Comprehensive Analysis of Charged Lepton Flavour Violation in the Symmetry Protected Type-I Seesaw

The type-I seesaw model is probably the most straightforward and best studied extension of the Standard Model that can account for the tiny active neutrino masses determined from neutrino oscillation data. In this article, we calculate the complete set of one-loop corrections to charged lepton flavour violating processes within this model. We give the results both using exact diagonalisation of the neutrino mass matrix, and at at leading order in the seesaw expansion (i.e. $\mathcal{O}(v^2/M_R^2)$). Furthermore, we perform the matching onto the $SU(2)_L$ invariant Standard Model Effective Field Theory at the dimension-6 level. These results can be used as initial conditions for the renormalisation group evolution from the right-handed neutrino scale down to the scale of the physical processes, which resums large logarithms. In our numerical analysis, we study the inverse seesaw limit, i.e. the symmetry protected type-I seesaw, where the Wilson coefficient of the Weinberg operator is zero such that sizeable neutrino Yukawas are permissible and relevant effects in charged lepton flavour violating observables are possible. We correlate the different charged lepton flavour violating processes, e.g. $\ell\to\ell^\prime\gamma$, $\ell\to3\ell^\prime$, $\mu\to e$ conversion and $Z\to \ell\ell^\prime$, taking into account the constraints from electroweak precision observables and tests of lepton flavour universality.