In this paper, we show that the ratio of the effective Jarlskog invariant $\widetilde{\cal J}$ for leptonic CP violation in three-flavor neutrino oscillations in matter to its counterpart ${\cal J}$ in vacuum $\widetilde{\cal J}/{\cal J} \approx 1/(\hat{C}^{}_{12} \hat{C}^{}_{13})$ holds as an excellent approximation, where $\hat{C}^{}_{12} \equiv \sqrt{1 - 2 \hat{A}^{}_* \cos 2θ^{}_{12} + \hat{A}^2_*}$ with $\hat{A}^{}_* \equiv a\cos^2 θ^{}_{13}/Δ^{}_{21}$ and $\hat{C}^{}_{13} \equiv \sqrt{1 - 2 A^{}_{\rm c} \cos 2θ^{}_{13} + A^2_{\rm c}}$ with $A^{}_{\rm c} \equiv a/Δ^{}_{\rm c}$. Here $Δ^{}_{ij} \equiv m^2_i - m^2_j$ (for $ij = 21, 31, 32$) stand for the neutrino mass-squared differences in vacuum and $θ^{}_{ij}$ (for $ij = 12, 13, 23$) are the neutrino mixing angles in vacuum, while $Δ^{}_{\rm c} \equiv Δ^{}_{31}\cos^2θ^{}_{12} + Δ^{}_{32} \sin^2 θ^{}_{12}$ and the matter parameter $a \equiv 2\sqrt{2}G^{}_{\rm F} N^{}_e E$ are defined. This result has been explicitly derived by improving the previous analytical solutions to the renormalization-group equations of effective neutrino masses and mixing parameters in matter. Furthermore, as a practical application, such a simple analytical formula has been implemented to understand the existence and location of the extrema of $\widetilde{\cal J}$.
The essences of the weak CP violation, the quark and lepton Jarlskog invariants, are determined toward future model buildings beyond the Standard Model (SM). The equivalence of two calculations of Jarlskog invariants gives a bound on the CP phase in some parametrization. Satisfying the unitarity condition, we obtain the CKM and MNS matrices from the experimental data, and present the results in matrix forms. The Jarlskog determinant $J^q$ in the quark sector is found to be $\sim 3.11\times 10^{-5}|\sin\delks|$ while $J^\ell$ in the leptonic sector is $\sim 2.96\times 10^{-2}|\sin\delksl|$ in t…
For neutrino propagation in matter, we show that the Jarlskog invariant, which controls the size of true CP violation in neutrino oscillation appearance experiments, factorizes into three pieces: the vacuum Jarlskog invariant times two simple two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. If the solar effective matter potential and the atmospheric effective $Δm^2$ are chosen carefully for these two resonance factors, then the fractional corrections to this factorization are an impressive 0.04\% or smaller. We also sho…
Working in the basis where the charged-lepton Yukawa matrix is diagonal and making the $τ$-dominance approximations, we analytically derive integral solutions to the one-loop renormalization-group equations (RGEs) for neutrino masses, flavor mixing angles, CP-violating phases and the Jarlskog invariant under the standard parametrization of the PMNS matrix in the standard model or its minimal supersymmetric extension for both Majorana and Dirac neutrinos. With these integral solutions, we carry out numerical calculations to investigate the RGE running of lepton flavor mixing parameters and the …
While Jarlskog-like flavor invariants are adequate for estimating CP-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. For the CKM contributions to the quark electric dipole moments (EDMs), or the PMNS contributions to lepton EDMs, the dominant diagrams have a rainbow topology whose flavor structure does not collapse to flavor invariants. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. The flavor structures in the quark and lepton sectors are systematically studied, assuming differe…
We study the Planck scale effects on Jarlskog determinant. Quantum gravitational (Planck scale) effects lead to an effective SU(2)_{L}\times U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix on electroweak symmetry breaking. We assume that gravitational interaction is flavor blind and compute the Jarlskog determinant due to the Planck scale effects. In the case of neutrino sector, the strength of CP violation is measured by Jarlskog determinant. In this paper, we assume CP violation arise from Planck scale ef…
In this paper, the flavor structure of quark and lepton EDMs in the SM and beyond is investigated using tools inspired from Minimal Flavor Violation. While Jarlskog-like flavor invariants are adequate for estimating CP-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. Our goal is to systematically construct these latter flavor structures in the quark and lepton sectors, assuming different mechanisms for generating neutrino masses. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. Fina…
Terrestrial matter effects in neutrino propagation are T-invariant, so that any observed T violation when neutrinos pass through the Earth, such as an asymmetry between the transition probabilities P(nu_mu -> nu_e) and P(nu_e -> nu_mu), would be a direct indication of T violation at the fundamental level. Matter effects do however modify the magnitudes of T-violating asymmetries, and it has long been known that resonant enhancement can lead to large effects for a range of plausible values of the relevant parameters. We note that the determinant of the commutator of the lepton mass matrices is …
The Jarlskog invariant which controls the size of intrinsic CP violation in neutrino oscillation appearance experiments is modified by Wolfenstein matter effects for neutrinos propagating in matter. In this paper we give the exact factorization of Jarlskog invariant in matter into the vacuum Jarlskog invariant times two, two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. We compare the location of the minima of the factorizing resonance factors with the location of the solar and atmospheric resonances, precisely defined. …
In fermion mixing phenomenology, the matrix of moduli squared, P=(|U|^2), is well-known to carry essentially the same information as the complex mixing matrix U itself, but with the advantage of being phase-convention independent. The matrix K (analogous to the Jarlskog CP-invariant J) formed from the real parts of the mixing matrix "plaquette" products is similarly invariant. In this paper, the P and K matrices are shown to be entirely equivalent, both being directly related (in the leptonic case) to the observable, locally L/E-averaged transition probabilities in neutrino oscillations. We st…
We consider future experiments to detect CP violation in neutrino oscillations and discuss how to test that all asymmetries are indeed described in terms of the single leptonic Jarlskog invariant as predicted in the absence of new physics effects.
We generalise our previous observation on the invariance of the Jarlskog determinant to matter effects in neutrino oscillations. Within the context of standard neutrino oscillation theory with matter effects, we present the complete set of (five) matter invariant observables for neutrino propagation in matter. We give some examples of their application.
As SMEFT is a framework of growing importance to analyze high-energy data, understanding its parameter space is crucial. The latter is commonly split into CP-even and CP-odd parts, but this classification is obscured by the fact that CP violation is actually a collective effect that is best captured by considering flavor-invariant combinations of Lagrangian parameters. First we show that fermion rephasing invariance imposes that several coefficients associated to dimension-six operators can never interfere with operators of dimension $\leq4$ and thus cannot appear in any physical observable at…
In the minimal supersymmetric standard model, we have studied the evolution of the neutrino flavor mixing by using the renormalization group equation(RGE) with the Georgi-Jarlskog texture for the Yukawa coupling matrices.For the large Yukawa coupling of the charged lepton, i.e.,$\tan\b \gg 1$, the neutrino flavor mixing increases significantly with running down to the electroweak scale by the RGE. If one wishes to get the large neutrino flavor mixing $\sin þ_{23}$ at the electroweak scale, which is suggested by the muon neutrino deficit in the atomospheric neutrino flux, the initial condition …
The renormalization-group equation (RGE) approach to neutrino matter effects is further developed in this work. We derive a complete set of differential equations for effective mixing elements, masses and Jarlskog-like invariants in presence of a light sterile neutrino. The evolutions of mixing elements as well as Jarlskog-like invariants are obtained by numerically solving these differential equations. We calculate terrestrial matter effects in long-baseline (LBL) experiments, taking NOvA, T2K and DUNE as examples. In both three-flavor and four-flavor frameworks, electron-neutrino survival pr…
We explain the imbalance of the flavor mixing angles between the quark and the lepton sectors in the context of the SU(5) GUT with the see-saw mechanism. The quark masses and the CKM matrix elements are obtained by using, respectively, the Fritzsch and Branco - Silva-Marcos form for the up- and down-quark Yukawa matrices (y^u and y^d) at the GUT scale. The charged-lepton Yukawa matrix (y^e) is the transpose of y^d, modified by the Georgi-Jarlskog factor. We show that the neutrino masses and mixing angles suggested by the recent solar and atmospheric neutrinos are then obtained from a simple te…
If the massive neutrinos are Majorana particles, neutrinoless double beta ($0νββ$) decay experiments are not enough to determine the Majorana phases. We carry out a systematic study of CP violation in neutrino-antineutrino oscillations. In these processes, CP-conserving parts involve six independent $0νββ$-like mass terms $\langle m\rangle_{αβ}$ and CP-violating parts are associated with nine independent Jarlskog-like parameters ${\cal V}^{ij}_{αβ}$ (for $α, β= e, μ, τ$ and $i, j = 1, 2,3$). With the help of current neutrino oscillation data, we illustrate the salient features of six independe…
We propose a model based on the gauge group $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ with an extra $S_{3}$ flavor symmetry, which accounts for the lepton masses and mixing. The small active neutrino masses are generated via a double seesaw mechanism. In this scenario, the spectrum of neutrinos presents very light, light and very heavy masses. The model predicts a quasidegenerate normal hierarchy active neutrino mass spectrum and the relation $Δm_{21}^{2}\ll Δm_{31}^{2}$ arises from effective six-dimensional operators. The obtained neutrino mixing parameters are in agreement with the neutri…
Matter effects may strongly enhance the Jarlskog factor J in T and CP-violating three-neutrino oscillation probabilities. However, we show that when J is enhanced, the same matter effects suppress the oscillating factors and increase the oscillation length. The net result is that there is no large enhancement in measurable probabilities for earth-bound experiments using neutrino parameters suggested by current experiments. We show that by an appropriate choice of the experimental parameters, neutrino energy and travel length, the T-violating probability can be enhanced by matter effects over t…
The inverse and linear seesaw scenarios are two typical extensions of the canonical seesaw mechanism, which contain much more sterile degrees of freedom but can naturally explain the smallness of three active neutrino masses at a sufficiently low energy scale (e.g., the TeV scale). To fully describe the mixing among three active neutrinos, three sterile neutrinos and three extra gauge-singlet neutral fermions in either of these two seesaw paradigms, we present the {\it first} full parametrization of the $9\times 9$ flavor mixing matrix in terms of 36 rotation angles and 36 CP-violating phases.…
Connecting Neutrino Masses, Dark Matter and Leptogenesis from $Δ(54)$ Flavor with Triple Inverse Seesaw
University of Science and Technology, Baridua（巴拉杜科技大学）；Institute for Plasma Research（等离子体研究所）；Rajiv Gandhi Institute of Petroleum Technology（拉吉夫·甘地石油技术研究所）；Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）；Banaras Hindu University（贝拿勒斯印度教大学）；Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学）
A structure is proposed for the mass matrices of the quarks and leptons that arises in a natural way from the assumption that the breaking of SO(10) gauge symmetry is achieved by the smallest possible set of vacuum expectation values. This structure explains well many features of the observed spectrum of quarks and leptons. It reproduces the Georgi-Jarlskog mass relations and postdicts the charm quark mass in reasonable agreement with data. It also predicts a large mixing angle between ν_μ and ν_τ, as suggested by atmospheric neutrino data. The mixing angles of the electron neutrino are predic…
We demonstrate that sizable neutrino flavor oscillations can be generated in a model with large extra spacetime dimensions even if the physics on the brane is flavor-diagonal, the bulk neutrino theory is flavor-neutral, and the brane/bulk couplings are flavor-blind. This is thus a compact model for addressing neutrino flavor oscillations in higher dimensions. We also discuss several phenomenological aspects of the ``bulk-mediated'' neutrino oscillations inherent in this model, and show that this model contains some potentially important new phenomenological features in the limit of large brane…
The Daya Bay Collaboration has recently observed neutrino oscillations in the nu_e-bar -> nu_e-bar disappearance channel, indicating that sin^2 theta_13 = 0.024 +(-) 0.005 (1 sigma) and theta_13 = 0 is already excluded at the 5.2 sigma confidence level. Now three neutrino mixing angles have been measured to a good degree of accuracy (theta_12 ~ 34^\circ, theta_23 ~ 45^\circ and theta_13 ~ 9^\circ). Motivated by these experimental results, we propose a novel lepton flavor mixing pattern, which predicts sin^2 theta_23 = 1/2, sin^2 theta_12 = (2+\sqrt{3})/(10+\sqrt{3}) ~ 0.318 and sin^2 theta_13 …
We comment on the paper ``Remarks on flavor-neutrino propagators and oscillation formulae'' [Phys. Rev. D64, 013011 (2001)]. We show that the conclusions presented in that paper do not apply to the exact field theoretical oscillation formulae obtained in the BV formalism (for three flavors) which are free from the dependence on arbitrary mass parameters, account for CP violation and reduce to the usual quantum mechanical (Pontecorvo) three flavor oscillation formulae in the relativistic limit.
The theory of neutrino flavor rotations is discussed in terms of wave function solutions to the Dirac equation with a neutrino mass matrix. We give a critical review of the nature of neutrino oscillations.
We study the correlation between CP violation in neutrino oscillations and leptogenesis in the framework with two heavy Majorana neutrinos and three light neutrinos. Among three unremovable CP phases, a heavy Majorana phase contributes to leptogenesis. We show how the heavy Majorana phase contributes to Jarlskog determinant $J$ as well as neutrinoless double $β$ decay by identifying a low energy CP violating phase which signals the CP violating phase for leptogenesis. For some specific cases of the Dirac mass term of neutrinos, a direct relation between lepton number asymmetry and $J$ is obtai…
We consider neutrino oscillations as non stationary phenomenon based on Schrodinger evolution equation and mixed states of neutrinos with definite flavors. We show that time-energy uncertainty relation plays a crucial role in neutrino oscillations. We compare neutrino oscillations with $B_{d}^{0}\leftrightarrows\bar B_{d}^{0}$ oscillations.
A short review on studies of neutrino flavor oscillations in moving with a constant speed matter is presented. Then neutrino flavor oscillations in matter moving with acceleration are considered. We develop an approach that is valid for both non-relativistic and relativistic matter motion. For both these cases the effective neutrino potentials in accelerating matter are obtained and neutrino flavor oscillation probabilities and the Mikheyev-Smirnov-Wolfenstein resonance conditions are evaluated. The obtained results in the limit of zero matter acceleration reproduce the corresponding expressio…
In the context of quantum field theory, we derive flavor energy uncertainty relations for neutrino oscillations. By identifying the non conserved flavor charges with the clock observables, we arrive at the Mandelstam Tamm version of time energy uncertainty relations. In the ultrarelativistic limit these relations yield the well known condition for neutrino oscillations. Ensuing non relativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of …
As a possible approach to the neutrino oscillation on the basis of quantum field theory, the expectation values of the flavor-neutrino currents are investigated by employing the finite-time transition matrix in the interaction representation. Such expectation values give us in the simplest form a possible way of treating the neutrino oscillation without recourse to any one flavor-neutrino states. The present paper is devoted to presenting the formulation and the main structures of the relevant expectation values.
We study spin and spin-flavor oscillations of Dirac neutrinos in a plane electromagnetic wave with circular polarization. The evolution of massive neutrinos with nonzero magnetic moments in the field of an electromagnetic wave is based on the exact solution of the Dirac-Pauli equation. We formulate the initial condition problem to describe spin-flavor oscillations in an electromagnetic wave. The transition probabilities for spin and spin-flavor oscillations are obtained. In case of spin-flavor oscillations, we analyze the transition and survival probabilities for different neutrino magnetic mo…
We analyze phenomenological aspects of the quantum field theoretical formulation of meson mixing and obtain the exact oscillation formula in the presence of the decay. This formula is different from quantum mechanical formula by additional high-frequency oscillation terms. In the infinite volume limit, the space of the flavor quantum states is unitarily inequivalent to the space of energy eigenstates.
Neutrino flavor oscillations are discussed in terms of two coupled Dirac fields. The interacting Lagrangian is diagonalized to obtain the exact eigenvalues and eigenfunctions. Flavor wave functions are then derived directly from the quantized neutrino fields. Probability density obtained by squaring these wave functions upon taking into account the neutrino chirality are in agreement with the standard neutrino oscillation probabilities.
Recently, it was pointed out that the solar and atmospheric neutrino deficits can be explained by oscillations between electroweak doublet and singlet neutrinos in the model of Majorana neutrinos. However, since the model includes no flavor mixing, it cannot explain the recent LSND result. We extend the model to include the flavor mixing, and obtain the explanation of the LSND result together with the solar and atmospheric neutrino deficits. The requirement for the neutrinos to be the hot dark matter selects out only the vacuum oscillation solution to the solar neutrino deficit.
We analyze neutrino oscillation for the general case when the initial neutrino is not in a pure flavor state. We show that, after such a neutrino beam propagates for a while, the probability of detecting any pure flavor state depends even on the CP-violating Majorana phases in the mixing matrix. The dependence remains even when energy spectrum of the initial beam is taken into account. We discuss various implications of this dependence.
We derive the reduction formula, which expresses the survival rate for the three-flavor neutrino oscillation by the two-flavor one, to the next-to-leading order in case there is one resonance due to the matter effect. We numerically find that the next-to-leading reduction formula is extremely accurate and the improvement is relevant for the precision test of solar neutrino oscillation and the indirect measurment of CP violation in the leptonic sector. We also derive the reduction formula, which is slightly different from that previously obtained, in case there are two resonances. We numericall…
We compare the effectiveness of various tests of three-flavor mixing in future long-baseline neutrino oscillation experiments. We analyze a representative case of mixing in a simplified three-flavor scheme, whose relevant parameters are one neutrino mass-square difference, $m^2$, and two mixing angles, $ψ$ and $ϕ$. We show that an unambiguous determination of $ψ$ and $ϕ$ requires flavor-appearance tests in accelerator experiments, as well as supplementary information from reactor experiments.
The standard theory of neutrino oscillations is reviewed, highlighting the main assumptions: the definition of the flavor states, the equal-momentum assumption and the time = distance assumption. It is shown that the standard flavor states are correct approximations of the states that describe neutrinos in oscillation experiments. The equal-momentum assumption is shown to be unnecessary for the derivation of the oscillation probability. The time = distance assumption derives from the wave-packet character of the propagating neutrinos. We present a simple quantum-mechanical wave-packet model wh…
A brief survey of the history of the neutrino oscillation is presented. Here emphasis is laid on the topics around the first proposal of neutrino flavor oscillation by Nagoya group in 60's. Main contents are presented in my opening address "Birth of Neutrino Oscillation" at the NOW' 98, Amsterdam, hep-ph/9811358, but added some detail of the other topics, especially a first calculation of decay processes $μ\to e + γ$ and $ν_2 \to ν_1 + γ$ in terms of neutrino flavor mixing, and some arguments relating to the massive neutrino.
Analytic formulas are presented for three flavor neutrino oscillations in matter in the plane wave approximation. We calculate in particular the time evolution operator in both mass and flavor bases. We also find the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter. The application of this to neutrino oscillations for both atmospheric and long baseline neutrinos in a mantle-core-mantle step function model of the Earth's matter density profile is discussed.
In this talk, we consider the interplay of fundamental and matter-induced T-violating effects in neutrino oscillations in matter. We present a simple approximative analytical formula for the T-violating probability asymmetry for three flavor neutrino oscillations in matter with an arbitrary density profile. We also discuss some implications of the obtained results. Since there are no T-violating effects in two flavor neutrino case (in the limit of vanshing $θ_{13}$ or $Δm_{21}^2$, the three flavor neutrino oscillations reduces to the two flavor ones), the T-violating probability asymmetry can,…
A unique description avoiding confusion is presented for all flavor oscillation experiments in which particles of a definite flavor are emitted from a localized source. The probability for finding a particle with the wrong flavor must vanish at the position of the source for all times. This condition requires flavor-time and flavor-energy factorizations which determine uniquely the flavor mixture observed at a detector in the oscillation region; i.e. where the overlaps between the wave packets for different mass eigenstates are almost complete. Oscillation periods calculated for ``gedanken'' t…
We clarify the domain needed for the mixing angles in three flavor neutrino oscillations. By comparing the ranges of the transition probabilities as functions of the domains of the mixing angles, we show that it is necessary and sufficient to let all mixing angles be in $[ 0, π/2 ]$. This holds irrespectively of any assumptions on the neutrino mass squared differences.
If one assumes solar and LSND neutrino oscillations to explain the corresponding data, then the atmospheric neutrino deficit cannot be accommodated within the Standard Model with three light flavors, unless one ignores the data's zenith-angle dependence. We propose a novel solution to this problem by postulating large anomalous diagonal $ν_τ$-quark interactions which affect $ν_μ- ν_τ$ oscillations traversing the Earth and induce the observed zenith-angle dependence.
We formulate direct, neutrino flavor-changing interactions in a framework that fits smoothly with the parameterization of two-and three-state mixing of massive neutrino states. We show that even small direct interaction strengths could have important consequences for the interpretation of currently running and proposed oscillation experiments. The oscillation amplitude and the borders of the allowed regions in two-and three-flavor mixing parameter space can be sensitieve to the presence of direct interactions when the transition probability is small. We use extensively the high sensitivity of …
A unique description avoiding confusion is presented for all flavor-oscillation experiments in which particles of a definite flavor are emitted from a localized source. The probability for finding a particle with the wrong flavor must vanish at the position of the source for all times. This condition requires flavor-time and flavor-energy factorizations which determine uniquely the flavor mixture observed at a detector in the oscillation region; i.e. where the overlaps between the wave packets for different mass eigenstates differ negligibly from 100\%. The translation of a ``gedanken'' experi…
Recent experimental research progress of solar neutrino and neutrino oscillation reveals that neutrinos do have nonzero mass, which poses a serious challenge to theoretical physics. Two symmetries, the common invariance under the space-time inversion and the invariance or violation to maximum under the space inversion are analyzed for Dirac equation or the equation for superluminal neutrino respectively. Then a simple three-flavor model containing only one parameter is proposed and the relations among neutrino oscillation, parity violation and superluminal property are emphasized.
The recent observations of atmospheric nu events from the Super-Kamiokande experiment are compatible with three-flavor neutrino oscillations, occurring dominantly in the nu_mu<--->nu_tau channel and subdominantly in the nu_mu<--->nu_e channel. We present an updated analysis of the three-flavor mass-mixing parameters consistent with the present phenomenology, including the latest 45 kTy data sample from Super-Kamiokande. A comparison with our previous results, based on 33 kTy data, shows that the oscillation evidence is strengthened, and that the neutrino mass-mixing parameters are constrained …
Viable neutrino and charged lepton masses and mixings are obtained by imposing a $S_3 \times Z_4 \times Z_3$ flavor symmetry in a model with a few additional Higgs. We use two $SU(2)_L$ triplet Higgs which are arranged as a doublet of $S_3$, and standard model singlet Higgs which are also put as doublets of $S_3$. We break the $S_3$ symmetry in this minimal model by giving vacuum expectation values (VEV) to the additional Higgs fields. Dictated by the minimum condition for the scalar potential, we obtain certain VEV alignments which allow us to maintain $μ-τ$ symmetry in the neutrino sector, w…
On the basis of quantum field theory, we consider a unified description of various processes accompanied by neutrinos, namely weak decays and oscillation processes. The structures of the expectation values of flavor-neutrino numbers with respect to neutrino-source hadron state are investigated. Due to the smallness of neutrino masses, we naturally obtain the old (i.e. pre-mixing) formulas of decay probabilities. Together, it is shown that the oscillation formulas, similar to the usual ones, are applied irrespectively of the details of neutrino-producing processes. The derived oscillation formu…
Neutrinos can undergo flavor--oscillations if they possess flavor--dependent couplings to the surrounding gravitational field (the VEP mechanism). The neutrino fields can be massless, in accord with the Minimal Standard Model, but at the expense of the Einstein Equivalence Principle. We show that it is possible to explain the observed Solar Neutrino data from the various experiments using the VEP solution in a realistic three--generation framework, and further note how the three--flavor model can offer larger allowed regions of parameter space over the two--flavor models.
We discuss here some flavor structure aspects of the complete theory of supersymmetry without R-parity addressed from the perspective of fitting neutrino oscillation data based on the recent Super-Kamiokande result. The single-VEV parametrization of supersymmetry without R-parity is first reviewed, illustrating some important features not generally appreciated. For the flavor structure discussions, a naive, flavor model independent, analysis is presented, from which a few interesting things can be learned.
The general formalism for the description of neutrino oscillations in arbitrary rapidly varying external fields is elaborated. We obtain the new effective Hamiltonian which determines the evolution of the averaged neutrino wave function. The general technique is applied to the neutrino oscillations in rapidly varying magnetic fields. We evaluate the transition probabilities of the neutrino spin-flavor oscillations in magnetic fields of the Sun and compare them with the numerical solutions of the Schroedinger equation with the exact Hamiltonian.
Superkamiokande atmospheric neutrino data for 535 days are analyzed in the framework of three flavor oscillations with mass hierarchy. It is shown that the best fit point is very close to the pure maximal $ν_μ\leftrightarrowν_τ$ case and $Δm^2 \simeq 7\times10^{-3}$ eV$^2$. The allowed region at 90 %CL is given and the implications to the long baseline experiments are briefly discussed.
Abstract We study the analytic expression for four flavor neutrino oscillation in the presence of matter. We calculate the time evolution operator on flavor and mass basis. We find the matter dependent mass square difference and neutrino transition probabilities for (3+1) four flavor neutrino oscillation.
The three neutrino mass matrices in the $SU(5)\times U(2)$ model are studied focusing on the neutrino oscillation experiments. The atmospheric neutrino anomaly could be explained by the large $ν_μ - ν_τ$ oscillation. The long baseline experiments are expected to detect signatures of the neutrino oscillation even if the atmospheric neutrino anomaly is not due to the neutrino oscillation. However, the model cannot solve the solar neutrino deficit while it could be reconciled with the LSND data.
We review the application of the relativistic quantum mechanics method for the description of neutrino oscillations for the studies of spin-flavor oscillations in background matter under the influence of a plane electromagnetic wave. Basing on the new exact solution of the Dirac-Pauli equation for a massive neutrino in the given external fields, we derive the transition probabilities for spin and spin-flavor oscillations. The obtained expressions are analyzed for different types of the neutrino magnetic moments. Our results are compared with findings of other authors.
