Lepton Mixing Matrices Research Articles

HIERARCHICAL MASSES AND UNIVERSAL MIXING IN QUARK–LEPTON MASS MATRICES

The universality hypothesis for quark and lepton mixing matrices (CKM and MNS) is further developed. This hypothesis explains why the CKM is almost diagonal whereas the MNS is almost maximally mixed. If this hypothesis is true, the Dirac CP violating phase of the MNS mixing matrix is bounded around π or 0. Quark–lepton mass matrices which realize this hypothesis are constructed, showing simple power law relations among mass matrices for up-type, down-type quarks and neutrinos.

Relatively large Theta13 from modification to the tri-bimaximal, bimaximal and democratic neutrino mixing matrices

Inspired by the indication of a relatively large θ 13 from accelerator and reactor neutrino oscillation experiments, we provide a systematic study of general modifications to the three well-studied neutrino mixing patterns, i.e., tri-bimaximal, bimaximal and democratic lepton mixing matrices. The correlation between θ 13 and the other two neutrino mixing angles are derived for each types of additional rotations. Predictions on θ 12 and θ 23 are also studied. Our study shows that, although some types of additional rotations are already excluded by the current global fit data of neutrino mixing angles, several types of additional rotations still survive. Our results may provide a guideline for the model building in neutrino physics.

Large $\theta_{13}^{\nu}$ and unified description of quark and lepton mixing matrices

We present a revised version of the so-called “yukawaon model”, which was proposed for the purpose of a unified description of the lepton mixing matrix U PMNS and the quark mixing matrix V CKM. It is assumed from a phenomenological point of view that the neutrino Dirac mass matrix M D is given with a somewhat different structure from the charged lepton mass matrix M e , although M D =M e was assumed in the previous model. As a result, the revised model predicts a reasonable value sin22θ 13∼0.07 with keeping successful results for other parameters in U PMNS as well as V CKM and quark and lepton mass ratios.

Comment on reparametrization invariance of quark–lepton complementarity

We study the complementarity between quark and lepton mixing angles (QLC), the sum of an angle in quark mixing and the corresponding angle in lepton mixing is π/4. Experimentally in the standard PDG parametrization, two such relations exist approximately. These QLC relations are accidental which only manifest themselves in the PDG parametrization. We propose reparametrization invariant expressions for the complementarity relations in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that |Vus/Vud|+|Ve2/Ve1|+|Vus/Vud||Ve2/Ve1|=1 and |Vcb/Vtb|+|Vμ3/Vτ3|+|Vcb/Vtb||Vμ3/Vτ3|=1. Expressions with deviations from exact complementarity are obtained. Implications of these relations are also discussed.

A new relation between quark and lepton mixing matrices

We propose a new relation between quark mixing matrix and lepton mixing matrix. Since the parameters in the quark sector are well determined, we employ them to describe the mixing of leptons. Phenomenologically, we study the neutrino oscillation probabilities for different channels, which can be measured precisely in forthcoming reactor and accelerator experiments. As an example of the applicability of our assumption, CP violation in the lepton sector is also discussed. In the latest T2K experiment, the range of the mixing angle θ13 is measured, and our prediction of θ13 is compatible with their result.

Unified description of quark and lepton mixing matrices based on a Yukawaon model

Based on a supersymmetric Yukawaon model with O(3) family symmetry, possible forms of quark and lepton mixing matrices are systematically investigated under a condition that the up-quark mass matrix form leads to the observed nearly tribimaximal mixing in the lepton sector. Although the previous model could not provide a good fitting of the observed quark mixing, the present model can give a reasonably good fitting not for lepton mixing but also the quark mixing by using a different origin of the $CP$ violation from one in the previous model.

Universal mass matrix for quarks and leptons andCPviolation

The measurements of the neutrino and quark mixing angles satisfy the empirical relations called Quark-Lepton Complementarity. These empirical relations suggest the existence of a correlation between the mixing matrices of leptons and quarks. In this work, we examine the possibility that this correlation between the mixing angles of quarks and leptons originates in the similar hierarchy of quarks and charged lepton masses and the seesaw mechanism type~I, that gives mass to the Majorana neutrinos. We assume that the similar mass hierarchies of charged lepton and quark masses allows us to represent all the mass matrices of Dirac fermions in terms of a universal form with four texture zeroes.

Unitarity boomerangs of quark and lepton mixing matrices

The most popular way to present mixing matrices of quarks (CKM) and leptons (PMNS) is the parametrization with three mixing angles and one CP-violating phase. There are two major options in this kind of parametrizations, one is the original Kobayashi–Maskawa (KM) matrix, and the other is the Chau–Keung (CK) matrix. In a new proposal by Frampton and He, a unitarity boomerang is introduced to combine two unitarity triangles, and this new presentation displays all four independent parameters of the KM parametrization in the quark sector simultaneously. In this Letter, we study the relations between KM and CK parametrizations, and also consider the quark–lepton complementarity (QLC) in the KM parametrization. The unitarity boomerang is discussed in the situation of the CK parametrization for comparison with that in the KM parametrization in the quark sector. Then we extend the idea of unitarity boomerang to the lepton sector, and check the corresponding unitarity boomerangs in the two cases of parametrizations.

Dependence of the quark-lepton complementarity on parametrizations of the Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata matrices

The quark-lepton complementarity (QLC) is very suggestive in understanding possible relations between quark and lepton mixing matrices. We explore the QLC relations in all the possible angle-phase parametrizations and point out that they can approximately hold in five parametrizations. Furthermore, the vanishing of the smallest mixing angles in the CKM and PMNS matrices can make sure that the QLC relations exactly hold in those five parametrizations. Finally, the sensitivity of the QLC relations to radiative corrections is also discussed.

Universal mass texture and quark-lepton complementarity

Recent measurements of the neutrino and quark mixing angles satisfy the empirical relations called quark-lepton complementarity. This empirical data suggests the existence of a correlation between the mixing matrices of leptons and quarks. In this work, we examine the possibility that this correlation between the mixing angles of quarks and leptons originates in the similar hierarchy of quarks and charged lepton masses and the seesaw mechanism type I that gives mass to the Majorana neutrinos. We asssume that the similar mass hierarchies of charged lepton masses and quark masses allows one to represent all the mass matrices of Dirac fermions in terms of a four zeros Fritzsch texture.

Unified triminimal parametrizations of quark and lepton mixing matrices

We present a detailed study on triminimal parametrizations of quark and lepton mixing matrices with different basis matrices. We start with a general discussion on the triminimal expansion of the mixing matrix and on possible unified quark and lepton parametrization using quark-lepton complementarity. We then consider several interesting basis matrices and compare the triminimal parametrizations with the Wolfenstein-like parametrizations. The usual Wolfenstein parametrization for quark mixing is a triminimal expansion around the unit matrix as the basis. The corresponding quark-lepton complementarity lepton mixing matrix is a triminimal expansion around the bimaximal basis. Current neutrino oscillation data show that the lepton mixing matrix is very well represented by the tribimaximal mixing. It is natural to take it as an expanding basis. The corresponding zeroth order basis for quark mixing in this case makes the triminimal expansion converge much faster than the usual Wolfenstein parametrization. The triminimal expansion based on tribimaximal mixing can be converted to the Wolfenstein-like parametrizations discussed in the literature. We thus have a unified description between different kinds of parametrizations for quark and lepton sectors: the standard parametrizations, the Wolfenstein-like parametrizations, and the triminimal parametrizations.

On-shell renormalization of the mixing matrices in Majorana neutrino theories

We generalize a recently proposed on-shell approach to renormalize the Cabibbo–Kobayashi–Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.

Unified parametrization for quark and lepton mixing angles

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 π/12 and π/5, respectively. The resulting 12-elements in the CKM and PMNS matrices, Vus and Ue2, are in this order irrational but simple algebraic numbers. We note that the cosine of π/5 is the golden ratio divided by two. The difference between π/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.

Suppressed flavor changing neutral current in new physics with shared flavor symmetry

Many extensions of the standard model (SM) generate contributions to flavor changing neutral current (FCNC) processes that must have sufficient flavor suppression to be consistent with experiments, if the new physics (NP) is associated with a scale of a TeV. Here we present a mechanism for suppressing the NP effects to FCNC processes while allowing for new non-SM $CP$ violating phases. We consider the possibility that the source of NP contributions to FCNC processes share the same flavor symmetry underlying the SM source of FCNC processes which are the quark and lepton mass matrices. We call this the principle of shared flavor symmetry. In the flavor symmetric limit, the quark and lepton mixing matrices have fixed forms and there are no NP FCNC processes. In the flavor symmetric limit, we take the quark mixing matrix to be the identity matrix and the lepton mixing matrix to be given by tri-bimaximal mixing. Realistic mixing matrices are obtained by the small breaking of the flavor symmetry. New contributions to FCNC processes arise because of nonuniversal breaking of the flavor symmetry in the quark and lepton mass matrices and the NP sources of FCNC processes. In particular, we will focus on new FCNC effects that arise due to the breaking of flavor symmetry only in the quark and charged lepton mass matrices but not in the NP sector. In this scenario, NP contributions to FCNC processes are linked to the source of flavor symmetry breaking in the quark and charged lepton mass matrices. The breaking of flavor symmetry in the NP sector is assumed to produce FCNC effects that are at most the size of NP FCNC effects due to the breaking of flavor symmetry in the quark and charged lepton mass matrices. To demonstrate the mechanism we use a two Higgs doublet model as an example of beyond the SM physics though one should be able to adapt this mechanism to other models of new physics.

NEUTRINO CP VIOLATING PARAMETERS FROM NONTRIVIAL QUARK–LEPTON CORRELATION: A S3 × GUT MODEL

We investigate the prediction on the lepton phases in theories with a nontrivial correlation between quark (CKM) and lepton (PMNS) mixing matrices. We show that the actual evidence, under the only assumption that the correlation matrix VM product of CKM and PMNS has a zero in the entry (1, 3), gives us a prediction for the three CP-violating invariants J, S1 and S2. A better determination of the lepton mixing angles will give stronger prediction for the CP-violating invariants in the lepton sector. These will be tested in the next generation experiments. To clarify how our prediction works, we show how a model based on a Grand Unified Theory and the permutation flavor symmetry S3 predicts [Formula: see text].

Testable deviations from exact tribimaximal mixing

A simple relation UPMNS=VCKM†UTB between the lepton and quark mixing matrices (UPMNS and VCKM) is speculated under an ansatz that UPMNS becomes an exact tribimaximal mixing UTB in a limit VCKM=1. By using the observed CKM mixing parameters, possible values of neutrino oscillation parameters are estimated: sin2θ13=0.024–0.028, sin22θ23=0.94–0.95 and tan2θ12=0.24–1.00 depending on phase conventions of UTB. Those values are testable soon by precision measurements in neutrino oscillation experiments.

Unified parametrization of quark and lepton mixing matrices in a tribimaximal pattern

Parametrization of the quark and lepton mixing matrices is the first attempt to understand the mixing of fermions. In this work, we parametrize the quark and lepton mixing matrices with the help of quark-lepton complementarity in a tribimaximal pattern of the lepton mixing matrix. In this way, we combine the parametrization of the two matrices. We apply this new parametrization to several physical quantities, and show its simplicity in the expression of, e.g., the Jarlskog parameter of $CP$ violation.

PREDICTIONS FROM NON-TRIVIAL QUARK-LEPTON COMPLEMENTARITY

The complementarity between the quark and lepton mixing matrices is shown to provide robust predictions. We obtain these predictions by first showing that the matrix VM, product of the quark (CKM) and lepton (PMNS) mixing matrices, may have a zero (1,3) entry which is favored by experimental data. We obtain that any theoretical model with a vanishing (1,3) entry of VM that is in agreement with quark data, solar, and atmospheric mixing angle leads to [Formula: see text]. This value is consistent with the present 90% CL experimental upper limit. We also investigate the prediction on the lepton phases. We show that the actual evidence, under the only assumption that the correlation matrix VM product of CKM and PMNS has a zero in the entry (1, 3), gives us a prediction for the three CP-violating invariants J, S1, and S2. A better determination of the lepton mixing angles will give stronger prediction for the CP-violating invariants in the lepton sector. These will be tested in the next generation experiments. Finally we compute the effect of non diagonal neutrino mass in li → ljγ in SUSY theories with non trivial Quark-Lepton complementarity and a flavor symmetry. The Quark-Lepton complementarity and the flavor symmetry strongly constrain the theory and we obtain a clear prediction for the contribution to μ → eγ and the τ decays τ → eγ and τ → μγ. If the Dirac neutrino Yukawa couplings are degenerate but the low energy neutrino masses are not degenerate, then the lepton decays are related among them by the VM entries. On the other hand, if the Dirac neutrino Yukawa couplings are hierarchical or the low energy neutrino masses are degenerate, then the prediction for the lepton decays comes from the CKM hierarchy.

Rephasing invariants of quark and lepton mixing matrices

Rephasing invariants of quark and lepton mixing matrices are obtained in the Standard Model extended by the seesaw mechanism, and in its low-energy effective theory with the dimension-five Majorana mass operator. We classify the basic invariants, discuss non-trivial relations between them, and determine the independent invariants which characterize all the information in the mixing matrices in a basis-independent way. We also discuss the restrictions on the allowed ranges for the mixing phases, and on the rephasing invariants, which follow from a discrete invariance of the Majorana mass matrix.

Neutrino mixings and leptonicCPviolation from CKM matrix and Majorana phases

The high scale mixing unification hypothesis recently proposed by three of us (R. N. M., M. K. P. and G. R.) states that if at the seesaw scale the quark and lepton mixing matrices are equal, then for quasidegenerate neutrinos radiative corrections can lead to large solar and atmospheric mixings and small reactor angle at the weak scale in agreement with data. Evidence for quasidegenerate neutrinos could, within this framework, be interpreted as being consistent with quark-lepton unification at high scale. In the current work, we extend this model to show that the hypothesis works quite successfully in the presence of $CP$-violating phases (which were set to zero in the first paper). In the case where the Pontecorvo-Maki-Nakagawa-Sakata matrix is identical to the Cabibbo-Kobayashi-Maskawa quark-mixing matrix at the seesaw scale, with a Dirac phase but no Majorana phase, the low energy Dirac phase is predicted to be ($\ensuremath{\simeq}0.3\ifmmode^\circ\else\textdegree\fi{}$) and leptonic $CP$-violation parameter ${J}_{CP}\ensuremath{\simeq}(4\ensuremath{-}8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and ${\ensuremath{\theta}}_{13}=3.5\ifmmode^\circ\else\textdegree\fi{}$. If on the other hand, the Pontecorvo-Maki-Nakagawa-Sakata matrix is assumed to also have non-negligible Majorana phase(s) initially, the resulting theory damps radiative magnification phenomenon for a large range of parameters but nevertheless has enough parameter space to give the two necessary large neutrino mixing angles. In this case, one has ${\ensuremath{\theta}}_{13}=3.5\ifmmode^\circ\else\textdegree\fi{}--10\ifmmode^\circ\else\textdegree\fi{}$ and $|{J}_{CP}|$ as large as 0.02--0.04 which are accessible to long baseline neutrino oscillation experiments.