Quark-lepton complementarity and tribimaximal neutrino mixing from discrete symmetry

Abstract

The quark-lepton complementarity (QLC) relations indicate a deep structure that interrelates quarks and leptons. We propose new scenarios, in a seesaw framework with discrete $A_4$ flavor symmetry, which can accommodate the QLC relations and the nonzero neutrino mixing angle $\theta_{13}$ together with all the available neutrino experimental data, in a consistent way to generate the Cabibbo-Kobayashi-Maskawa (CKM) matrix for the quark mixing. Certain effective dimension-5 operators are introduced, which induce a deviation of the lepton mixing matrix from the tribimaximal mixing (TBM) pattern and lead the quark mixing matrix to the CKM one in form. We explicitly demonstrate three different possibilities of constructing the charged lepton mixing matrix and point out that the {\it phases} of whose elements play a crucial role to satisfy the QLC relations. We find that for the reactor mixing angle $\theta_{13}$ its possible values can vary around the center value $\sin \theta_{13} \simeq \lambda /\sqrt{2}$ ($\lambda \simeq 0.22$ being the Cabbibo angle) and have the lower bound $\theta_{13} \gtrsim 3.5^{\circ}$. We also show that sizable leptonic CP violation characterized by the Jarlskog invariant $|J_{\rm CP}|\sim{\cal O}(10^{-2})$ is allowed, which is expected to be tested in the future experiments such as the upcoming long baseline neutrino oscillation ones.