  Various distributions over the angles of the emitted photon, especially over
the azimuthal angle, in the one-meson radiative decay of the polarized $\tau$
lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, have been investigated. In connection
with this, the photon phase space is discussed in more detail since in the case
of the polarized $\tau$ lepton it is not trivial. The decay matrix element
contains both the inner bremsstrahlung and the resonance (structural)
contributions. The azimuthal dependence of some observables have been
calculated. They are the asymmetry of the differential decay width caused by
the $\tau$ lepton polarization, the Stokes parameters of the emitted photon
itself and the correlation parameters describing the influence of $\tau$-lepton
polarization on the photon Stokes parameters. The numerical estimation was done
in the $\tau$ lepton rest frame for arbitrary direction of the $\tau$ lepton
polarization 3-vector. The vector and axial-vector form factors describing the
structure-dependent part of the decay amplitude are determined using the chiral
effective theory with resonances (R$\chi$T). It was found that the features of
the azimuthal distributions allows to separate various terms in the
spin-dependent contribution. The so-called up-down and right-left asymmetries
are also calculated.

High Energy Physics - Phenomenology