Radiative Generation of Leptonic CP Violation

Abstract

Three CP-violating phases of the $3\times 3$ lepton flavor mixing matrix $V$ are entangled with one another in the renormalization-group evolution from the seesaw scale ($\hat{I}{›}_{\mathrm{SS}}\sim 10^{14}$ GeV) to the electroweak scale ($\hat{I}{›}_{\mathrm{EW}}\sim 10^2$ GeV). Concerning the Dirac phase $\hat{I}´$, we show that $\hat{I}´=90^{\circ }$ at $\hat{I}{›}_{\mathrm{EW}}$ can be radiatively generated from $\hat{I}´=0^{\circ }$ at $\hat{I}{›}_{\mathrm{SS}}$ in the minimal supersymmetric standard model, if three neutrino masses are nearly degenerate. As for the Majorana phases $\ddot{I}$ and $\ddot{I}ƒ$, it is also possible to radiatively generate $\ddot{I}=90^{\circ }$ or $\ddot{I}ƒ=90^{\circ }$ at $\hat{I}{›}_{\mathrm{EW}}$ from $\ddot{I}=0^{\circ }$ or $\ddot{I}ƒ=0^{\circ }$ at $\hat{I}{›}_{\mathrm{SS}}$. The one-loop renormalization-group equations for the Jarlskog invariant and two off-diagonal asymmetries of $V$ are derived, and their running behaviors from $\hat{I}{›}_{\mathrm{SS}}$ to $\hat{I}{›}_{\mathrm{EW}}$ are numerically illustrated.

RevTex 20 pages, 5 figures. More discussions added. Phys. Rev. D (in press)