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

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