Global bounds on heavy neutrino mixing

Abstract

General bounds on the mixing between heavy and active neutrinos from a complete set of 28 observables are derived. Two scenarios are analysed and compared: (i) a general scenario in which an arbitrary number of heavy neutrinos is integrated out without any further assumption; (ii) only three heavy neutrinos are included and the light neutrino masses and mixings as measured in neutrino oscillations experiments are generated. A $1 -2$ $\sigma$ preference for non-zero heavy mixing is founded and implies some interesting correlations in the more constrained scenario (ii). At the $2\sigma$ level, the bounds on all the squared mixings are extremely similar in both scenarios. If only Lepton Flavour Conserving processes are included, they range from $\mathcal{O}(10^{-2})$ to $\mathcal{O}(10^{-4})$. Adding Lepton Flavor Violating observables as $\mu\rightarrow e\gamma$ to the analysis improves the bound in the $\mu-e$ sector by one order of magnitude.