<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>radiative decay and pion structure form factors

Abstract

The decay mode of the $\ensuremath{\tau}$ lepton ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ is calculated in terms of the axial-vector and vector structure-dependent form factors of the pion, which also describe the radiative $\ensuremath{\pi}$ decay ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{l}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{l}\ensuremath{\gamma}$. The isospin-rotated vector form factor is related (as usual) to the decay ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$, as well as to ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$. These reactions thus serve to probe the isospin structure of the vector form factor, as well as the momentum-transfer dependence of both form factors. The numbers expected in the $\ensuremath{\tau}$ radiative decay are calculated using vector-meson-dominance estimates for the form factors.