High scale mixing unification for Dirac neutrinos

Starting with the high scale mixing unification hypothesis, we investigate the renormalization-group evolution of mixing parameters and masses for Dirac-type neutrinos. Following this hypothesis, the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing angles and phase are taken to be identical to the Cabibbo-Kobayashi-Maskawa (CKM) ones at a unifying high scale. Then they are evolved to a low scale using renormalization-group equations. The notable feature of this hypothesis is that renormalization-group evolution with quasidegenerate mass pattern can explain largeness of leptonic mixing angles even for Dirac neutrinos. The renormalization-group evolution “naturally” results in a nonzero and small value of leptonic mixing angle ${\theta }_{13}$. One of the important predictions of this work is that the mixing angle ${\theta }_{23}$ is nonmaximal and lies only in the second octant. We also derive constraints on the allowed parameter range for the supersymmetry breaking and unification scales for which this hypothesis works. The results are novel and can be tested by present and future experiments.

Figure 1

The RG evolution of the neutrino masses $m_i(i=1,2,3)$, quark ${\theta }_{ij}^q(i,j=1,2,3)$ and leptonic mixing angles ${\theta }_{ij}$, and neutrino Dirac phase $\delta$ and $J_{\mathrm{CP}}$ with respect to the RG scale $\mu$, from the unification scale ($2\times {10}^{16}\mathrm{GeV}$) to low scale ($M_Z$). The SUSY breaking scale and $\tan \beta$ are taken as 2 TeV and 55, respectively.

Figure 2

The behavior of leptonic mixing angle ${\theta }_{13}$ with ${\theta }_{23}$. In plotting this figure we have kept ${\theta }_{12}$ fixed at its lower end of the $3\sigma$ range and all other oscillation parameters within their $3\sigma$ range.

Figure 3

The variation of $\xi$ with the SUSY breaking scale. The vertically shaded region is disallowed by LHC SUSY searches [43] whereas the horizontal one lies outside the $3\sigma$ range of $\xi$ [44].

Figure 4

The variation of $\xi$ with the unification scale. The shaded region lies outside the allowed parameter range of $\xi$ [44].