Quark–lepton complementarity with lepton and quark mixing data predict θ13 PMNS=(9+1 -2)°

Abstract

The complementarity between the quark and lepton mixing matrices is shown to provide a robust prediction for the neutrino mixing angle θ P M N S 13. We obtain this prediction by first showing that the matrix V M , product of the CKM and PMNS mixing matrices, may have a zero (1,3) entry which is favored by experimental data. Hence models with bimaximal or tribimaximal forms of the correlation matrix V M are quite possible. Any theoretical model with a vanishing (1,3) entry of V M that is in agreement with quark data, solar, and atmospheric mixing angle leads to θ P M N S 13 = (9 +1−2 ) • . This value is consistent with the present 90% CL experimental upper limit.

Quark-lepton complementarity predictions for θ 23 pmns and CP violation

“…in terms of the angles of the correlation matrix V c (r.h.s. ): We can see that this is exactly the equation 21 of the work [32]. From the figure we can clearly see that the allowed range for sin 2 θ 13 of V c corresponding to the experimental range of sin 2 θ pmns 13 is quite wide including sin 2 θ 13 = 0.…”

“…The main motivation of the present work is to re-visit the QLC Model, which we proposed in 2007 [32]. The work came into light, when its predictions for the reactor mixing angle θ pmns 13 = (9 +1 −2 ) • was found to be in strong agreement with the experimental results [3][4][5][6][7].…”

“…The reason behind such a situation is that the estimation of this element V 13 c is weighted heavily by the value θ pmns 13 as compared to the other PMNS angles and CKM parameters. So, keeping θ pmns 13 free to vary flatly between 0.00 to 0.32 as we did in [32] the non-trivial combination PMNS angles, λ's and other non-restricted phases etc. leads to the probability density of the element V 13 c to peak at zero.…”

“…V 13 c = 0, we need to look for some relevant flavour models. As per our model procedure, in order to constrain the lepton mixing parameter namely the less constrained ones θ pmns 23 and the three lepton CP violating phase invariants (J, S 1 , S 2 ) we use the inverse equation [32] …”

Flavor physics of leptons and dipole moments

“…As a consequence of that, a S 3 flavor permutation symmetry, softly broken into S 2 , gives us the prediction of V M 13 = 0 [275] and the correlations between CP-violating phases and the mixing angle 12 [276]. The six generators of the S 3 flavor symmetry are the elements of the permutation group of three objects.…”