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 ($Λ_{\rm SS} \sim 10^{14}$ GeV) to the electroweak scale ($Λ_{\rm EW} \sim 10^2$ GeV). Concerning the Dirac phase $δ$, we show that $δ=90^\circ$ at $Λ_{\rm EW}$ can be radiatively generated from $δ=0^\circ$ at $Λ_{\rm SS}$ in the minimal supersymmetric standard model, if three neutrino masses are nearly degenerate. As for the Majorana phases $ρ$ and $σ$, it is also possible to radiatively generate $ρ=90^\circ$ or $σ= 90^\circ$ at $Λ_{\rm EW}$ from $ρ=0^\circ$ or $σ= 0^\circ$ at $Λ_{\rm SS}$. The one-loop renormalization-group equations for the Jarlskog invariant and two off-diagonal asymmetries of $V$ are derived, and their running behaviors from $Λ_{\rm SS}$ to $Λ_{\rm EW}$ are numerically illustrated.