Perspectives for detecting lepton flavour violation in left-right symmetric models

We investigate lepton flavour violation in a class of minimal left-right symmetric models where the left-right symmetry is broken by triplet scalars. In this context we present a method to consistently calculate the triplet-Yukawa couplings which takes into account the experimental data while simultaneously respecting the underlying symmetries. Analysing various scenarios, we then calculate the full set of tree-level and one-loop contributions to all radiative and three-body flavour-violating fully leptonic decays as well as $\mu-e$ conversion in nuclei. Our method illustrates how these processes depend on the underlying parameters of the theory. To that end we observe that, for many choices of the model parameters, there is a strong complementarity between the different observables. For instance, in a large part of the parameter space, lepton flavour violating $\tau$-decays have a large enough branching ratio to be measured in upcoming experiments. Our results further show that experiments coming online in the immediate future, like Mu3e and BELLE II, or longer-term, such as PRISM/PRIME, will probe significant portions of the currently allowed parameter space.