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

A bstract In the context of Standard Model extensions via Majorana sterile fermions, the presence of additional CP violating phases (Dirac and Majorana) has been shown to be at source of important effects in charged lepton flavour violating (cLFV) transitions and decays. Here we will consider further angular observables that can be studied for polarised τ and μ cLFV decays. These include, among others, parity asymmetries and time-reversal asymmetries for generic cLFV 3-body decays, $$ {\ell}_{\alpha}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℓ</mml:mi> <mml:mi>α</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> → $$ {\ell}_{\beta}^{+}{\ell}_{\gamma}^{+}{\ell}_{\delta}^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℓ</mml:mi> <mml:mi>β</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:msubsup> <mml:mi>ℓ</mml:mi> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:msubsup> <mml:mi>ℓ</mml:mi> <mml:mi>δ</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> </mml:math> . We address relevant correlations between the different classes of observables, and show that one can have sizeable asymmetries, which can be used to further probe this interesting class of SM extensions. Our study leads to the prediction of particular patterns of angular observables, which would allow to potentially falsify the model, should a cLFV signal be observed.