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 struc ture dependent radiation in the radiative decays and point meson, hadr onic structure dependent and short distance contributions in the virtu al corrections. Our result for the radiative correction to the ratio G amma(tau --> pi nu(tau)(gamma))/Gamma(pi --> mu nu(mu)(gamma)) is delt a 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) = (0.9 0 +/- 0.22) %.