Using the massive helicity formalism we calculate the five-body average square amplitude of the decays $\tau^{ -}\to \ell_i^{ -} \ell_i^{ +} \ell_j^{ -} \bar{ \nu}_{ j} \nu_{ \tau}$ $(\ell=e,\,\mu)$ within the Standard Model (SM), we then introduce a dimension-five effective vertex $\Gamma^{ \tau\tau \gamma}$ in order to determine the feasibility of imposing limits on the tau anomalous magnetic dipole moment ($a_\tau$) via the current or future experimental measurements of the branching ratio for the decay $\tau^{ -}\to e^{ -} e^{ +} e^{ -} \bar{ \nu}_{ e} \nu_{ \tau}$.
Categories: hep-ph