Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases: From $M_{\rm Z}$ to $\Lambda_{\rm GUT}$

Abstract

We derive renormalization group equations for neutrino masses, leptonic mixing angles and CP-violating phases running at energies above the seesaw threshold, both in the Standard Model and in the Minimal Supersymmetric Standard Model extended with three right-handed neutrinos. With these equations, we carry out a systematic study of the radiative correction that may arise to neutrino parameters, via their renormalization group evolution from the electroweak scale ($M_{\rm Z}$) to the scale of Grand Unified theories ($\Lambda_{\rm GUT}$). We study in detail three typically interesting neutrino mass patterns: normal hierarchy, near degeneracy and inverted hierarchy. Magnitudes of possible corrections in each case are carefully investigated. We also emphasize the significance of CP-violating phases in controlling the evolution behavior of all neutrino parameters.