Lepton Mixing Matrices Research Articles

Five texture zeros in the lepton sector and neutrino oscillations at DUNE

In this work, we have assumed special structures for the charged and neutral mass matrices in the lepton sector, inspired by structures for the up and down quark mass matrices that result by assuming a certain number of symmetrical zeros in their entries named texture zeros. A prediction of the lepton mixing matrix results from the rotation matrices that diagonalize the mass matrices in the neutral and charged lepton sectors. The use of texture zeros reduces the number of spurious parameters to the minimal ones needed to explain observations i.e., charged lepton masses and neutrino oscillation parameters. Specifically, we have considered the case of five texture zeros and we have confronted the resulting lepton mixing matrices with current measurements in the neutrino sector. Finally, sensitivities to the independent parameters in the mixing predicted by the nonequivalent forms were studied using simulated events at the DUNE neutrino oscillation experiment. We have found that DUNE is sensitive to nonzero $CP$ violation allowed in the models.

Informationally Complete Characters for Quark and Lepton Mixings

A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters κ of a finite group G. Here, we introduce a d-dimensional Hilbert space with d = c c ( G ) , the number of conjugacy classes of G. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of a d-dimensional Pauli group over the characters of these representations. Groups with small d that satisfy these rules coincide in a large part with viable ones derived so far for reproducing simultaneously the CKM (quark) and PNMS (lepton) mixing matrices.

New Partial Symmetries from Group Algebras for Lepton Mixing

Recent stringent experiment data of neutrino oscillations induces partial symmetries such as Z2 and Z2×CP to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A specific lepton mixing pattern could correspond to a set of equivalent elements of a group algebra. The transformation which interchanges the elements could express a residual CP symmetry. Lepton mixing matrices from S3 group algebras are of the trimaximal form with the μ−τ reflection symmetry. Accordingly, elements of S3 group algebras are equivalent to Z2×CP. Comments on S4 group algebras are given. The predictions of Z2×CP broken from the group S4 with the generalized CP symmetry are also obtained from elements of S4 group algebras.

Representing seesaw neutrino models and their motion in lepton flavour space

We discuss how seesaw neutrino models can be graphically represented in lepton flavour space. We examine various popular models and show how this representation helps understanding their properties and connection with experimental data showing in particular how certain texture zero models are ruled out. We also introduce a new matrix, the bridging matrix, that brings from the light to the heavy neutrino mass flavour basis, showing how this is related to the orthogonal matrix and how different quantities are easily expressed through it. We then show how one can randomly generate orthogonal and leptonic mixing matrices uniformly covering all flavour space in an unbiased way (Haar-distributed matrices). Using the isomorphism between the group of complex rotations and the Lorentz group, we also introduce the concept of Lorentz boost in flavour space for a seesaw model and how this has an insightful physical interpretation. Finally, as a significant application, we consider N2-leptogenesis. Using current experimental values of low energy neutrino parameters, we show that the probability that at least one flavoured decay parameter of the lightest right-handed neutrino is smaller than unity is about 49% (to be compared with the tiny probability that the total decay parameter is smaller than unity, P (KI< 1) ∼ 0.1%, confirming the crucial role played by flavour effects). On the other hand when m1 ≳ 0.1 eV this probability reduces to less than 5%, showing how also N2-leptogenesis disfavours degenerate light neutrinos.

Lepton mixing predictions from S4 in the tridirect CP approach to two right-handed neutrino models

We perform an exhaustive analysis of all possible breaking patterns arising from $S_4\rtimes H_{CP}$ in a new {\it tri-direct CP approach} to the minimal seesaw model with two right-handed neutrinos, and construct a realistic flavour model along these lines. According to this approach, separate residual flavour and CP symmetries persist in the charged lepton, `atmospheric' and `solar' right-handed neutrino sectors, i.e. we have {\it three} symmetry sectors rather than the usual two of the {\it semi-direct CP approach} (charged leptons and neutrinos). Following the {\it tri-direct CP approach}, we find twenty-six kinds of independent phenomenologically interesting mixing patterns. Eight of them predict a normal ordering (NO) neutrino mass spectrum and the other eighteen predict an inverted ordering (IO) neutrino mass spectrum. For each phenomenologically interesting mixing pattern, the corresponding predictions for the PMNS matrix, the lepton mixing parameters, the neutrino masses and the effective mass in neutrinoless double beta decay are given in a model independent way. One breaking pattern with NO spectrum and two breaking patterns with IO spectrum corresponds to form dominance. We find that the lepton mixing matrices of three kinds of breaking patterns with NO spectrum and one form dominance breaking pattern with IO spectrum preserve the first column of the tri-bimaximal (TB) mixing matrix, i.e. yield a TM1 mixing matrix.

Predicting neutrino oscillations with “bi-large” lepton mixing matrices

We propose two schemes for the lepton mixing matrix U=Ul†Uν, where U=Ul refers to the charged sector, and Uν denotes the neutrino diagonalization matrix. We assume Uν to be CP conserving and its three angles to be connected with the Cabibbo angle in a simple manner. CP violation arises solely from the Ul, assumed to have the CKM form, Ul≃VCKM, suggested by unification. Oscillation parameters depend on a single parameter, leading to narrow ranges for the “solar” and “accelerator” angles θ12 and θ23, as well as for the CP phase, predicted as δCP∼±1.3π.

Neutrino mixing in SO(10) GUTs with a non-Abelian flavor symmetry in the hidden sector

The relation between the mixing matrices of leptons and quarks, ${U}_{\mathrm{PMNS}}\ensuremath{\approx}{V}_{\mathrm{CKM}}^{\ifmmode\dagger\else\textdagger\fi{}}{U}_{0}$, where ${U}_{0}$ is a matrix of special forms [e.g., bimaximal (BM) and tribimaximal], can be a clue for understanding the lepton mixing and neutrino masses. It may imply the grand unification and the existence of a hidden sector with certain symmetry that generates ${U}_{0}$ and leads to the smallness of neutrino masses. We apply the residual symmetry approach to obtain ${U}_{0}$. The residual symmetries of both the visible and hidden sectors are ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$. Their embedding in a unified flavor group is considered. We find that there are only several possible structures of ${U}_{0}$, including the BM mixing and matrices with elements determined by the golden ratio. Realization of the BM scenario based on the SO(10) grand unified theory with the ${S}_{4}$ flavor group is presented. Generic features of this scenario are discussed, in particular, the prediction of $CP$ phase $144\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\lesssim}{\ensuremath{\delta}}_{\mathrm{CP}}\ensuremath{\lesssim}210\ifmmode^\circ\else\textdegree\fi{}$ in the minimal version.

Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries

We discussed the scenario that a discrete flavor group combined with CP symmetry is broken to Z2 × CP in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free parameters θl and θν varying in the range of [0, π). As an example, we comprehensively study the lepton mixing patterns which can be derived from the flavor group Δ(6n2) and CP symmetry. Three kinds of phenomenologically viable lepton mixing matrices are obtained up to row and column permutations. We further extend this approach to the quark sector. The precisely measured quark mixing angles and CP invariant can be accommodated for certain values of the free parameters θu and θd. A simultaneous description of quark and lepton flavor mixing structures can be achieved from a common flavor group Δ(6n2) and CP, and accordingly the smallest value of the group index n is n = 7.

CP symmetry and lepton mixing from a scan of finite discrete groups

Including the generalized CP symmetry, we have performed a comprehensive scan of leptonic mixing patterns which can be obtained from finite discrete groups with order less than 2000. Both the semidirect approach and its variant are considered. The lepton mixing matrices which can admit a good agreement with experimental data can be organized into eight different categories up to possible row and column permutations. These viable mixing patterns can be completely obtained from the discrete flavor groups $\Delta(6n^2)$, $D^{(1)}_{9n,3n}$, $A_5$ and $\Sigma(168)$ combined with CP symmetry. We perform a detailed analytical and numerical analysis for each possible mixing pattern. The resulting predictions for lepton mixing parameter, neutrinoless double decay and flavored leptogenesis are studied.

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

In the light of recent experimental results on $\theta_{13}^{pmns}$, we re-investigate the complementarity between the quark and lepton mixing matrices and obtain predictions for most unsettled neutrino mixing parameters like $\theta_{23}^{pmns}$ and CP violating phase invariants $J$, $S_1$ and $S_2$. This paper is motivated by our previous work where in a QLC model we predicted the value for $\theta_{13}^{pmns}=(9{^{+1}_{-2}})^\circ$, which was found to be in strong agreement with the experimental results. In the QLC model the non-trivial correlation between CKM and PMNS mixing matrices is given by a correlation matrix ($V_{c}$). We do numerical simulation and estimate the texture of the $V_{c}$ and in our findings we get a small deviation from the Tri-Bi-Maximal (TBM) texture and a large from the Bi-Maximal one, which is consistent with the work already reported in literature. In the further investigation we obtain quite constrained limits for $sin^2{\theta_{23}^{pmns}}= 0.4235_{-0.0043}^{+0.0032}$ that is narrower to the existing ones. We also obtain the constrained limits for the three CP violating phase invariants $J$, $S_1$ and $S_2$: as $J < 0.0315$, $S_{1} <0.12$ and $S_{2} <0.08$, respectively.

Standard Model fermion masses and mixing angles generated in 3HDM

We present a framework to generate the mass hierarchies and mixing angles of the fermionic sector of the Standard Model with two extra Higgs doublets and one right-handed neutrino. The masses of the first and second generation are generated by small quantum effects, explaining the hierarchy with the third generation. The model also generates a natural hierarchy between the first and second generation after the assumption that the Yukawa couplings are of rank 1. All the quark and lepton mixing matrices can also be generated by quantum effects, reproducing the hierarchies of the experimental values. The parameters generated radiatively depend logarithmically on the heavy Higgs masses. Therefore this framework can be reconciled with the stringent limits on flavour violation by postulating a sufficiently large new physics scale.

Spontaneous violation of mirror symmetry

A symmetry violation model is considered for a system that can spontaneously choose between identical states which differ from each other only in weak properties (R-L). Such mirror symmetry allows reproduction of observed qualitative properties of quark and lepton mixing matrices. The lepton mixing matrix evidences in this case in favor of the inverse mass spectrum and the Dirac nature of SM neutrino. Notwithstanding the Dirac properties of neutrino, an exchange of lepton numbers such as $e^{-}+\mu^{+}\rightarrow e^{+}+\mu^{-}$ is possible but with only leptons participating in the process.

Lepton mixing from the hidden sector

Experimental results indicate a possible relation between the lepton and quark mixing matrices of the form U_PMNS \approx V_CKM^\dagger U_X, where U_X is a matrix with special structure related to the mechanism of neutrino mass generation. We propose a framework which can realize such a relation. The main ingredients of the framework are the double seesaw mechanism, SO(10) Grand Unification and a hidden sector of theory. The latter is composed of singlets (fermions and bosons) of the GUT symmetry with masses between the GUT and Planck scale. The interactions in this sector obey certain symmetries G_hidden. We explore the conditions under which symmetries G_hidden can produce flavour structures in the visible sector. Here the key elements are the basis-fixing symmetry and mediators which communicate information about properties of the hidden sector to the visible one. The interplay of SO(10) symmetry, basis-fixing symmetry identified as Z2 x Z2 and G_hidden can lead to the required form of U_X. A different kind of new physics is responsible for generation of the CKM mixing. We present the simplest realizations of the framework which differ by nature of the mediators and by symmetries of the hidden sector.

A microscopic approach to quark and lepton masses and mixings

In recent papers, a microscopic model for the SM Higgs mechanism has been proposed, and an idea how to determine the 24 quark and lepton masses of all three generations has emerged in that framework. This idea is worked out in detail here by accommodating the fermion masses and mixings to microscopic parameters. The top quark mass can be given in terms of the Fermi scale and of certain exchange couplings of isospin vectors obeying a tetrahedral symmetry. The observed hierarchy in the family spectrum is attributed to a natural hierarchy in the microscopic couplings. The neutrinos will be shown to vibrate within the potential valleys of the system, thus retaining very tiny masses. This is related to a Goldstone effect inside the internal dynamics. A discussion of the quark and lepton mixing matrices is also included. The mixing angles of the PMNS matrix are calculated for an example set of parameters, and a value for the CP-violating phase is given.

The double mass hierarchy pattern: Simultaneously understanding quark and lepton mixing

The charged fermion masses of the three generations exhibit the two strong hierarchies m3≫m2≫m1. We assume that also neutrino masses satisfy mν3>mν2>mν1 and derive the consequences of the hierarchical spectra on the fermionic mixing patterns. The quark and lepton mixing matrices are built in a general framework with their matrix elements expressed in terms of the four fermion mass ratios, mu/mc, mc/mt, md/ms and ms/mb, and me/mμ, mμ/mτ, mν1/mν2 and mν2/mν3, for the quark and lepton sector, respectively. In this framework, we show that the resulting mixing matrices are consistent with data for both quarks and leptons, despite the large leptonic mixing angles. The minimal assumption we take is the one of hierarchical masses and minimal flavor symmetry breaking that strongly follows from phenomenology. No special structure of the mass matrices has to be assumed that cannot be motivated by this minimal assumption. This analysis allows us to predict the neutrino mass spectrum and set the mass of the lightest neutrino well below 0.01 eV. The method also gives the 1σ allowed ranges for the leptonic mixing matrix elements. Contrary to the common expectation, leptonic mixing angles are found to be determined solely by the four leptonic mass ratios without any relation to symmetry considerations as commonly used in flavor model building. Still, our formulae can be used to build up a flavor model that predicts the observed hierarchies in the masses — the mixing follows then from the procedure which is developed in this work.

Roots of Unity and Lepton Mixing Patterns from Finite Flavour Symmetries

The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem.

Lepton mixing, residual symmetries, and trigonometric Diophantine equations

In this paper, we study residual symmetries in the lepton sector. Our first concern is the symmetry of the charged lepton mass matrix in the basis where the Majorana neutrino mass matrix is diagonal, which is strongly constrained by the requirement that the symmetry group generated by residual symmetries is finite. In a recent work R. M. Fonseca and W. Grimus found that there exists a set of constraint equations that can be completely solved, which is essential in their approach to the classification of lepton mixing matrices that are fully determined by residual symmetries. In this paper, a method to handle trigonometric Diophantine equations is introduced. We will show that the constraint equations found by Fonseca and Grimus can also be solved by this method. Detailed derivation and discussion will be presented in a self-contained way. In addition, we will also show that, in the case where residual symmetries satisfy a reality condition, this method can be used to solve the equation constraining parameters in the symmetry assignment that controls the group structure generated by residual symmetries and is directly related to mixing matrix elements.

Flavour models with three Higgs generations

We construct models with a spontaneously broken $SU(3)_F$ flavour symmetry where three generations of Higgs multiplets transform in a flavour-triplet representation. The models are embedded in a supersymmetric Pati-Salam GUT framework, which includes left-right symmetry. We study the possible flavon representations and show that a model with flavons in the decuplet representation is able to reproduce the hierarchy structure of the quark and lepton mass and mixing matrices. This result requires no additional structure or fine-tunings except for an extra $Z_4$ discrete symmetry in the superpotential.

Classification of lepton mixing matrices from finite residual symmetries

Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level.

Double seesaw mechanism and lepton mixing

We present a general framework for models in which the lepton mixing matrix is the product of the maximal mixing matrix U_\omega\ times a matrix constrained by a well-defined Z_2 symmetry. Our framework relies on neither supersymmetry nor non-renormalizable Lagrangians nor higher dimensions; it relies instead on the double seesaw mechanism and on the soft breaking of symmetries. The framework may be used to construct models for virtually all the lepton mixing matrices of the type mentioned above which have been proposed in the literature.