Prospects for discovery of the \tau^- \to \pi^- \ell^+ \ell^- \nu_\tau decays

Abstract

We study the phenomenology of the \tau^- \to \pi^- \nu_\tau \ell^+ \ell^- decays (\ell = e, \mu), predicting the respective branching ratios and di-lepton invariant-mass spectra. In addition to the model-independent (QED) contributions, we investigate the structure-dependent (SD) terms, encoding features of the hadronization of QCD currents. The relevant form factors are evaluated by supplementing Chiral Perturbation Theory with the inclusion of the lightest (axial-)vector resonance multiplet as dynamical fields. The Lagrangian couplings are fully predicted requiring the known QCD asymptotic behavior to the relevant Green functions and associated form factors in the limit of an infinite number of colours. As a consequence we predict that the \tau^- \to \pi^- \nu_\tau e^+ e^- decays should be discovered soon while this is not granted for the \ell = \mu case.