Narrow Results

If the sterile neutrino mass matrix in an otherwise conventional see-saw model has a rank less than the number of flavors, it is possible to produce pseudo-Dirac neutrinos. In a two-flavor, sterile rank 1 case, we demonstrate analytic conditions for large active mixing induced by the existence of (and coupling to) the sterile neutrino components. For the three-flavor, rank 1 case, "3+2" scenarios with large mixing also devolve naturally as we show by numerical examples. We observe that, in this approach, small mass differences can develop naturally without any requirement that masses themselves are small. Additionally, we point out that significant three-channel mixing and limited experimental resolution can combine to produce extracted two-channel mixing parameters at variance with the actual values.

We conduct a detailed analysis of the phenomenology of two predictive see-saw scenarios which lead to the Quark-Lepton Complementarity relation θ₁₂+θ_C = π/4. The neutrino mixing observables and their correlations, neutrinoless double beta decay, lepton flavor violating decays such as μ → eγ and leptogenesis are discussed. The features which allow to distinguish the scenarios are identified.

We point out that in SUSY flipped SU(5) model the bilarge neutrino mixing which can be accommodated in the lepton Yukawa couplings can induce interesting flavor mixings for the left-handed charged slepton and right-handed up-type squark. FCNC processes such as τ → μ + γ, mixing and t → u, c + h⁰ are predicted.

I recount briefly the history of neutrino tribimaximal mixing and the use of the discrete family symmetry A₄ in obtaining it.

In this note I mainly focus on the neutrino physics part in my talk and report the most recent progress made in ¹. It is seen that the Majorana features of neutrinos and SO(3) gauge flavor symmetry can simultaneously explain the smallness of neutrino masses and nearly tri-bimaximal neutrino mixing when combining together with the mechanism of approximate global U(1) family symmetry. The mixing angle θ₁₃ and CP-violating phase are in general nonzero and testable experimentally at the allowed sensitivity. The model also predicts the existence of vector-like Majorana neutrinos and charged leptons as well as new Higgs bosons, some of them can be light and explored at the LHC and ILC.

Assuming the Majorana nature of massive neutrinos, we generalize the Friedberg-Lee neutrino mass model to include CP violation in the neutrino mass matrix M_ν. The most general case with all the free parameters of M_ν being complex is discussed. We show that a favorable neutrino mixing pattern (with θ₁₂ ≈ 35.3°, θ₂₃ = 45°, θ₁₃ ≠ 0° and δ = 90°) can naturally be derived from M_ν, if it has an approximate or softly-broken μ-τ symmetry. We also point out a different way to obtain the nearly tri-bimaximal neutrino mixing pattern with δ = 0° and non-vanishing Majorana phases.

Based on a neutrino mass matrix model in which a 2 ↔ 3 symmetry is only broken by a phase parameter, it is investigated how the lepton mixing matrix can deviate from the so-called tribimaximal mixing under a condition that CP is maximally violated.

In the context of quantum field theory (QFT), we compute the amplitudes of weak interaction processes such as W⁺ →e⁺ + ν_e and W⁺ →e⁺ + ν_μ by using different representations of flavor states for mixed neutrinos. Analyzing the short time limit of the above amplitudes, we find that the neutrino states defined in QFT as eigenstates of the flavor charges lead to results consistent with lepton charge conservation. On the contrary, the Pontecorvo flavor states produce a violation of lepton charge in the vertex, which is in contrast with what expected at tree level in the Standard Model.

The phenomenology of 3-neutrino mixing and of the related Dirac and Majorana leptonic CP violation is reviewed. The leptogenesis scenario of generation of the baryon asymmetry of the Universe, which is based on the see-saw mechanism of neutrino mass generation, is considered. The results showing that the CP violation necessary for the generation of the baryon asymmetry of the Universe in leptogenesis can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U are briefly reviewed.

We consider the so-called "eV seesaw" scenario, with right-handed Majorana mass M_R at eV order, extended to four lepton generations. The fourth generation gives a heavy pseudo-Dirac neutral lepton, which largely decouples from other generations and is relatively stable. The framework naturally gives three active and three sterile neutrinos. We update a previous numerical analysis of a 3+3 study of the LSND anomaly, taking into account the more recent results from the MiniBooNE experiment. In particular, we study the implications for the third mixing angle sin² θ₁₃, as well as CP violation. We find that current data do not seriously constrain more than one sterile neutrinos.

Fermion mixing is generally believed to be a low-energy manifestation of an underlying theory whose energy scale is much larger than the electroweak scale. In this paper we investigate the possibility that the parameters describing lepton mixing actually arise from the low-energy behavior of the neutrino interacting fields. In particular, we conjecture that the measured value of the mixing angles for a given process depends on the number of unobservable flavor states at the energy of the process. We provide a covariant implementation of such conjecture, draw its consequences in a two-neutrino family approximation and compare these findings with current experimental data. Finally we show that this infrared origin of mixing will be manifest at the Ice Cube DeepCore array, which measures atmospheric oscillations at energies much larger than the tau lepton mass; it will hence be experimentally tested in a short time scale.

It is investigated what constraints are imposed on the so-called yukawaon model when we regard quarks and leptons as of SU(5) (i = 1, 2, 3: index of U(3) family symmetry). In past yukawaon models, the effective Yukawa coupling constants are given by vacuum expectation values of fields Y_f ("yukawaons") as . In order to build a model without a cutoff scale Λ, vector-like fields are introduced in addition to the conventional quarks and leptons. The U(3) family symmetry is broken at 〈Y_f〉~10¹³GeV.

Assuming that neutrinos acquire radiative seesaw Majorana masses through their interactions with dark matter, i.e. scotogenic from the Greek "scotos" meaning darkness, and using the non-Abelian discrete symmetry A₄, we propose a model of neutrino masses and mixing with nonzero θ₁₃ and necessarily large leptonic CP violation, allowing both the normal and inverted hierarchies of neutrino masses, as well as quasi-degenerate solutions.

Recently, several reactor oscillation experiments have successively measured a nonzero value for the neutrino mixing angle θ₁₃, which is greater than five standard deviations. Within framework of the μ from ν Supersymmetric Standard Model (μνSSM), three tiny neutrino masses are generated at the tree level through TeV scale seesaw mechanism. In this work, we analyze the neutrino masses and mixing in the μνSSM with a "top-down" method, assuming neutrino mass spectrum with normal ordering or inverted ordering.

In the spirit of a previous study of the tetrahedral group T ≃A₄, we discuss a minimalist scheme to derive the neutrino mixing matrix using the double tetrahedral group T′, the double cover of T. The new features are three distinct two-dimensional representations and complex Clebsch–Gordan coefficients, which can result in a geometric source of CP violation in the neutrino mass matrix. In an appendix, we derive explicitly the relevant group theory for the tetrahedral group T and its double cover T′.

The phenomenology of 3-neutrino mixing, the current status of our knowledge about the 3-neutrino mixing parameters, including the absolute neutrino mass scale, and of the Dirac and Majorana CP violation in the lepton sector, are reviewed. The problems of CP violation in neutrino oscillations and of determining the nature — Dirac or Majorana — of massive neutrinos, are discussed. The seesaw mechanism of neutrino mass generation and the related leptogenesis scenario of generation of the baryon asymmetry of the universe, are considered. The results showing that the CP violation necessary for the generation of the baryon asymmetry of the universe in leptogenesis can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U, are briefly reviewed.

We present a model of neutrino mixing based on the flavor group Δ(27) in order to account for the observation of a nonzero reactor mixing angle (θ₁₃). The model provides a common flavor structure for the charged-lepton and the neutrino sectors, giving their mass matrices a "circulant-plus-diagonal" form. Mass matrices of this form readily lead to mixing patterns with realistic deviations from tribimaximal mixing, including nonzero θ₁₃. With the parameters constrained by existing measurements, our model predicts an inverted neutrino mass hierarchy. We obtain two distinct sets of solutions in which the atmospheric mixing angle lies in the first and the second octants. The first (second) octant solution predicts the lightest neutrino mass, m₃~29 meV(m₃~65 meV) and the CP phase, , offering the possibility of large observable CP violating effects in future experiments.

Using the fact that the neutrino mixing matrix , where U_e and U_ν result from the diagonalization of the charged lepton and neutrino mass matrices, we analyze the predictions based on the sum rules which the Dirac phase δ present in U satisfies when U_ν has a form dictated by, or associated with, discrete flavor symmetries and U_e has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to U_ν, so that the reactor, atmospheric and solar neutrino mixing angles θ₁₃, θ₂₃ and θ₁₂ have values compatible with the current data.

Experiments on neutrino oscillations have uncovered several small parameters, θ₁₃ being a prominent one. Others are the solar mass splitting vis-à-vis the atmospheric one and the deviation of θ₂₃ from maximal mixing. In this talk, (talk given at the International Conference on Massive Neutrinos, Singapore, 9–13 February 2015) we elaborate on a neutrino mass model based on the see-saw mechanism in which the mixing angles to start with are either vanishing (θ₁₃ and θ₁₂) or π/4 (θ₂₃). The atmospheric mass splitting is taken as a part of this initial structure but the solar splitting is absent. A perturbative contribution, originating from a Type-I see-saw, results in nonzero values of θ₁₃, θ₁₂, , and shifts θ₂₃ slightly from π/4, interrelating them all. The model incorporates CP-violation, the phase δ being close to 3π/2 for (a) quasidegeneracy or (b) inverted mass ordering. It will be put to test as the neutrino parameters get better determined.

We study the effects of Majorana neutrino phases in lepton flavor violation and the origin of matter–antimatter asymmetry through the mechanism of leptogenesis within the framework of a model where both type I and type II seesaw mechanisms can contribute to tiny neutrino masses. We parametrize the type I seesaw mass matrix by assuming it to give rise to a tri-bimaximal (TBM) type neutrino mixing which predicts ${\theta }_{13}=0$. The type II seesaw mass matrix is then constructed in such a way that the necessary deviation from TBM mixing and the best fit values of neutrino parameters can be obtained when both type I and type II seesaw contributions are taken into account. Considering both subleading as well as equally dominating type II seesaw term, we first constrain the Majorana CP phases from the requirement of producing correct baryon asymmetry through leptogenesis and then incorporating the experimental bounds on lepton flavor violating decays $\mu \to e+\gamma$ and $\mu \to e+e+e$.

In this paper, we study all possible neutrino mass matrices with one zero element and two equal nonzero elements, known as hybrid texture neutrino mass matrices. In the diagonal charged lepton basis, we consider 39 such possible cases which are consistent with the latest neutrino data. Using the two constraints on neutrino mass matrix elements imposed by hybrid textures, we numerically evaluate the neutrino parameters like the lightest neutrino mass $m_{\mathrm{\text{lightest}}}$, one Dirac CP phase $\delta$ and two Majorana CP phases $\alpha$, $\beta$ by using the global fit $3\sigma$ values of three mixing angles and two mass squared differences. We then constrain this parameter space by using the cosmological upper bound on the sum of absolute neutrino masses given by Planck experiment. We also calculate the effective neutrino mass $m_{\nu }^{\mathrm{\text{eff}}}$ for this region of parameter space which can have relevance in future neutrinoless double beta decay experiments. We finally discriminate between these hybrid texture mass matrices from the requirement of producing correct baryon asymmetry through type I seesaw leptogenesis. We also constrain the light neutrino parameter space as well as the lightest right-handed neutrino mass from the constraint on baryon asymmetry of the Universe from Planck experiment.

We consider the $A_4$, $S_4$ and $A_5$ discrete lepton flavor symmetries broken down to nontrivial residual symmetries in the charged lepton and neutrino sectors in such a way that at least one of them is a $Z_2$. Such symmetry breaking patterns lead to predictions for some of the three neutrino mixing angles and/or the Dirac CP violation phase $\delta$ of the neutrino mixing matrix. First, we perform a statistical analysis of these predictions, which uses as input the latest global data on the neutrino mixing parameters. We find 14 phenomenologically viable cases. Further, we assess the viability of these cases taking into account the prospective uncertainties in the determination of the mixing angles, planned to be achieved in current and future neutrino oscillation experiments. We find that only six cases would be compatible with the assumed prospective data. We show that this number will be further reduced by a precision measurement of $\delta$.

Considerable information has been obtained about neutrino mixing matrix. Present data show that in the particle data group (PDG) parametrization, the 2–3 mixing angle and the CP violating phase are consistent with ${𝜃}_{23}=\pi /4$ and ${\delta }_{\mathrm{\text{PDG}}}=-\pi /2$, respectively. A lot of efforts have been devoted to constructing models in realizing a mixing matrix with these values. However, the particular angles and phase are parametrization convention dependent. The meaning about the specific values for mixing angle and phase needs to be clarified. Using the well-known nine independent ways of parametrizing the mixing matrix, we show in detail how the mixing angles and phase change with conventions even with the 2–3 mixing angle to be $\pi /4$ and the CP violating phase to be $-\pi /2$. The original Kobayashi–Maskawa and an additional one belong to such a category. The other 6 parametrizations have mixing angles and phase very different values from those in the PDG parametrization although the physical effects are the same. Therefore one should give the specific parametrization convention when making statements about values for mixing angles and phase.

In this paper, we study the phenomenological implications of enforcing one texture zero on the inverse matrix of the neutrino mass matrix $M_{\nu }^{\mathrm{\text{TM}}}$ that can lead to the trimaximal mixing. It is found that the condition of $M_{12}^{-1}=0$, $M_{13}^{-1}=0$, $M_{22}^{-1}=0$, $M_{23}^{-1}=0$ or $M_{33}^{-1}=0$ can hold in the case of normal neutrino mass ordering, while the condition of $M_{11}^{-1}=0$, $M_{12}^{-1}=0$, $M_{13}^{-1}=0$, $M_{22}^{-1}=0$ or $M_{33}^{-1}=0$ can hold in the case of inverted neutrino mass ordering, where $M_{ij}^{-1}$ (for $i$, $j=1,2,3$) denotes the $ij$ entry of the inverse matrix of $M_{\nu }^{\mathrm{\text{TM}}}$. The ranges of the absolute neutrino mass scale and three CP phases for these cases to hold are studied in some detail. The implications of these cases for the effective neutrino mass $M_{ee}^{}$ which controls the rates of the neutrino-less double beta decay processes are also given.

In this paper, we present a model independent analysis of Leptonic CP violation for some well-known mixing scenarios. In particular, we considered modified schemes for bimaximal (BM), democratic (DC), hexagonal (HG) and tribimaximal (TBM) mixing for our numerical investigation. These model independent corrections to mixing matrices are parametrized in terms of complex rotation matrices $(U)$ with related modified PMNS matrix of the forms $\left(U_{ij}^l\cdot V_M,V_M\cdot U_{ij}^r\right)$ where $U_{ij}^{l,r}$ is a complex rotation in $ij$ sector and $V_M$ is unperturbed mixing scheme. We present generic formulae for mixing angles, Dirac CP phase $({\delta }_{\mathrm{\text{CP}}})$ and Jarlskog invariant $(J_{\mathrm{\text{CP}}})$ in terms of correction parameters. The parameter space of each modified mixing case is scanned for fitting neutrino mixing angles using ${\chi }^2$ approach and the corresponding predictions for Leptonic CP phase $({\delta }_{\mathrm{\text{CP}}})$ and Jarlskog invariant $(J_{\mathrm{\text{CP}}})$ has been evaluated from allowed parameter space. The obtained ranges are reported for all viable cases.

The trimaximal mixing scheme is one of the widely studied neutrino mixing schemes. However, the predicted solar neutrino mixing angle ${\theta }_{12}$ and the reactor neutrino mixing angle ${\theta }_{13}$ cannot simultaneously realize their best-fit values. To address this issue, a minimal modification to the trimaximal mixing scheme is proposed. The modified trimaximal mixing scheme can simultaneously predict the best-fit values of ${\theta }_{12}$ and ${\theta }_{13}$ using an additional real parameter introduced via the modification.

This article is a reflection and reminiscence of Harald Fritzsch’s contributions to the High Energy Particle Physics scene in Singapore, namely in 1978, 2008 to 2022. It also captures rare moments of Harald’s fun, light-hearted times and conversations beneath his stoic demeanor.

In this paper, we study the phenomenological implications of two minor zeros in neutrino mass matrix using trimaximal mixing matrix. In this context, we analyzed 15 possible cases of two minor zeros in neutrino mass matrix and found only two cases, namely, class $A_1$ and class $A_2$, that are compatible with the present neutrino oscillation data. We present correlations of several neutrino oscillation parameters and give prediction of the total neutrino mass, the values of effective Majorana mass, the effective electron anti-neutrino mass and CP violating Majorana phases for these two classes. We also explore the degree of fine tuning in the elements of neutrino mass matrix for the allowed classes. Moreover, we propose a flavor model within the seesaw model along with $Z_8$ symmetry group that can generate such classes.