Europhys. Lett.
Volume 75, Number 2, July 2006
Page(s) 248 - 253
Section The physics of elementary particles and fields
Published online 14 June 2006
Europhys. Lett., 75 (2), pp. 248-253 (2006)
DOI: 10.1209/epl/i2006-10101-2

Neutrino mixing and CP violation from Dirac-Majorana bimaximal mixture and quark-lepton unification

J. Harada

Asia Pacific Center for Theoretical Physics - Pohang 790-784, Korea

received 20 February 2006; accepted in final form 26 May 2006
published online 14 June 2006

We demonstrate that only two ansätze can produce the features of the neutrino mixing angles. The first ansatz comes from the quark-lepton grand unification; $\nu_{Di} = V_{CKM}\ensuremath \nu_{\alpha}$ is satisfied for left-handed neutrinos, where $\nu_{Di}\equiv \ensuremath
(\nu_{D1},\nu_{D2},\nu_{D3})$ are the Dirac mass eigenstates and $\nu_{\alpha}\ensuremath \equiv (\nu_e, \nu_\mu, \nu_\tau)$ are the flavour eigenstates. The second ansatz comes from the assumption; $\nu_{Di}
= U_{bimaximal} \nu_{i}$ is satisfied between the Dirac mass eigenstates $\nu_{Di}$ and the light Majorana neutrino mass eigenstates $\nu_{i}\equiv \ensuremath(\nu_1, \nu_2, \nu_3)$, where Ubimaximal is the $3 \times 3$ rotation matrix that contains two maximal mixing angles and a zero mixing. By these two ansätze, the Maki-Nakagawa-Sakata lepton flavour mixing matrix is given by $U_{MNS} = \ensuremath V_{CKM}^\dagger U_{bimaximal}$. We find that in this model the novel relation $\theta_{sol} + \theta_{13} = \pi/4$ is satisfied, where $\theta_{sol}$ and $\theta_{13}$ are solar and CHOOZ angle, respectively. This "Solar-CHOOZ Complementarity" relation indicates that only if the CHOOZ angle $\theta_{13}$ is sizable, the solar angle $\theta_{sol}$ can deviate from the maximal mixing. Our predictions are $\theta_{sol} = 36^\circ$, $\theta_{13}
= 9^\circ$ and $\theta_{atm} = 45^\circ$, which are consistent with experiments. We also infer the CP violation in neutrino oscillations. The leptonic Dirac CP phase $\delta_{MNS}$ is predicted as $\sin \delta_{MNS} \simeq A \lambda^2 \eta$, where $A,
\lambda, \eta$ are the CKM parameters in Wolfenstein parametrization. In contrast to the quark CP phase $\delta_{CKM}
\simeq {\cal O}(1)$, the leptonic Dirac CP phase is very small, $\delta_{MNS} \ensuremath \simeq 0.8^\circ$. Furthermore, we remark that the ratio of the Jarlskog CP violation factor for quarks and leptons is important, because the large uncertainty on $\eta$ is cancelled out in the ratio, $R_J \equiv \ensuremath J_{CKM}/J_{MNS} \simeq 4\sqrt{2} A
\lambda^3 \simeq 5 \times 10^{-2}$.

14.60.Pq - Neutrino mass and mixing.

© EDP Sciences 2006