In models where the Standard Model is extended by Majorana fermions, interference effects due to the presence of
CP violating phases have been shown to play a crucial role in lepton number violating processes.
However, important effects can also arise in lepton number conserving, but charged lepton flavour violating (cLFV) transitions and decays.
Here we show that the presence of CP violating (Dirac and Majorana) phases can have a striking
impact for the predicted rates of cLFV observables.
We explore the interference effects in several cLFV observables, carrying for the first time a thorough analysis of the different observables and the implications for future observation.
We discuss how the presence of leptonic CP violating phases might lead to a loss of correlation between observables (typically present in simple SM extensions via heavy sterile fermions),
or even to the suppression of certain channels; these effects can be interpreted as suggestive of non-vanishing phases.