Running of Low-Energy Neutrino Masses, Mixing Angles and CP Violation

Abstract

We calculate the running of low-energy neutrino parameters from the bottom up, parameterizing the unknown seesaw parameters in terms of the dominance matrix $R$. We find significant running only if the $R$ matrix is non-trivial and the light-neutrino masses are moderately degenerate. If the light-neutrino masses are very hierarchical, the quark-lepton complementarity relation $\theta_c + \theta_{12} = \pi/4$ is quite stable, but $\theta_{13,23}$ may run beyond their likely future experimental errors. The running of the oscillation phase $\delta$ is enhanced by the smallness of $\theta_{13}$, and jumps in the mixing angles occur in cases where the light-neutrino mass eigenstates cross.