Deviation from tri-bimaximal mixing and large reactor mixing angle

Recent observations for a non-zero _θ13${\theta }_{13}$ have come from various experiments. We study a model of lepton mixing with a 2–3 flavor symmetry to accommodate the sizable _θ13${\theta }_{13}$ measurement. In this work, we derive deviations from the tri-bimaximal (TBM) pattern arising from breaking the flavor symmetry in the neutrino sector, while the charged leptons contribution has been discussed in a previous work. Contributions from both sectors towards accommodating the non-zero _θ13${\theta }_{13}$ measurement are presented.     

Comparing trimaximal mixing and its variants with deviations from tri-bimaximal mixing

We analyze in detail the predictions of “trimaximal” neutrino mixing, which is defined by a mixing matrix with identical second column elements. This column is therefore identical to the second column in the case of tri-bimaximal mixing. We also generalize trimaximal mixing by assuming that the other rows and columns of the mixing matrix individually can have the same forms as for tri-bimaximal mixing. The phenomenology of these alternative scenarios and their mixing angle and CP phase correlations are studied. We emphasize how trimaximal mixing scenarios can be distinguished experimentally from broken tri-bimaximal mixing.     

Admixture of quasi-Dirac and Majorana neutrinos with tri-bimaximal mixing

We propose a realization of the so-called bimodal/schizophrenic model proposed recently. We assume S₄, the permutation group of four objects as flavor symmetry giving tri-bimaximal lepton mixing at leading order. In these models the second massive neutrino state is assumed quasi-Dirac and the remaining neutrinos are Majorana states. In the case of inverse mass hierarchy, the lower bound on the neutrinoless double beta decay parameter mee is about two times that of the usual lower bound, within the range of sensitivity of the next generation of experiments.     

Deviations from tri-bimaximal neutrino mixing using type II seesaw

We study the possibility of generating deviations from tri-bimaximal (TBM) neutrino mixing to explain the non-zero reactor mixing angle within the framework of both type I and type II seesaw mechanisms. The type I seesaw term gives rise to the μ–τ   symmetric TBM pattern of neutrino mass matrix as predicted by generic flavor symmetry models like _A4$A_4$ whereas the type II seesaw term gives rise to the required deviations from TBM pattern to explain the non-zero _θ13${\theta }_{13}$. Considering extremal values of Majorana CP phases such that the neutrino mass eigenvalues have the structure (_m1,−_m2,_m3)$(m_1,-m_2,m_3)$ and (_m1,_m2,_m3)$(m_1,m_2,m_3)$, we numerically fit the type I seesaw term by taking oscillation as well as cosmology data and then compute the predictions for neutrino parameters after the type II seesaw term is introduced. We consider a minimal structure of the type II seesaw term and check whether the predictions for neutrino parameters lie in the 3σ range. We also outline two possible flavor symmetry models to justify the minimal structure of the type II seesaw term considered in the analysis.     

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α≈90°$\alpha \approx 90\text{°}$. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5)$\mathit{SU}(5)$, a discrete family symmetry such as A₄$A_4$ or S₄$S_4$, a shaping symmetry including products of Z₂${\mathbb{Z}}_2$ and Z₄${\mathbb{Z}}_4$ groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α≈90°$\alpha \approx 90\text{°}$ by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.     

A4-based tri-bimaximal mixing within inverse and linear seesaw schemes

We consider tri-bimaximal lepton mixing within low-scale seesaw schemes where light neutrino masses arise from TeV scale physics, potentially accessible at the Large Hadron Collider (LHC). Two examples are considered, based on the A₄$A_4$ flavor symmetry realized within the inverse or the linear seesaw mechanisms. Both are highly predictive so that in both the light neutrino sector effectively depends only on three mass parameters and one Majorana phase, with no CP violation in neutrino oscillations. We find that the linear seesaw leads to a lower bound for neutrinoless double beta decay while the inverse seesaw does not. The models also lead to potentially sizeable decay rates for lepton flavor violating processes, tightly related by the assumed flavor symmetry.     

Realizing tri-bimaximal mixing in minimal seesaw model with S4 family symmetry

In this Letter, we realize the tri-bimaximal mixing in the lepton sector in the context of minimal seesaw in which only two right-handed neutrinos are introduced, with the discrete group S4 as the family symmetry. In order to constrain the form of superpotential, a Z3 symmetry is also introduced. In the model, the mass matrices for charged leptons and right-handed neutrinos are diagonal. The unitary matrix that diagonalizes the light Majorana neutrino mass matrix is exact tri-bimaximal at LO, and is corrected by small quantities of O(0.01) at NLO. The mechanism to get the particular scalar VEV alignments used is also presented. Phenomenologically, the mass spectrum is of normal hierarchy with m₁=0, and ∑mi and |mee| are about 0.058 eV and 0.003 eV respectively.     

New parametrisation of tri-bimaximal mixings

Recent neutrino oscillation data indicates tri-bimaximal mixings. In this communication we propose degenerate, inverted hierarchical and normal hierarchical structures of neutrino mass matrices in terms of two input parameters. These mass matrices not only predict tri-bimaximal mixings but also neutrino oscillation mass parameters comparable with experimental data. We consider contribution of Type-II seesaw formula and observe possible deviations from tri-bimaximal mixings.     

Bouncing alternatives to inflation

Although the inflationary paradigm is the most widely accepted explanation for the current cosmological observations, it does not necessarily correspond to what actually happened in the early stages of our Universe. To decide on this issue, two paths can be followed: first, all the possible predictions it makes must be derived thoroughly and compared with available data, and second, all the imaginable alternatives must be ruled out. Leaving the first task to all other contributors of this volume, we concentrate here on the second option, focusing on the bouncing alternatives and their consequences.     

Possible tests of neutrino maximal mixing and comments on matter effects

We show in a simple and general way that matter effects do not contribute to the average value of the transition probabilities of solar ν_e's into other states in the case of maximal mixing of any number of massive neutrinos. We also show that future solar neutrino experiments (Super-Kamiokande and SNO) will allow to test the model with maximal mixing of three massive neutrinos in a way that does not depend on the initial solar neutrino flux.     

Diffusion approximations to cascade mixing

In two recent studies^{1, 2} of cascade mixing, the process in which energetic ion bombardment can redistribute the atomic components of a multielemental target via recoil processes, a diffusion approximation has been assumed, apparently with signif-icantly different results². It is the purpose of this communication to reveal the close similarity of the two existing treatments and to indicate some important modifications and extensions.     

Explosive Instability due to four-wave mixing

It is known that an explosive instability can occur when nonlinear waves propagate in certain media that admit 3-wave mixing. The purpose of this Letter is to show that explosive instabilities can occur even in media that admit no 3-wave mixing. Instead, the instability is caused by 4-wave mixing: four resonantly interacting wave trains gain energy from a background, and all blowup in a finite time. Unlike singularities associated with self-focussing, these singularities can occur with no spatial structure-the waves blowup everywhere in space simultaneously. We have not yet investigated the effect of spatial structure on a 4-wave explosive instability.     

Hybrid approach to high-frequency microfluidic mixing

We report the experimental verification of the predicted chaotic mixing characteristics for a polydimethylsioxane microfluidic chip, based on the mechanism of multistage cross-channel flows. While chaotic mixing can be achieved within short passage distances, there is an optimal side channel flow pulsation frequency beyond which the mixing becomes ineffective. Based on the physical understanding of a Poincaré section analysis, we propose the installation of passive flow baffles in the main microfluidic channel to facilitate high-frequency mixing. The combined hybrid approach enables chaotic mixing at enhanced frequency and reduced passage distance in two-dimensional flows.     

Deviation from tri-bimaximal mixings through flavour twisters in inverted and normal hierarchical neutrino mass models

We explore a novel possibility for lowering the solar mixing angle (θ ₁₂) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle (θ ₂₃ = 45°) and zero reactor angle (θ ₁₃ = 0°) in the inverted and normal hierarchical neutrino mass models having 2–3 symmetry. This can be done through the identification of a flavour twister term in the texture of neutrino mass matrix and the variation of such term leads to lowering of solar mixing angle. For the observed ranges of Δm ₂₁² and Δm ₂₃², we calculate the predictions on tan² θ ₁₂ = 0.5, 0.45, 0.35 for different input values of the parameters in the neutrino mass matrix. We also observe a possible transition from inverted hierarchical model having even CP parity (Type-IHA) to inverted hierarchical model having odd CP parity (Type-IHB) in the first two mass eigenvalues, when there is a change in input values of parameters in the same mass matrix. The present work differs from the conventional approaches for the deviations from tri-bimaximal mixing, where the 2–3 symmetry is broken, leading to θ ₂₃ ≠ 45° and θ ₁₃ ≠ 0°.