau)(gamma))/Gamma(K --> mu nu(mu)(gamma)), we obtain delta R(tau/K) = (0.90 +/- 0.22) %.