Maximal Mixing Research Articles

Fermion masses and mixing angles from SU(3) family symmetry and unification

We develop a bottom–up approach to constructing a theory of fermion masses and mixing angles based on the gauge group SU(3)×G where SU(3) is a family symmetry and G contains a unified group such as SO(10) or its Pati–Salam subgroup, together with other discrete symmetries. We construct a realistic model and show that it can provide an excellent description of quark and lepton masses and mixing angles, including almost maximal atmospheric mixing and the LMA MSW solar neutrino solution. We predict a neutrino mixing angle θ13 near the current limit. The model provides the basis for a new solution to the flavour problem with a characteristic soft SUSY breaking mass spectrum.

A discrete symmetry group for maximal atmospheric neutrino mixing

We propose a discrete non-abelian symmetry group which enforces maximal atmospheric neutrino mixing, while θ13=0 and the solar mixing angle θ12 remains undetermined; without finetuning, θ12 will be large but non-maximal. Our extension of the Standard Model has three right-handed neutrino singlets νR and implements the seesaw mechanism. Furthermore, we have an enlarged scalar sector with three Higgs doublets and two scalar gauge singlets; the latter have masses and vacuum expectation values of the order of the seesaw scale. Lepton mixing stems exclusively from the νR Majorana mass matrix, where non-diagonal elements are generated by the vacuum expectation values of the scalar singlets. The model predicts a neutrino mass spectrum with m3>m2>m1, and the effective Majorana mass of neutrinoless ββ decay is equal to m1m2/m3.

Probing the seesaw mechanism with neutrino data and leptogenesis

In the framework of the seesaw mechanism with three heavy right-handed Majorana neutrinos and no Higgs triplets we carry out a systematic study of the structure of the right-handed neutrino sector. Using the current low-energy neutrino data as an input and assuming hierarchical Dirac-type neutrino masses $m_{Di}$, we calculate the masses $M_i$ and the mixing of the heavy neutrinos. We confront the inferred properties of these neutrinos with the constraints coming from the requirement of a successful baryogenesis via leptogenesis. In the generic case the masses of the right-handed neutrinos are highly hierarchical: $M_i \propto m_{Di}^2$; the lightest mass is $M_1 \approx 10^3 - 10^6$ GeV and the generated baryon-to-photon ratio $\eta_B\lesssim 10^{-14}$ is much smaller than the observed value. We find the special cases which correspond to the level crossing points, with maximal mixing between two quasi-degenerate right-handed neutrinos. Two level crossing conditions are obtained: ${m}_{ee}\approx 0$ (1-2 crossing) and $d_{12}\approx 0$ (2-3 crossing), where ${m}_{ee}$ and $d_{12}$ are respectively the 11-entry and the 12-subdeterminant of the light neutrino mass matrix in the basis where the neutrino Yukawa couplings are diagonal. We show that sufficient lepton asymmetry can be produced only in the 1-2 crossing where $M_1 \approx M_2 \approx 10^{8}$ GeV, $M_3 \approx 10^{14}$ GeV and $(M_2 - M_1)/ M_2 \lesssim 10^{-5}$.

Search for νμ→νe oscillations in the NOMAD experiment

We present the results of a search for νμ→νe oscillations in the NOMAD experiment at CERN. The experiment looked for the appearance of νe in a predominantly νμ wide-band neutrino beam at the CERN SPS. No evidence for oscillations was found. The 90% confidence limits obtained are Δm2<0.4 eV2 for maximal mixing and sin2(2θ)<1.4×10−3 for large Δm2. This result excludes the LSND allowed region of oscillation parameters with Δm2≳10 eV2.

Inverting the seesaw formula

By inverting the seesaw formula we determine the heavy neutrino mass matrix. The impact on the baryogenesis via leptogenesis and the radiative lepton decays in supersymmetric models is described. Links to neutrinoless double beta decay are also briefly discussed. The analysis leads to two distinct matrix models. One has small mixings while the other has one maximal mixing. Both cannot give a sufficient amount of baryon asymmetry. Then we also comment on a different form of the Dirac neutrino mass matrix, which does provide sufficient baryon asymmetry. In a supersymmetric scenario the branching ratios of radiative lepton decays are enhanced for this model.

Atmospheric neutrino oscillations with MACRO

We present the latest results on the study of atmospheric neutrino oscillations with the MACRO detector at Gran Sasso. Two sub-samples of events have been analysed, both in terms of absolute flux and zenith angle distribution: high energy events (with 〈 E ν 〉 ⋍ 50 GeV) and low energy events (with 〈 E v 〉 ⋍ 4 GeV). The high energy sample has been used also to check the ν μ Hν sterile oscillation hypothesis and to estimate neutrino energies using Multiple Coulomb Scattering (MCS) informations. All these analyses are mutually consistent and strongly favour the ν μ ⇌ ν τ oscillation hypothesis with maximal mixing and Δm 2 = 2.5 · 10 −3eV 2.

Exploring the sensitivity of current and future experiments toθ⊙

However the allowed range of $\theta_{\odot}$ ($\theta_{12}$) did not change much with the inclusion of the KamLAND results. In this paper we probe if future data from KamLAND can increase the accuracy of the allowed range in $\theta_{\odot}$ and conclude that even after 3 kton-year of statistics and most optimistic error estimates, KamLAND {\it may} find it hard to significantly improve the bounds on the mixing angle obtained from the solar neutrino data. We discuss the $\theta_{12}$ sensitivity of the survival probabilities in matter (vacuum) as is relevant for the solar (KamLAND) experiments. We find that the presence of matter effects in the survival probabilities for $^8B$ neutrinos give the solar neutrino experiments SK and SNO an edge over KamLAND, as far as $\theta_{12}$ sensitivity is concerned, particularly near maximal mixing. Among solar neutrino experiments we identify SNO as the most promising candidate for constraining $\theta_{12}$ and make a projected sensitivity test for the mixing angle by reducing the error in the neutral current measurement at SNO. Finally we argue that the most accurate bounds on $\theta_{12}$ can be achieved in a reactor experiment, if the corresponding baseline and energy can be tuned to a minimum in the survival probability. We propose a new reactor experiment which can give the value of $\tan^2\theta_{12}$ to within 14%. We also discuss the future Borexino and LowNu experiments.

Neutrino physics and astrophysics with the MACRO experiment at the Gran Sasso lab

The results of the MACRO experiment on atmospheric neutrino oscillations are presented and discussed. The data concern different event topologies with average neutrino energies of ~ 4 and ~ 50 GeV. The Multiple Coulomb Scattering of muons in the MACRO absorbers was used to estimate the neutrino energy of each event of the higher energy sample. The angular distributions, the absolute fluxes and the L/E distribution favour nu_mu <--> nu_tau oscillations with maximal mixing and Delta m^2=0.0025 eV^2. Results are presented on the searches for astrophysical sources of high energy muon neutrinos, for bursts of electron antineutrinos from stellar gravitational collapses and on indirect searches for WIMPs from the Earth and from the Sun.

The Flavor Symmetry

Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S_3, we suggest a minimal S_3 invariant extension of the standard model. We find that in the leptonic sector, the exact S_3 x Z_2 symmetry, which allows 6 real independent parameters with two CP-violating phases, is consistent with experimental data and predicts a maximal mixing of the atmospheric neutrinos, and that the third neutrino is the lightest neutrino. With the exact S_3 only, there are 10 real parameters and five phases in the quark sector. A set of values of these parameters that are consistent with experimental observations is given.

Radiatively generatedνeoscillations: General analysis, textures, and models

We study the consequences of assuming that the mass scale ${\ensuremath{\Delta}}_{\ensuremath{\bigodot}}$ corresponding to the solar neutrino oscillations and mixing angle ${U}_{e3}$ corresponding to the electron neutrino oscillation at CHOOZ are radiatively generated through the standard electroweak gauge interactions. All the leptonic mass matrices having zero ${\ensuremath{\Delta}}_{\ensuremath{\bigodot}}$ and ${U}_{e3}$ at a high scale lead to a unique low energy value for the ${\ensuremath{\Delta}}_{\ensuremath{\bigodot}}$ which is determined by the (known) size of the radiative corrections, solar and the atmospheric mixing angle and the Majorana mass of the neutrino observed in neutrinoless double beta decay. This prediction leads to the following consequences. (i) The MSSM radiative corrections generate only the dark side of the solar neutrino solutions. (ii) The inverted mass hierarchy $(m,\ensuremath{-}m,0)$ at the high scale fails in generating the LMA solution but it can lead to the LOW or vacuum solutions. (iii) The ${\ensuremath{\Delta}}_{\ensuremath{\bigodot}}$ generated in models with maximal solar mixing at a high scale is zero to the lowest order in the radiative parameter. It tends to get suppressed as a result of this and lies in the vacuum region. We discuss specific textures which can lead to the LMA solution in the present framework and provide a gauge theoretical realization of this in the context of the seesaw model.

Extra-dimensions, isosinglet charged leptons and neutrino factories

Isosinglet fermions naturally arise in a variety of extensions of the Standard Model, in particular in models with extra-dimensions. In this paper, we study the effect of the addition of a new isosinglet charged lepton to the standard spectrum, with special emphasis on implications for neutrino asymmetries to be measured at future neutrino factories. Lepton flavour violation in neutral current and lepton universality constraints are extensively discussed. We show that New Physics effects in ν e – ν μ CP asymmetries are significantly enhanced due to leptonic maximal mixings but still too small to give a signature at future neutrino factories. A signal for CP asymmetries in ν μ – ν τ channel due to New Physics could be observed at 1–3 σ if lepton-flavour-violating τ decays are seen in a very close future in B-factories like Belle experiment.

Evolution of maximal coherence and nonlinear mixing in an ionizing three-level medium

We have carried out a numerical investigation of the influence of photoionization, causing neutral atom depletion and accompanying electron impact dephasing, on a stimulated Raman adiabatic passage (STIRAP) scheme in a dense medium of three-level atoms. The nonlinear mixing from the large (maximal) coherence generated during the population transfer is calculated within the framework of a time-dependent model for a single atom with simplified propagation appropriate to a thin slab of material. For definiteness and consistency of the atomic parameters employed we have treated a scheme in atomic calcium. For generation of intense vacuum ultraviolet fields, laser intensities in the range from 100 ${\mathrm{k}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ to 1 ${\mathrm{M}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ are required, and these are found to cause significant ionization of the atom. We find that at atomic densities $g{10}^{16}/{\mathrm{cm}}^{3}$ the effects of electron impact dephasing on the coherence evolution is very significant and will dominate over other dephasing mechanisms. In contrast at lower densities $\ensuremath{\sim}{10}^{14}/{\mathrm{cm}}^{3}$ (compatible with a sealed vapor cell) the conversion efficiency is relatively unaffected by electron impact dephasing. We conclude that in general photoionization depletion and electron impact dephasing will be significant in maximal coherence wave mixing and STIRAP population transfer schemes operated at high density.

Maximal atmospheric neutrino mixing in an SU(5) model

We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the $U(1)_F$ symmetry associated with a suitably defined family number $F$, together with a $\mathbbm{Z}_2$ symmetry which does not commute with $F$. $U(1)_F$ is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in addition, $U(1)_F$ is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale $10^{16} \mathrm{GeV} < m_U < 10^{19} \mathrm{GeV}$; indeed, we have found a particular solution to this problem which yields results almost identical to the ones of the Minimal Supersymmetric Standard Model.

S2Lpermutation symmetry for left-handedμandτfamilies and neutrino oscillations in anSU(3)L×U(1)Ngauge model

We construct an ${\mathrm{SU}(3)}_{L}\ifmmode\times\else\texttimes\fi{}{U(1)}_{N}$ gauge model based on an ${S}_{2L}$ permutation symmetry for left-handed $\ensuremath{\mu}$ and $\ensuremath{\tau}$ families, which provides the almost maximal atmospheric neutrino mixing and the large solar neutrino mixing of the large mixing angle type. Neutrinos acquire one-loop radiative masses induced by the radiative mechanism of the Zee type as well as tree level masses induced by the type II seesaw mechanism utilizing interactions of lepton triplets with an $\mathrm{SU}(3)$-sextet scalar. The atmospheric neutrino mixing controlled by the tree-level and radiative masses turns out to be almost maximal owing to the presence of ${S}_{2L}$ supplemented by a ${Z}_{4}$ discrete symmetry. These symmetries ensure the near equality between the ${\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ radiative masses dominated by contributions from heavy leptons contained in the third members of lepton triplets, whose Yukawa interactions conserve ${S}_{2L}$ even after the spontaneous breaking. The solar neutrino mixing controlled by radiative masses, including a ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ mass, which are taken to be of similar order, turns out to be described by large solar neutrino mixing angles.

CPviolation in bilarge lepton mixing

We propose a scheme of lepton mixing in which the unitary matrix that diagonalizes the neutrino mass matrix is bimaximal and the deviation from the bimaximal of the lepton mixing matrix is due to the unitary matrix that diagonalizes the charged-lepton mass matrix. This matrix is assumed to be hierarchical, like the quark mixing matrix. It is shown that in general it is possible to have a sizable value for $|{U}_{e3}|$ together with an effective two-neutrino maximal mixing in solar neutrino experiments. If the effective mixing in solar neutrino experiments is less than maximal, as indicated by current data, $|{U}_{e3}|$ is bounded from below. Furthermore, in general the violation of $\mathrm{CP}$ could be relatively large.

Radiative origin of solar scale and Ue3

We make a general study of possibility of generating solar scale Δ⊙ and the CHOOZ angle Ue3 radiatively by assuming that they are zero at some high scale. The most general neutrino mass matrix leading to this result is determined in a CP conserving theory. This matrix contains four independent parameters which can be fixed in terms of physical observables. The standard weak radiative corrections then lead to non-zero Δ⊙ and Ue3 without drastically altering the other tree level results. As a consequence, both Δ⊙ and Ue3 are predicted in terms of other physically observable parameters. These predictions are insensitive to specific form of the neutrino mass matrix. The solar scale and Ue3 are strongly correlated with the effective neutrino mass mee probed in neutrinoless double beta decay. In particular, the LMA solution to the solar neutrino problem arise for mee close to the present experimental limit. An example of specific texture is presented which predicts maximal atmospheric mixing and tan2θ⊙≈0.5 for the solar mixing angle θ⊙.

Stringent constraints on cosmological neutrino-antineutrino asymmetries from synchronized flavor transformation

We assess a mechanism which can transform neutrino-antineutrino asymmetries between flavors in the early universe, and confirm that such transformation is unavoidable in the near bimaximal framework emerging for the neutrino mixing matrix. We show that the process is a standard Mikheyev-Smirnov-Wolfenstein flavor transformation dictated by a synchronization of momentum states. We also show that flavor ``equilibration'' is a special feature of maximal mixing, and carefully examine new constraints placed on neutrino asymmetries. In particular, the big bang nucleosynthesis limit on electron neutrino degeneracy $|{\ensuremath{\xi}}_{e}|\ensuremath{\lesssim}0.04$ does not apply directly to all flavors, yet confirmation of the large-mixing-angle solution to the solar neutrino problem will eliminate the possibility of degenerate big bang nucleosynthesis.

Before and After: How has the SNO NC measurement changed things?

We present "Before and After" global oscillation solutions, as well as predicted "Before and After" values and ranges for ten future solar neutrino observables (for BOREXINO, KamLAND, SNO, and a generic p-p neutrino detector). We have performed global analyses using the full SNO day-night energy spectrum and, alternatively, just the SNO CC and NC rates and the day-night asymmetry.The ``Before'' case includes all solar neutrino data (and some theoretical improvements) available prior to April 20, 2002 and the ``After'' case includes, in addition, the new SNO data on the CC, NC, and day-night asymmetry. The LMA solution is the only currently allowed MSW oscillation solution at ~99% CL. The LOW solution is allowed only at more than 2.5 sigma, SMA at 3.7 sigma or 4.7 sigma (depending upon analysis strategy), and pure sterile oscillations at 4.7sigma. Small mixing angles are ``out''(pure sterile is ``way out''); MSW with large mixing angles is definitely ``in''. Vacuum oscillations are allowed at 3 sigma, but not a 2 sigma. Precise maximal mixing is excluded at 3.2 sigma for MSW solutions and at 2.8 sigma for vacuum solutions. Most of the predicted values for future observables for the BOREXINO, KamLAND, and future SNO measurements are changed only by minor amounts by the inclusion of the recent SNO data. In order to test the robustness of the allowed neutrino oscillation regions and the predictions for future observables, we have carried out calculations using a variety of strategies to analyze the SNO and other solar neutrino data.

A hidden hierarchy of neutrino masses

The Dirac masses of neutrinos can exhibit a strong hierarchy even if the Majorana masses of the right-handed neutrinos are degenerate and the hierarchy of the mass scales governing the oscillations of solar and atmospheric neutrinos is rather small. This phenomenon results from the see-saw mechanism and the algebraic structure of the effective mass operator for the active neutrinos. The large hierarchy of the Dirac masses is drastically modified by a symmetric unitary matrix R acting in the flavor space. A realistic pattern of neutrino masses and mixing is obtained. Maximal mixing for atmospheric neutrinos is attributed to the charged lepton sector. Large mixing in solar neutrino oscillations is due to the neutrino sector. Small U e3 is a natural consequence of the model. The masses of the active neutrinos are given by μ 3≈ Δm @ 2 and μ 1/ μ 2≈tan 2 θ ⊙.

Global analysis with SNO: Toward the solution of the solar neutrino problem

We perform a global analysis of the latest solar neutrino data including the Solar Neutrino Observatory (SNO) result on the charged current (CC) event rate. This result further favors the large mixing angle (LMA) Mikheyev-Smirnov-Wolfenstein (MSW) solution of the solar neutrino problem. The best fit values of parameters we find are $\ensuremath{\Delta}{m}^{2}=(4.8--5.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5} {\mathrm{eV}}^{2},$ ${\mathrm{tan}}^{2}\ensuremath{\theta}=0.35--0.38,$ ${f}_{\mathrm{B}}=1.08--1.12,$ and ${f}_{\mathrm{hep}}=1--4,$ where ${f}_{\mathrm{B}}$ and ${f}_{\mathrm{hep}}$ are the boron and ${}^{3}\mathrm{He}+p$ (hep) neutrino fluxes in units of the corresponding fluxes in the standard solar model (SSM). With respect to this best fit point the low $\ensuremath{\Delta}{m}^{2}$ (LOW) MSW solution is accepted at 90% C.L. The vacuum oscillation solution (VAC) with $\ensuremath{\Delta}{m}^{2}=1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} {\mathrm{eV}}^{2},$ gives a good fit to the data provided that the boron neutrino flux is substantially smaller than the SSM flux ${(f}_{\mathrm{B}}\ensuremath{\sim}0.5).$ The small mixing angle (SMA) solution is accepted at about the $3\ensuremath{\sigma}$ level. We find that vacuum oscillations to a sterile neutrino, VAC(sterile), with ${f}_{\mathrm{B}}\ensuremath{\sim}0.5$ also give a rather good global fit to the data. All other sterile neutrino solutions are strongly disfavored. We check the quality of the fit by constructing the pull-off diagrams of observables for the global solutions. Maximal mixing is allowed at the $3\ensuremath{\sigma}$ level in the LMA region and at 95% C.L. in the LOW region. Predictions for the day-night asymmetry, spectrum distortion, and ratio of the neutral to charged current event rates [NC]/[CC] at SNO are calculated. In the best fit points of the global solutions we find ${A}_{\mathrm{DN}}^{\mathrm{CC}}\ensuremath{\approx}7--8%$ for the LMA, $\ensuremath{\sim}3%$ for the LOW, and $2\ensuremath{-}3%$ for the SMA regions. In the LMA region the asymmetry can be as large as $15--20%.$ Observation of ${A}_{\mathrm{DN}}^{\mathrm{CC}}&gt;5%$ will further favor the LMA solution. It will be difficult to see the distortion of the spectrum expected for LMA as well as LOW solutions. However, future SNO spectral data can significantly affect the VAC and SMA solutions. We present the expected values of the BOREXINO event rate for global solutions.