Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2006-03-12
Phys.Lett. B637 (2006) 279-286
Physics
High Energy Physics
High Energy Physics - Phenomenology
RevTex 13 pages. Slight modifications made for the text, Table I and references. Results and conclusions unchanged. Accepted f
Scientific paper
10.1016/j.physletb.2006.04.038
Taking the standard parametrization of three-flavor neutrino mixing, we carefully examine the evolution of three CP-violating phases $(\delta, \alpha^{}_1, \alpha^{}_2)$ with energy scales in the realistic limit $\theta^{}_{13} \to 0$. If $m^{}_3$ vanishes, we find that the one-loop renormalization-group equation (RGE) of $\delta$ does not diverge and its running has no quasi-fixed point. When $m^{}_3 \neq 0$ holds, we show that the continuity condition derived by Antusch {\it et al} is always valid, no matter whether the $\tau$-dominance approximation is taken or not. The RGE running of $\delta$ undergoes a quasi-fixed point determined by a nontrivial input of $\alpha^{}_2$ in the limit $m^{}_1 \to 0$. If three neutrino masses are nearly degenerate, it is also possible to arrive at a quasi-fixed point in the RGE evolution of $\delta$ from the electroweak scale to the seesaw scale or vice versa. Furthermore, the continuity condition and the quasi-fixed point of CP-violating phases in another useful parametrization are briefly discussed.
Luo Shu
Xing Zhi-zhong
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