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

• Received 21 November 2012

DOI:https://doi.org/10.1103/PhysRevD.87.013012