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Register a new userPerturbative Estimates of Lepton Mixing Angles in Unified Models
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Many unified models predict two large neutrino mixing angles, with the charged lepton mixing angles being small and quark-like, and the neutrino masses being hierarchical. Assuming this, we present simple approximate analytic formulae giving the lepton mixing angles in terms of the underlying high energy neutrino mixing angles together with small perturbations due to both charged lepton corrections and renormalisation group (RG) effects, including also the effects of third family canonical normalization (CN). We apply the perturbative formulae to the ubiquitous case of tri-bimaximal neutrino mixing at the unification scale, in order to predict the theoretical corrections to mixing angle predictions and sum rule relations, and give a general discussion of all limiting cases.
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We propose a new parametrization for the quark and lepton mixing matrices: the two 12-mixing angles (the Cabibbo angle and the angle responsible for solar neutrino oscillations) are at zeroth order pi/12 and pi/5, respectively. The resulting 12-elements in the CKM and PMNS matrices, V_{us} and U_{e2}, are in this order irrational but simple algebraic numbers. We note that the cosine of pi/5 is the golden ratio divided by two. The difference between pi/5 and the observed best-fit value of solar neutrino mixing is of the same order as the difference between the observed value and the one for tri-bimaximal mixing. In order to reproduce the central values of current fits, corrections to the zeroth order expressions are necessary. They are small and of the same order and sign for quarks and leptons. We parametrize the perturbations to the CKM and PMNS matrices in a triminimal way, i.e., with three small rotations in an order corresponding to the order of the rotations in the PDG-description of mixing matrices.
Inspired by a new relation $theta_{13}^{rm PMNS}={theta_C}/{sqrt{2}}$ observed from the relatively large $theta_{13}^{rm PMNS}$, we find that the combination of this relation with the quark-lepton complementarity and the self-complementarity results in correlations of the lepton mixing angles with the quark mixing angles. We find that the three mixing angles in the PMNS matrix are all related to the Wolfenstein parameter $lambda$ in the quark mixing, so they are also correlated. Consequently, the PMNS matrix can be parameterized by $lambda$, A, and a Dirac CP-violating phase $delta$. Such parametrizations for the PMNS matrix have the same explicitly hierarchical structure as the Wolfenstein parametrization for the CKM matrix in the quark mixing, and the bimaximal mixing pattern is deduced at the leading order. We also discuss implications of these phenomenological relations in parametrizations.
We discuss the constraints of lepton mixing angles from lepton number violating processes such as neutrinoless double beta decay, (mu^-)-(e^+) conversion and K decay, $K^- to pi^+mu^-mu^-$ which are allowed only if neutrinos are Majorana particles. The rates of these processes are proportional to the averaged neutrino mass defined by $<m_{ u} >_{a b}equiv |sum_{j=1}^{3}U_{a j} U_{b j}m_j|$ in the absence of right-handed weak coupling. Here $a, b (j)$ are flavour(mass) eigen states and $U_{a j}$ is the left-handed lepton mixing matrix. We obtain the consistency conditions which are satisfied irrelevant to the concrete values of CP violation phases (three phases in Majorana neutrinos). These conditions constrain the lepton mixing angles, neutrino masses $m_i$ and (< m_{ u} >_{a b}). By using these constraints we obtain the limits on the averaged neutrino masses for (mu^-)-(e^+) conversion and K decay, $K^- to pi^+mu^-mu^-$.
We propose two phenomenological scenarios of lepton mass matrices and show that either of them can exactly give rise to tan^2theta_{13} = m_e/(m_e + 2m_mu), tan^2theta_{23} = m_mu/(m_e + m_mu) and tan^2theta_{12} = (m_e m_2 + 2m_mu m_1)/(m_e m_1 + 2m_mu m_2) in the standard parametrization of lepton flavor mixing. The third relation, together with current experimental data, predicts a normal but weak hierarchy for the neutrino mass spectrum. We also obtain theta_{13} approx 2.8^circ for the smallest neutrino mixing angle and J approx 1.1% for the Jarlskog invariant of leptonic CP violation, which will soon be tested in the long-baseline reactor and accelerator neutrino oscillation experiments. A seesaw realization of both scenarios is briefly discussed.
We investigate a model on an extra dimension $S^1$ where plenty of effective boundary points described by point interactions (zero-thickness branes) are arranged. After suitably selecting the conditions on these points for each type of five-dimensional fields, we realize the tiny active neutrino masses, the charged lepton mass hierarchy, and lepton mixings with a CP-violating phase, simultaneously. Not only the quarks but also the leptons configurations are generated in a unified way with acceptable accuracy, with neither the see-saw mechanism nor symmetries in Yukawa couplings, by suitably setting the model parameters, even though their flavor structures are dissimilar each other. One remarkable point is that a complex vacuum expectation value of the five-dimensional Higgs doublet in this model becomes the common origin of the CP violation in both quark and lepton sectors. The model can be consistent with the results of the precision electroweak measurements and Large Hadron Collider experiments.
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