Global constraints on heavy neutrino mixing

We derive general constraints on the mixing of heavy Seesaw neutrinos with the SM fields from a global fit to present flavour and electroweak precision data. We explore and compare both a completely general scenario, where the heavy neutrinos are integrated out without any further assumption, and the more constrained case were only 3 additional heavy states are considered. The latter assumption implies non-trivial correlations in order to reproduce the correct neutrino masses and mixings as observed by oscillation data and thus some qualitative differences can be found with the more general scenario. The relevant processes analyzed in the global fit include searches for Lepton Flavour Violating (LFV) decays, probes of the universality of weak interactions, CKM unitarity bounds and electroweak precision data. In particular, a comparative and detailed study of the present and future sensitivity of the different LFV experiments is performed. We find a mild $1-2\sigma$ preference for non-zero heavy neutrino mixing of order 0.03-0.04 in the electron and tau sectors. At the $2\sigma$ level we derive bounds on all mixings ranging from 0.1 to 0.01 with the notable exception of the $e-\mu$ sector with a more stringent bound of 0.005 from the $\mu \to e \gamma$ process.