Azimuthal distributions in radiative decay of polarized $\tau$ lepton

TL;DR

This paper investigates the angular distributions, especially azimuthal, in the radiative decay of polarized tau leptons, analyzing how polarization affects photon emission patterns and asymmetries using chiral effective theory.

Contribution

It provides a detailed analysis of azimuthal distributions and polarization effects in tau decay, incorporating resonance contributions and offering methods to distinguish different spin-dependent terms.

Findings

Azimuthal distributions reveal features of spin-dependent contributions.

Calculated asymmetries help separate structural and bremsstrahlung effects.

Numerical estimates in tau rest frame for arbitrary polarization directions.

Abstract

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.