About The Polarized $\tau$ Lepton Radiative Decay

Abstract

The polarization effects in the one-meson radiative decay of the polarized $\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, have been investigated. We present the analytical results for the $t-$distribution of the partial differential widths, which responsible for different polarization phenomena, in the case of the photon energy cut: $\omega>X$. These quantities depend on the invariant mass squared $t$ of the pseudoscalar meson and photon and the photon energy cut $X.$ Our analytical formulae, in terms of the weak vector and axial-vector form factors, describing the structure-dependent part of the decay amplitude, are valid also for the decay $\tau^{\pm}\to K^{\pm}\,\nu_\tau\,\gamma$ after trivial substitutions of the corresponding constants. We demonstrate the essential decrease of the inner bremsstrahlung contribution in comparison with the structural one with increase of the photon cut energy. In numerical calculations the vector and axial-vector form factors are determined using the chiral effective theory with resonances (R$\chi$T).