Twisted flavors and tribimaximal neutrino mixing

A new framework for handling flavor symmetry breaking in the neutrino sector is discussed where the source of symmetry breaking is traced to the global property of right-handed neutrinos in extra-dimensional space. Light neutrino phenomenology has rich and robust predictions such as the tribimaximal form of generation mixing, controlled mass spectrum, and no need of flavor mixing couplings in the theory.     

Determining horizontal symmetry from neutrino mixing

We argue that the best way to determine horizontal symmetry is from neutrino mixing and proceed to show that the only finite group capable of yielding the tribimaximal mixing for all Yukawa couplings is S4, or any group containing it. The method used is largely group theoretical, but it can be implemented by dynamical schemes in which the Higgs expectation values introduced to break S4 spontaneously are uniquely determined up to an unknown scale for each.     

Nonzero θ13 for neutrino mixing in the context of A4 symmetry

In the original 2004 paper which first derived tribimaximal mixing in the context of A(4), i.e., the non-Abelian finite symmetry group of the tetrahedron, as its simplest application, it was also pointed out how θ(13) ≠ 0 may be accommodated. On the strength of the new T2K result that 0.03(0.04) ≤ sin(2)2θ(13) ≤ 0.28(0.34) for δ(CP) = 0 and normal (inverted) neutrino mass hierarchy, we perform a more detailed analysis of how this original idea may be realized in the context of A(4).     

Unitary parametrization of perturbations to tribimaximal neutrino mixing

Current experimental data on neutrino mixing are very well described by tribimaximal mixing. Accordingly, any phenomenological parametrization of the Maki-Nakagawa-Sakata-Pontecorvo matrix must build upon tribimaximal mixing. We propose one particularly natural parametrization, which we call "triminimal." The three small deviations of the Particle Data Group angles from their tribimaximal values, and the PDG phase, parametrize the triminimal mixing matrix. As an important example of the utility of this new parametrization, we present the simple resulting expressions for the flavor-mixing probabilities of atmospheric and astrophysical neutrinos. As no foreseeable experiment will be sensitive to more than second order in the small parameters, we expand these flavor probabilities to second order.     

Comparative Analysis of CP Violation in the Exponential and Standard Parametrizations of the Neutrino Mixing Matrix

Physics of Atomic Nuclei - A comparative analysis of neutrino mixing in the standard, cobimaximal, tribimaximal, and exponential parametrizations is performed. The logarithm of the mixing matrix...     

Lepton family symmetries for neutrino masses and mixing

I review some of the recent progress (up to December 2005) in applying non-Abelian discrete symmetries to the family structure of leptons, with particular emphasis on the tribimaximal mixing ansatz of Harrison, Perkins and Scott.     

Magic neutrino mass matrix and the Bjorken–Harrison–Scott parameterization

Observed neutrino mixing can be described by a tribimaximal MNS matrix. The resulting neutrino mass matrix in the basis of a diagonal charged lepton mass matrix is both 2–3 symmetric and magic. By a magic matrix, I mean one whose row sums and column sums are all identical. I study what happens if 2–3 symmetry is broken but the magic symmetry is kept intact. In that case, the mixing matrix is parameterized by a single complex parameter U_e3, in a form discussed recently by Bjorken, Harrison, and Scott.     

O(3) flavor symmetry and an empirical neutrino mass matrix

Based on a new approach to quark and lepton masses, where the mass spectra originate in vacuum expectation values of O(3)-flavor 1+5$\mathbf{1}+\mathbf{5}$ (gauge singlet) scalars, a neutrino mass matrix of a new type is speculated. The mass matrix is described in terms of the up-quark and charged lepton masses, and, by assuming a special flavor basis, it can be accommodated to a nearly tribimaximal mixing without explicitly assuming a discrete symmetry. Quark mass relations are also discussed based on the new approach.     

A<Subscript>4</Subscript> symmetry and lepton masses and mixing

Stimulated by Ma’s idea, which explains the tribimaximal neutrino mixing by assuming an A₄ flavor symmetry, a lepton mass matrix model is investigated. A Frogatt–Nielsen-type model is assumed, and the flavor structures of the masses and mixing are caused by the VEVs of SU(2)_L singlet scalars φ_i ^u and φ_i ^d (i=1,2,3), which are assigned to 3 and (1 ,1 ’,1 ”) of A₄, respectively. Possible charged lepton and neutrino mass spectra and mixing are investigated.     

The 3-3-1 model with <Emphasis Type="Italic">S</Emphasis><Subscript>4</Subscript> flavor symmetry

We construct a 3-3-1 model based on family symmetry S ₄ responsible for the neutrino and quark masses. The tribimaximal neutrino mixing and the diagonal quark mixing have been obtained. The new lepton charge \(\mathcal{L}\) related to the ordinary lepton charge L and a SU(3) charge by \(L=\frac{2}{\sqrt{3}}T_{8}+\mathcal{L}\) and the lepton parity P _l =(?) ^L known as a residual symmetry of L have been introduced which provide insights in this kind of model. The expected vacuum alignments resulting in potential minimization can origin from appropriate violation terms of S ₄ and \(\mathcal{L}\). The smallness of seesaw contributions can be explained from the existence of such terms too. If P _l is not broken by the vacuum values of the scalar fields, there is no mixing between the exotic and the ordinary quarks at tree level.     

Yukawaon model in the quark sector and nearly tribimaximal neutrino mixing

For the purpose of deriving the observed nearly tribimaximal neutrino mixing, a possible yukawaon model in the quark sector is investigated. Five observable quantities (2 up-quark mass ratios and 3 neutrino mixing parameters sin²2θ_atm, tan²θ_solar and |U₁₃|) are excellently fitted by two parameters (one in the up-quark sector and another one in the right-handed Majorana neutrino sector).     

Is the size of <Emphasis Type="Italic">θ</Emphasis> <Subscript>13</Subscript> related to the smallness of the solar mass splitting?

θ₁₃ is small compared to the other neutrino mixing angles. The solar mass splitting is about two orders smaller than the atmospheric splitting. We indicate how both could arise from a perturbation of a more symmetric structure. The perturbation also affects the solar mixing angle and can tweak alternate mixing patterns such as tribimaximal, bimaximal, or other variants to viability. For real perturbations only normal mass ordering with the lightest neutrino mass less than 10^?2 eV can accomplish this goal. Both mass orderings can be accommodated by going over to complex perturbations if the lightest neutrino is heavier. The CP-phase in the lepton sector, fixed by θ₁₃ and the lightest neutrino mass, distinguishes different options.     

Quark–lepton complementarity with lepton and quark mixing data predict θ<Subscript>13</Subscript><Superscript>PMNS</Superscript>=(9<Superscript>+1</Superscript><Subscript>-2</Subscript>)°

The complementarity between the quark and lepton mixing matrices is shown to provide a robust prediction for the neutrino mixing angle θ₁₃ ^PMNS. 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 the 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, which is in agreement with the quark data, and the solar and the atmospheric mixing angle leads to θ₁₃ ^PMNS=(9⁺¹ _-2)^°. This value is consistent with the present 90% CL experimental upper limit. PACS 14.60.Pq; 14.60.Lm; 96.40.Tv     

Neutrino mixing matrices with relatively large <Emphasis Type="Italic">θ</Emphasis><Subscript>13</Subscript> and with texture one-zero

The recent T2K, MINOS and Double Chooz oscillation data hint at a relatively large θ ₁₃, which can be accommodated by some general modification of the tribimaximal/bimaximal/democratic mixing matrices. Using such matrices we analyze several Majorana mass matrices with texture one-zero and show whether they satisfy the normal or the inverted mass hierarchy and are phenomenologically viable or not.     

VMD, the WZW Lagrangian and ChPT: The third mixing angle

We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian . This allows to rely on radiative decays of light mesons ( and ) in order to extract some numerical information of relevance to ChPT: a value for , a quark mass ratio of , and a negligible departure from the Gell-Mann–Okubo mass formula. The mixing angles are and . We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle is actually quite appropriate and algebraically related to the mixing pattern presently preferred by the ChPT community. For instance the traditional is functionally related to the ChPT and fulfills . The vanishing of , supported by all data on radiative decays, gives a novel relation between mixing angles and the violation of nonet symmetry in the pseudoscalar sector. Finally, it is shown that the interplay of nonet symmetry breaking through U(3) SU(3) U(1) satisfies all requirements of the physics of radiative decays without any need for additional glueballs. Received: 20 June 2000 / Published online: 23 October 2000     

Predicting lepton flavor mixing from Δ(48) and generalized CP symmetries

We propose to understand the mixing angles and CP-violating phases from the Δ(48) family symmetry combined with the generalized CP symmetry. A model-independent analysis is performed by scanning all the possible symmetry breaking chains. We find a new mixing pattern with only one free parameter, excellent agreement with the observed mixing angles can be achieved and all the CP-violating phases are predicted to take nontrivial values. This mixing pattern is testable in the near future neutrino oscillation and neutrinoless double-beta decay experiments. Finally, a flavor model is constructed to realize this mixing pattern.     

Optical anisotropy and the direction of polarization of exciton emissions in a semiconductor quantum dot:Effect of heavy-and light-hole mixing

The dependence of the directions of polarization of exciton emissions, fine structure splittings(FSS), and polarization anisotropy on the light-and heavy-hole(LH–HH) mixing in semiconductor quantum dots(QDs) is investigated using a mesoscopic model. In general, all QDs have a four-fold exciton ground state. Two exciton states have directions of polarization in the growth-plane, while the other two are along the growth direction of the QD. The LH–HH mixing does affect the FSS and polarization anisotropy of bright exciton states in the growth-plane in the low symmetry QDs(e.g., C_(2V),C_S, C_1), while it has no effect on the FSS and polarization anisotropy in high symmetry QDs(e.g., C_(3V), D_(2d)). When the hole ground state is pure HH or LH, the bright exciton states in the growth-plane are normal to each other. The LH–HH mixing affects the relative intensities and directions of bright exciton states in the growth-plane of the QD. The polarization anisotropy of exciton emissions in the growth-plane of the QD is independent of the phase angle of LH–HH mixing but strongly depends on the magnitude of LH–HH mixing in low symmetry QDs.     

SU(N) elastic rescattering in B and D decays

The treatment of elastic final-state interactions (FSIs) under a symmetry group is presented. The proposed model is based on Watson's theorem, i.e. on symmetry properties of the -matrix and on its unitarity. This theorem provides an easy way to introduce rescattering effects by defining final-state interactions mixing matrices. A symmetry group fixes the structure of such mixing matrices, and the passage from one group to another is studied (for example, SU(2) to SU(3)). Mixings among two charmless pseudoscalar decay product states will be systematically analyzed. Finally, these mixing matrices will be used on quark diagram parametrizations of B and D decay amplitudes. This will have some important consequences on the definition of quark diagrams. It will be argued that these diagrams should not contain any FSI effects, i.e. they should be real (except for CKM factors). FSIs are then introduced at the hadronic level, by mixing basic quark diagram topologies. Received: 17 December 1998 / Revised version: 17 February 1999 / Published online: 28 September 1999     

高温超导体氧振模的混合

为解释高温超导晶体的声子Ｒａｍａｎ偏振谱，本文提出两个Ａ＿（ｌｇ）－对称声子模相混的机制。对Ｙ—Ｂａ—Ｃｕ—Ｏ单晶，按偏振Ｒａｍａｎ谱强度比计算了两个Ａ＿（ｌｇ）－振动模的耦合系数。