Running CP-violating Phases of Majorana Neutrinos

Abstract

Three CP-violating phases of the $3\times 3$ lepton flavor mixing matrix $V$, denoted as $\delta$, $\rho$ and $\sigma$ in a useful phase convention, are entangled with one another in the one-loop renormalization-group equations. We show that $\delta =90^{\circ }$ at the electroweak scale (${\Lambda }_{\mathrm{EW}}\sim 10^2$ GeV) can be radiatively generated from $\delta =0^{\circ }$ at the seesaw scale (${\Lambda }_{\mathrm{SS}}\sim 10^{14}$ GeV) in the minimal supersymmetric standard model, provided three neutrino masses are nearly degenerate. As for the Majorana phases $\rho$ and $\sigma$, it is also possible to radiatively generate $\rho =90^{\circ }$ or $\sigma =90^{\circ }$ at ${\Lambda }_{\mathrm{EW}}$ from $\rho =0^{\circ }$ or $\sigma =0^{\circ }$ at ${\Lambda }_{\mathrm{SS}}$. This observation opens a new and interesting window for model building, in order to understand possible connection between the phenomena of CP violation at low- and high-energy scales.

Comments: PoS style 4 pages. Talk given at the International Europhysics Conference on High Energy Physics, July 21st - 27th 2005, Lisboa, Portugal