Maximal Atmospheric Neutrino Mixing Research Articles

Investigating the Hybrid Textures of Neutrino Mass Matrix for Near Maximal Atmospheric Neutrino Mixing

We have studied that the implication of a large value of the effective Majorana neutrino mass in case of neutrino mass matrices has either two equal elements and one zero element (popularly known as hybrid texture) or two equal cofactors and one zero minor (popularly known as inverse hybrid texture) in the flavor basis. In each of these cases, four out of sixty phenomenologically possible patterns predict near maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. This feature remains irrespective of the experimental data on solar and reactor mixing angles. In addition, we have also performed the comparative study of all the viable cases of hybrid and inverse hybrid textures at 3σ CL.

MaximalCPviolation in minimal seesaw model

In the minimal seesaw model, we derive required constraints on Dirac neutrino masses inducing maximal CP violation in neutrino oscillations. If the maximal atmospheric neutrino mixing is further assumed, Dirac neutrino masses are uniquely determined to respect $\mu$-$\tau$ flavored CP symmetry for neutrinos.

Maximal CP violation in flavor neutrino masses

Since flavor neutrino masses [Formula: see text] can be expressed in terms of [Formula: see text], mutual dependence among [Formula: see text] is derived by imposing some constraints on [Formula: see text]. For appropriately imposed constraints on [Formula: see text] giving rise to both maximal CP violation and the maximal atmospheric neutrino mixing, we show various specific textures of neutrino mass matrices including the texture with [Formula: see text] derived as the simplest solution to the constraint of [Formula: see text], which is required by the constraint of [Formula: see text] for [Formula: see text]. It is found that Majorana CP violation depends on the phase of [Formula: see text].

Δ(27) family symmetry and neutrino mixing

The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. This structure may be related to the existence of a discrete non-Abelian family symmetry. In this paper the family symmetry is the non-Abelian discrete group Δ(27), a subgroup of SU(3) with triplet and anti-triplet representations. Different frameworks are constructed in which the mixing follows from combining fermion mass terms with the vacuum structure enforced by the discrete symmetry. Mass terms for the fermions originate from familon triplets, anti-triplets or both. Vacuum alignment for the family symmetry breaking familons follows from simple invariants.

Testable constraint on near-tribimaximal neutrino mixing

General lowest order perturbations to hermitian squared mass matrices of leptons are considered away from the tribimaximal (TBM) limit in which a weak flavor basis with mass diagonal charged leptons is chosen. The three measurable TBM deviants are expressed linearly in terms of perturbation induced dimensionless coefficients appearing in the charged lepton and neutrino flavor eigenstates. With unnatural cancellations assumed to be absent and the charged lepton perturbation contributions to their flavor eigenstates argued to be small, we analytically derive the following result. Within lowest order perturbations, a deviation from maximal atmospheric neutrino mixing and the amount of CP violation in neutrino oscillations cannot both be large (i.e. $12$-$17 \% $), posing the challenge of verification to forthcoming experiments at the intensity frontier.

Near maximal atmospheric neutrino mixing in neutrino mass models with two texture zeros

The implications of a large value of the effective Majorana neutrino mass for a class of two texture zero neutrino mass matrices have been studied in the flavor basis. It is found that these textures predict near maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. It is noted that this prediction is independent of the values of solar and reactor neutrino mixing angles. We present the symmetry realization of these textures using the discrete cyclic group $Z_3$. It is found that the texture zeros realised in this work remain stable under renormalization group running of the neutrino mass matrix from the seesaw scale to the electroweak scale, at one loop level.

μ–τ interchange symmetry and lepton mixing

AbstractWe focus on the use of a μ–τ interchange symmetry to explain features of lepton mixing, especially maximal atmospheric neutrino mixing. We review two models which achieve this goal and are based on the seesaw mechanism and on the soft breaking of the family‐lepton‐number symmetries. We also note that that symmetry may be embedded in a generalized CP symmetry. We show that, in the context of some of our models, arguments of naturalness may be used for explaining the smallness of the mass ratio mμ / mτ.

Maximal CP violation in lepton mixing from a model with Δ(27) flavour symmetry

We propose a simple mechanism which enforces $\left| {{U_{\mu j}}} \right| = \left| {{U_{\tau j}}} \right|\forall j = 1,2,3$ in the lepton mixing matrix U. This implies maximal atmospheric neutrino mixing and a maximal CP-violating phase but does not constrain the reactor mixing angle θ 13. We implement the proposed mechanism in two renormalizable seesaw models which have features strongly resembling those of models based on a flavour symmetry group Δ(27). Among the predictions of the models, there is a determination, although ambiguous, of the absolute neutrino mass scale, and a stringent correlation between the absolute neutrino mass scale and the effective Majorana mass in neutrinoless double-beta decay.

Near maximal atmospheric mixing in neutrino mass matrices with two vanishing minors

In the flavor basis there are seven cases of two vanishing minors in the neutrino mass matrix which can accommodate the present neutrino oscillation data including the recent T2K data. It is found that two of these cases, namely B5 and B6 predict near maximal atmospheric neutrino mixing in the limit of large effective neutrino mass. This feature remains irrespective of the values of solar and reactor mixing angles. A non-zero reactor mixing angle is naturally accommodated in these textures.

Sensitivity to neutrino mixing parameters with atmospheric neutrinos

We have analyzed the atmospheric neutrino data to study the octant of $\theta_{23}$ and the precision of the oscillation parameters for a large Iron CALorimeter (ICAL) detector. The ICAL being a tracking detector has the ability to measure the energy and the direction of the muon with high resolution. From bending of the track in magnetic field it can also distinguish its charge. We have generated events by Nuance and then considered only the muons (directly measurable quantities) produced in charge current interactions in our analysis. This encounters the main problem of wide resolutions of energy and baseline. The energy-angle correlated two dimensional resolution functions are used to migrate the energy and the zenith angle of the neutrino to those of the muon. A new type of binning has been introduced to get better reflection of the oscillation pattern in chi-square analysis. Then the marginalization of the $\chi^2$ over all parameters has been carried out for neutrinos and anti-neutrinos separately. We find that the measurement of $\theta_{13}$ is possible at a significant precision with atmospheric neutrinos. The precisions of $\Delta m_{32}^2$ and $\sin^2\theta_{23}$ are found $\sim$ 8% and 38%, respectively, at 90% CL. The discrimination of the octant as well as the deviation from maximal mixing of atmospheric neutrinos are also possible for some combinations of ($\theta_{23}, ~\theta_{13}$). We also discuss the impact of the events at near horizon on the precision studies.

A three-parameter neutrino mass matrix with maximal CP violation

Using the seesaw mechanism, we construct a model for the light-neutrino Majorana mass matrix which yields trimaximal lepton mixing together with maximal CP violation and maximal atmospheric-neutrino mixing. We demonstrate that, in our model, the light-neutrino mass matrix retains its form under the one-loop renormalization-group evolution. With our neutrino mass matrix, the absolute neutrino mass scale is a function of | U e 3 | and of the atmospheric mass-squared difference. We study the effective mass in neutrinoless ββ decay as a function of | U e 3 | , showing that it contains a fourfold ambiguity.

A light pseudoscalar in a model with lepton family symmetry O(2)

We discuss a realization of the non-abelian group O(2) as a family symmetry for the lepton sector. The reflection contained in O(2) acts as a mu-tau interchange symmetry, enforcing--at tree level--maximal atmospheric neutrino mixing and a vanishing mixing angle theta_13. The small ratio m_mu/m_tau (muon over tau mass) gives rise to a suppression factor in the mass of one of the pseudoscalars of the model. We argue that such a light pseudoscalar does not violate any experimental constraint.

Cosmological Constraints for the Cold Dark Matter and Model Building Based on the Flavor Symmetric Radiative Seesaw Model

It is now clear that the masses of the neutrino sector are much lighter than those of the other three sectors.There are many attempts to explain the neutrino masses radiatively by means of inert Higgses, which don't have vacuum expectation values. Then one can discuss cold dark matter candidates, because of no needing so heavy particles and having a $Z_2$ parity symmetry corresponding to the R-parity symmetry of the MSSM. The most famous work would be the Zee model. Recently a new type model along this line of thought was proposed by Mr. E. Ma. We paid attention to this idea. We introduce a flavor symmetry based on a dihedral group $D_6$ to constrain the Yukawa sector. For the neutrino sector, we find that the maximal mixing of atmospheric neutrinos is realized, it can also be shown that only an inverted mass spectrum, the value of $|V_{MNS_{13}}|$ is 0.0034 and so on. When one extends the Higgs sector, it leads to FCNCs mediated by Higgs fields generally. But in our model, the FCNCs are (of course) suppressed for the experiments sufficiently. For the fermionic CDM candidates, we find that the mass of the CDM and the inert Higgs should be larger than about 230 and 300 GeV, respectively. If we restrict ourselves to a perturbative regime, they should be lighter than about 750 GeV.

Inverted mass hierarchy from scaling in the neutrino mass matrix: Low and high energy phenomenology

Best-fit values of recent global analyses of neutrino data imply large solar neutrino mixing, vanishing ${U}_{e3}$, and a nonmaximal atmospheric neutrino mixing angle ${\ensuremath{\theta}}_{23}$. We show that these values emerge naturally by the hypothesis of scaling in the Majorana neutrino mass matrix, which states that the ratios of its elements are equal. It also predicts an inverted hierarchy for the neutrino masses. We point out several advantages and distinguishing tests of the scaling hypothesis compared to the ${L}_{e}\ensuremath{-}{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ flavor symmetry, which is usually assumed to provide an understanding of the inverted hierarchy. Scenarios which have initially vanishing ${U}_{e3}$ and maximal atmospheric neutrino mixing are shown to be unlikely to lead to nonmaximal ${\ensuremath{\theta}}_{23}$ while simultaneously keeping ${U}_{e3}$ zero. We find a peculiar ratio of the branching ratios $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ in supersymmetric seesaw frameworks, which only depends on atmospheric neutrino mixing and results in $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ being unobservable. The consequences of the scaling hypothesis for high energy astrophysical neutrinos at neutrino telescopes are also investigated. Then we analyze a seesaw model based on the discrete symmetry ${D}_{4}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ leading to scaling in the low energy mass matrix and being capable of generating the baryon asymmetry of the Universe via leptogenesis. The relevant $CP$ phase is identical to the low energy Majorana phase, and successful leptogenesis requires an effective mass for neutrinoless double beta decay larger than 0.045 eV.

Formula omitted

We consider corrections to vanishing Ue3 and maximal atmospheric neutrino mixing originating from the relation U=Uℓ†Uν, where U is the PMNS mixing matrix and Uℓ(Uν) is associated with the diagonalization of the charged lepton (neutrino) mass matrix. We assume that in the limit of Uℓ or Uν being the unit matrix, one has Ue3=0 and θ23=π/4, while the solar neutrino mixing angle is a free parameter. Well-known special cases of the indicated scenario are the bimaximal and tri-bimaximal mixing schemes. If Ue3≠0 and θ23≠π/4 due to corrections from the charged leptons, |Ue3| can be sizable (close to the existing upper limit) and we find that the value of the solar neutrino mixing angle is linked to the magnitude of CP violation in neutrino oscillations. In the alternative case of the neutrino sector correcting Ue3=0 and θ23=π/4, we obtain a generically smaller |Ue3| than in the first case. Now the magnitude of CP violation in neutrino oscillations is connected to the value of the atmospheric neutrino mixing angle θ23. We find that both cases are in agreement with present observations. We also introduce parametrization independent “sum-rules” for the oscillation parameters.

WHAT DOES μ - τ SYMMETRY IMPLY ABOUT LEPTONIC CP VIOLATION?

The μ - τ symmetry can reproduce the consistent results with experimental data of θ13, and θ23 (θ13, and θ23 respectively denote the νe - ντ, and νμ - ντ, mixing angles). However, we can not address the issue of the leptonic CP violation in μ - τ symmetric models. So we add the μ - τ symmetry breaking part to include the CP violation. We characterize leptonic CP violation in terms of three phases, where one is conventional phase δ and others are additional phases ρ and γ. These δ, ρ and γ are, respectively, the phases of νe - ντ, νe - νμ and νμ - ντ mixings. The ρ and γ are redundant but the effect of ρ remains in the leptonic CP violation which is characterized by δ + ρ. The δ arises from the μ - τ symmetry breaking part of the Meμ and Meτ while ρ arises from of μ - τ symmetric part of the Meμ and Meτ, where Mij stands for ij (i,j = e,μ,τ) element of M(= [Formula: see text] for Mν being a flavor neutrino mass matrix). Moreover, θ23 can be exactly estimated to be: [Formula: see text] ( sin θ ∝ sin θ13 cos (δ + ρ)[Formula: see text], sin ϕ ∝ Mμμ - Mττ, where [Formula: see text] is the solar neutrino mass difference squared). The conditions of maximal atmospheric neutrino mixing are given by [Formula: see text] and Mμμ = Mττ,which indicate maximal Dirac CP violation.

NEUTRINO MIXING: FROM THE BROKEN μ-τ SYMMETRY TO THE BROKEN FRIEDBERG–LEE SYMMETRY

I argue that the observed flavor structures of leptons and quarks might imply the existence of certain flavor symmetries. The latter should be a good starting point to build realistic models towards deeper understanding of the fermion mass spectra and flavor mixing patterns. The μ-τ permutation symmetry serves for such an example to interpret the almost maximal atmospheric neutrino mixing angle (θ23 ~ 45°) and the strongly suppressed CHOOZ neutrino mixing angle (θ13 < 10°). In this talk I like to highlight a new kind of flavor symmetry, the Friedberg–Lee symmetry, for the effective Majorana neutrino mass operator. Luo and I have shown that this symmetry can be broken in an oblique way, such that the lightest neutrino remains massless but an experimentally-favored neutrino mixing pattern is achievable. We get a novel prediction for θ13 in the CP-conserving case: sin θ13 = tan θ12|(1 - tan θ23)/(1 + tan θ23)|. Our scenario can simply be generalized to accommodate CP violation and be combined with the seesaw mechanism. Finally I stress the importance of probing possible effects of μ-τ symmetry breaking either in terrestrial neutrino oscillation experiments or with ultrahigh-energy cosmic neutrino telescopes.

Correlation between leptonicCPviolation andμ−τsymmetry breaking

Considering the {mu}-{tau} symmetry, we discuss a direct linkage between phases of flavor neutrino masses and leptonic CP violation by determining three eigenvectors associated with M=M{sub {nu}}{sup {dagger}}M{sub {nu}} for a complex flavor neutrino mass matrix M{sub {nu}} in the flavor basis. Since the Dirac CP violation is absent in the {mu}-{tau} symmetric limit, leptonic CP violation is sensitive to the {mu}-{tau} symmetry breaking, whose effect can be evaluated by perturbation. It is found that the Dirac phase ({delta}) arises from the {mu}-{tau} symmetry breaking part of M{sub e{mu}}{sub ,e{tau}} and an additional phase ({rho}) is associated with the {mu}-{tau} symmetric part of M{sub e{mu}}{sub ,e{tau}}, where M{sub ij} stands for an ij matrix element (i,j=e,{mu},{tau}). The phase {rho} is redundant and can be removed but leaves its effect in the Dirac CP violation characterized by sin({delta}+{rho}). The perturbative results suggest the exact formula of mixing parameters including that of {delta} and {rho}, which turns out to be free from the effects of the redundant phases. As a result, it is generally shown that the maximal atmospheric neutrino mixing necessarily accompanies either sin{theta}{sub 13}=0 or cos({delta}+{rho})=0, the latter of which indicates maximal CP violation, where {theta}{sub 13} is the {nu}{submore » e}-{nu}{sub {tau}} mixing angle.« less

Flavor symmetry L μ-L τ and quasidegenerate neutrinos

Current data implies three simple forms of the neutrino mass matrix, each corresponding to the conservation of a nonstandard lepton charge. While models based on L e and L e-L μ-L τ are well known, little attention has been paid to L μ-L τ. A low-energy mass matrix conserving L μ-L τ implies quasidegenerate light neutrinos. Moreover, it is μ-τ symmetric and therefore (in contrast to L e and L e-L μ-L τ) automatically predicts maximal atmospheric neutrino mixing and zero U e3. A seesaw model based on L μ-L τ is investigated and testable predictions for the neutrino mixing observables are given. Renormalization group running below and in between the seesaw scales is taken into account in our analysis, both numerically and analytically.

Erratum: Bounds on the neutrino mixing angles andCPphase for anSO(10)model with lopsided mass matrices [Phys. Rev. D72, 013001 (2005)

The bounds on the neutrino mixing angles and CP Dirac phase for an SO(10) model with lopsided mass matrices, arising from the presence of ${\bf 16}_H$ and $\bar{\bf 16}_H$ Higgs representations, are studied by variation of the one real and three unknown complex input parameters for the right-handed Majorana neutrino mass matrix. The scatter plots obtained favor nearly maximal atmospheric neutrino mixing, while the reactor neutrino mixing lies in the range $10^{-5} \lsim \sin^2 \theta_{13} \lsim 1 \times 10^{-2}$ with values greater than $10^{-3}$ most densely populated. A rather compelling scenario within the model follows, if we restrict the three unknown complex parameters to their imaginary axes and set two of them equal. We then find the scatter plots are reduced to narrow bands, as the mixing angles and CP phase become highly correlated and predictive. The bounds on the mixing angles and phase then become $0.45 \lsim \sin^2 \theta_{23} \lsim 0.55$, $0.38 \lsim \tan^2 \theta_{12} \lsim 0.50$, $0.002 \lsim \sin^2 \theta_{13} \lsim 0.003$, and $60^\circ \lsim \pm \delta_{CP} \lsim 85^\circ$. Moreover, successful leptogenesis and subsequent baryogenesis are also obtained, with $\eta_B$ increasing from $(2.7 to 6.3) \times 10^{-10}$ as $\sin^2 \theta_{23}$ increases from 0.45 to 0.55.