Radiative Generation of Leptonic CP Violation

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 (${\mathrm{\Lambda }}_{\mathrm{S}\mathrm{S}}\sim {10}^{14}$ GeV) to the electroweak scale (${\mathrm{\Lambda }}_{\mathrm{E}\mathrm{W}}\sim {10}^2$ GeV). Concerning the Dirac phase $\delta$, we show that $\delta ={90}^{\circ }$ at ${\mathrm{\Lambda }}_{\mathrm{E}\mathrm{W}}$ can be radiatively generated from $\delta =0^{\circ }$ at ${\mathrm{\Lambda }}_{\mathrm{S}\mathrm{S}}$ in the minimal supersymmetric standard model, if 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 ${\mathrm{\Lambda }}_{\mathrm{E}\mathrm{W}}$ from $\rho =0^{\circ }$ or $\sigma =0^{\circ }$ at ${\mathrm{\Lambda }}_{\mathrm{S}\mathrm{S}}$. The one-loop renormalization-group equations for the Jarlskog invariant and two off-diagonal asymmetries of $V$ are derived, and their running behaviors from $\Lambda_{\rm SS}$to$\Lambda_{\rm EW}$ are numerically illustrated.