Exploring asymmetries in three-body cLFV lepton decays: probing CP violation in HNL extensions of the SM

In extensions of the Standard Model with Majorana sterile fermions, additional Dirac and Majorana CP-violating phases can have a significant impact on charged lepton flavour violating (cLFV) transitions and decays. We investigate angular observables associated with polarised $\mu$ and $\tau$ cLFV three-body decays, ${\mathrm{\ell }}_{\alpha }^{+}\to {\mathrm{\ell }}_{\beta }^{+}{\mathrm{\ell }}_{\gamma }^{+}{\mathrm{\ell }}_{\delta }^{-}$, including parity- and time-reversal asymmetries. We analyse the correlations between different cLFV observables, showing that sizeable asymmetries can arise over experimentally accessible regions of parameter space. The resulting patterns of angular observables provide powerful probes of this class of Standard Model extensions and, in the event of a cLFV signal, could offer a means to test or potentially falsify the underlying framework.