Renormalization group running of neutrino parameters in the inverse seesaw model

We perform a detailed study of the renormalization group equations in the inverse seesaw model. Especially, we derive compact analytical formulas for the running of the neutrino parameters in the standard model and the minimal supersymmetric standard model, and illustrate that, due to large Yukawa coupling corrections, significant running effects on the leptonic mixing angles can be naturally obtained in the proximity of the electroweak scale, perhaps even within the reach of the LHC. In general, if the mass spectrum of the light neutrinos is nearly degenerate, the running effects are enhanced to experimentally accessible levels, well suitable for the investigation of the underlying dynamics behind the neutrino mass generation and the lepton flavor structure. In addition, the effects of the seesaw thresholds are discussed, and a brief comparison to other seesaw models is carried out.

Figure 1

The RG evolution behavior of the three leptonic mixing angles as functions of the energy scale $\mu$ in the SM. We use $M_0=1\mathrm{TeV}$ and $\epsilon =0.3$ as input parameters at the seesaw scale. The colored regions correspond to values of the leptonic mixing angles within their $1\sigma$ confidence intervals in the ND case, while the solid, dashed, and dotted curves denote the same confidence intervals in the ID case.

Figure 2

The RG evolution behavior of the three leptonic mixing angles as functions of the energy scale $\mu$ in the MSSM with $\tan \beta =10$ (upper plots) and $\tan \beta =50$ (lower plots), respectively. The input values of the masses of the heavy singlets and the Yukawa couplings are the same as those in Fig. 1.

Figure 3

The RG evolution behavior of the three leptonic mixing angles as functions of the energy scale $\mu$ in the SM with the masses of the heavy neutrinos being 1, 10, and 100 TeV, respectively. The input values of the Yukawa couplings are the same as those in Fig. 1.

Figure 4

The RG evolution behavior of the three leptonic mixing angles as functions of the energy scale $\mu$ in the MSSM with the masses of the heavy neutrinos being 1, 10, and 100 TeV, respectively. Similar to Fig. 3, we use $\tan \beta =10$ for the upper plots and $\tan \beta =50$ for the lower plots. The input values of the Yukawa couplings are the same as those in Fig. 1.

Figure 5

The RG evolution behavior of the masses of the light neutrinos (left plot) and the $CP$-violating phases (right plot) as functions of the energy scale $\mu$ in the ND case. We use $Y_{\nu }=\mathrm{diag}(0.3,0.1,0.1)$ and $M_0=1\mathrm{TeV}$ as an example. In the left plot, the solid, dashed, and dotted curves correspond to the cases of the SM, the MSSM with $\tan \beta =10$, and $\tan \beta =50$, respectively. In the right plot, we show the case of the SM only.

Figure 6

An example of the RG evolution of the leptonic mixing angles with a nondiagonal $Y_{\nu }$ in the SM. We focus on the NH case and use $m_1=0.01\mathrm{eV}$ as a sample value.

Figure 7

Realizations of the bimaximal (left plot) and the tri-bimaximal (right plot) neutrino mixing patterns at the GUT scale. Here we only consider the ND case. In addition, for simplicity, we use $M_0=1\mathrm{TeV}$ for all the heavy singlets and take all the $CP$-violating phases to be zero. The solid, dashed, and dotted curves represent the SM, the MSSM with $\tan \beta =10$, and $\tan \beta =50$, respectively.