Azimuthal distributions in radiative decay of a polarized τ lepton

Resumo

We investigate various distributions over emitted photon angles, especially over the azimuthal angle, in the one-meson radiative decay of the polarized τ lepton, τ^– → π^–γν_τ. In connection with this, the photon phase space is discussed in more detail because it is nontrivial in the case of a polarized τ lepton. The decay matrix element contains both the inner bremsstrahlung and the resonance (structural) contributions. The azimuthal dependence of some observables are calculated. They are the asymmetry of the differential decay width caused by the τ-lepton polarization, the Stokes parameters of the emitted photon itself, and the correlation parameters describing the influence of τ-lepton polarization on the photon Stokes parameters. A numerical estimation is done in the τ-lepton rest frame for an arbitrary direction of the τ-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 (RχT). It is found that the features of the azimuthal distributions allows separating various terms in the spin-dependent contribution. The so-called up–down and right–left asymmetries are also calculated.