Radiative corrections to the leptonic DiracCP-violating phase

Abstract

Since the smallest leptonic mixing angle ${\ensuremath{\theta}}_{13}$ has been measured to be relatively large, it is quite promising to constrain or determine the leptonic Dirac $CP$-violating phase $\ensuremath{\delta}$ in future neutrino oscillation experiments. Given some typical values of $\ensuremath{\delta}=\ensuremath{\pi}/2$, $\ensuremath{\pi}$, and $3\ensuremath{\pi}/2$ at the low energy scale, as well as current experimental results of the other neutrino parameters, we perform a systematic study of radiative corrections to $\ensuremath{\delta}$ by using the one-loop renormalization group equations in the minimal supersymmetric standard model and the universal extra-dimensional model. It turns out that $\ensuremath{\delta}$ is rather stable against radiative corrections in both models, except for the minimal supersymmetric standard model with a very large value of $\mathrm{tan}\ensuremath{\beta}$. Both cases of Majorana and Dirac neutrinos are discussed. In addition, we use the preliminary indication of $\ensuremath{\delta}=({1.08}_{\ensuremath{-}0.31}^{+0.28})\ensuremath{\pi}$ or $\ensuremath{\delta}=({1.67}_{\ensuremath{-}0.77}^{+0.37})\ensuremath{\pi}$ from the latest global-fit analyses of data from neutrino oscillation experiments to illustrate how it will be modified by radiative corrections.