Description Of Neutrino Oscillations Research Articles

A geometrical look at neutrino oscillation probabilities with non-standard interactions

In this talk, we discuss an alternative description of neutrino flavor oscillations using leptonic unitarity triangles (LUT) which allows for geometric visualization of neutrino oscillations. After a brief review of the LUT description of neutrino oscillations for propagation in vacuum and in matter with standard interactions, we discuss how we can extend this approach to describe neutrino oscillations in presence of new physics. We consider non-standard neutrino interactions (NSI) as the toy model of new physics. The content presented in this talk is based on Ref. [1].

Non-standard neutrino oscillations: perspective from unitarity triangles

We formulate an alternative approach based on unitarity triangles to describe neutrino oscillations in presence of non-standard interactions (NSI). Using perturbation theory, we derive the expression for the oscillation probability in case of NSI and cast it in terms of the three independent parameters of the leptonic unitarity triangle (LUT). The form invariance of the probability expression (even in presence of new physics scenario as long as the mixing matrix is unitary) facilitates a neat geometric view of neutrino oscillations in terms of LUT. We examine the regime of validity of perturbative expansions in the NSI case and make comparisons with approximate expressions existing in literature. We uncover some interesting dependencies on NSI terms while studying the evolution of LUT parameters and the Jarlskog invariant. Interestingly, the geometric approach based on LUT allows us to express the oscillation probabilities for a given pair of neutrino flavours in terms of only three (and not four) degrees of freedom which are related to the geometric properties (sides and angles) of the triangle. Moreover, the LUT parameters are invariant under rephasing transformations and independent of the parameterization adopted.

Sum rules and asymptotic behaviors of neutrino mixing and oscillations in matter

Similar to the case in vacuum, it is straightforward to describe neutrino oscillations in matter with the effective lepton flavor mixing matrix and neutrino mass-squared differences (i, j = 1, 2, 3). By calculating two sets of sum rules of and , we have derived exact expressions of and (for α, β = e, μ, τ and i = 1, 2, 3) and discussed the asymptotic behaviors of and and in very dense matter (i.e., in the limit of the matter parameter approaching infinity).

Neutrino Oscillations in Dense Matter

We propose a modification of the electroweak theory, where the fermions with the same electroweak quantum numbers are combined in multiplets and are treated as different quantum states of a single particle. The developed approach enables one to calculate the probabilities of the processes taking place in the detector at long distances from the particle source. Calculations of higher-order processes including the computation of the contributions due to radiative corrections can be performed in the framework of the perturbation theory using the regular diagram technique. As a result, we obtain the analog to the Dirac--Schwinger equation of quantum electrodynamics describing neutrino oscillations and its spin rotation in dense matter.

New Ambiguity in Probing CP Violation in Neutrino Oscillations.

If neutrinos get mass via the seesaw mechanism the mixing matrix describing neutrino oscillations can be effectively nonunitary. We show that in this case the neutrino appearance probabilities involve a new CP phase ϕ associated with nonunitarity. This leads to an ambiguity in extracting the "standard" three-neutrino phase δ_{CP}, which can survive even after neutrino and antineutrino channels are combined. Its existence should be taken into account in the planning of any oscillation experiment aiming at a robust measurement of δ_{CP}.

Predictive model of radiative neutrino masses

We present a simple and predictive model of radiative neutrino masses. It is a special case of the Zee model which introduces two Higgs doublets and a charged singlet. We impose a family-dependent Z_4 symmetry acting on the leptons, which reduces the number of parameters describing neutrino oscillations to four. A variety of predictions follow: The hierarchy of neutrino masses must be inverted; the lightest neutrino mass is extremely small and calculable; one of the neutrino mixing angles is determined in terms of the other two; the phase parameters take CP-conserving values with \delta_{CP} = \pi; and the effective mass in neutrinoless double beta decay lies in a narrow range, m_{\beta \beta} = (17.6 - 18.5) meV. The ratio of vacuum expectation values of the two Higgs doublets, tan\beta, is determined to be either 1.9 or 0.19 from neutrino oscillation data. Flavor-conserving and flavor-changing couplings of the Higgs doublets are also determined from neutrino data. The non-standard neutral Higgs bosons, if they are moderately heavy, decay dominantly into \mu and \tau with prescribed branching ratios. Observable rates for the decays \mu \to e \gamma and \tau \to 3\mu are predicted if these scalars have masses in the range of 150-500 GeV.

Lepton flavor mixing in the Wolfenstein scheme

We mimic the Wolfenstein scheme of quark flavor mixing to describe neutrino oscillations in the standard model. We identify the parameter $\lambda$ with the experimentally measured value of the mixing element responsible for atmospheric neutrino oscillations. The matrix elements responsible for solar neutrino oscillations and the Chooz angle are taken to be proportional to $\lambda^2$ and $\lambda^3$, respectively. Using present world average data on neutrinos, we derive bounds on the other parameters $A$, $\rho$, and $\eta$, of the new scheme.

Calculating error bars for neutrino mixing parameters

One goal of contemporary particle physics is to determine the mixing angles and mass-squared differences that constitute the phenomenological constants that describe neutrino oscillations. Of great interest are not only the best-fit values of these constants but also their errors. Some of the neutrino oscillation data is statistically poor and cannot be treated by normal (Gaussian) statistics. To extract confidence intervals when the statistics are not normal, one should not utilize the value for $\ensuremath{\Delta}{\ensuremath{\chi}}^{2}$ versus confidence level taken from normal statistics. Instead, we propose that one should use the normalized likelihood function as a probability distribution; the relationship between the correct $\ensuremath{\Delta}{\ensuremath{\chi}}^{2}$ and a given confidence level can be computed by integrating over the likelihood function. This allows for a definition of confidence level independent of the functional form of the ${\ensuremath{\chi}}^{2}$ function; it is particularly useful for cases in which the minimum of the ${\ensuremath{\chi}}^{2}$ function is near a boundary. We point out that the question of what is the probability that a parameter is not zero is more precisely worded as what is the maximum confidence level at which the value of zero is not included. We present two pedagogic examples and find that the proposed method yields confidence intervals that can differ significantly from those obtained by using the value of $\ensuremath{\Delta}{\ensuremath{\chi}}^{2}$ from normal statistics. For example, we find that for the T2K experiment the value of $\ensuremath{\Delta}{\ensuremath{\chi}}^{2}$ corresponding to a confidence level of 90$%$ is 3.57 rather than the normal statistics value of 2.71.

Neutrino Oscillations: Entanglement, Energy-Momentum Conservation and QFT

We consider several subtle aspects of the theory of neutrino oscillations which have been under discussion recently. We show that the $S$-matrix formalism of quantum field theory can adequately describe neutrino oscillations if correct physics conditions are imposed. This includes space-time localization of the neutrino production and detection processes. Space-time diagrams are introduced, which characterize this localization and illustrate the coherence issues of neutrino oscillations. We discuss two approaches to calculations of the transition amplitudes, which allow different physics interpretations: (i) using configuration-space wave packets for the involved particles, which leads to approximate conservation laws for their mean energies and momenta; (ii) calculating first a plane-wave amplitude of the process, which exhibits exact energy-momentum conservation, and then convoluting it with the momentum-space wave packets of the involved particles. We show that these two approaches are equivalent. Kinematic entanglement (which is invoked to ensure exact energy-momentum conservation in neutrino oscillations) and subsequent disentanglement of the neutrinos and recoiling states are in fact irrelevant when the wave packets are considered. We demonstrate that the contribution of the recoil particle to the oscillation phase is negligible provided that the coherence conditions for neutrino production and detection are satisfied. Unlike in the previous situation, the phases of both neutrinos from $Z^0$ decay are important, leading to a realization of the Einstein-Podolsky-Rosen paradox.

Describing neutrino oscillations in matter with Magnus expansion

We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of perturbation theory. We show that the Magnus expansion provides better convergence of series: the restoration of unitarity leads to smaller deviations from the exact results especially in the regions of large transition probabilities. Various expansions are obtained depending on a basis of neutrino states and a way one splits the Hamiltonian into the self-commuting and non-commuting parts. In particular, we develop the Magnus expansion for the adiabatic perturbation theory which gives the best approximation. We apply the formalism to the neutrino oscillations in matter of the Earth and show that for the solar oscillation parameters the second order Magnus adiabatic expansion has better than 1% accuracy for all energies and trajectories. For the atmospheric Δ m 2 and small 1–3 mixing the approximation works well (<3% accuracy for sin 2 θ 13 = 0.01 ) outside the resonance region 2.7–8 GeV.

An accurate analytic description of neutrino oscillations in matter

A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.

Perturbative exponential expansion and matter neutrino oscillations

We derive an analytical description of neutrino oscillations in matter based on the Magnus exponential representation of the time evolution operator. Our approach is valid in a wide range of the neutrino energies and properly accounts for the modifications that the respective probability transitions suffer when neutrinos originated in different sources traverse the Earth. The present approximation considerably improves over other perturbative treatments existing in the current literature. Furthermore, the analytical expressions derived inside the Magnus framework are remarkably simple, which facilitates their practical use. When applied to the calculation of the day-night asymmetry in the solar neutrino flux our result reproduces the numerical calculation with an accuracy better than 1% for the first-order approximation. When the approximation is extended to the second order, the accuracy of the method is further improved by almost 1 order of magnitude, and it is still better than 5% even for neutrino energies as large as 100 MeV. In the GeV regime characteristic of atmospheric and accelerator neutrinos this accuracy is complemented by a good reproduction of the position of the maxima in the flavor transition probabilities.

Spin-flavor oscillations of neutrinos in rapidly varying external fields

Spin-flavor oscillations of neutrinos in rapidly varying external fields are studied. A method for describing neutrino oscillations in arbitrary rapidly varying external fields is developed. An effective Hamiltonian that describes the evolution of the averaged neutrino wave function is obtained. Neutrino oscillations in rapidly varying magnetic fields are considered on the basis of the general formalism developed in this study. Neutrino transitions in a superposition of a constant and a rotating (in space) magnetic field that are transverse with respect to the neutrino velocity are studied. The probabilities of transitions in spin-flavor oscillations of neutrinos in the magnetic fields of the Sun are estimated. Numerical solutions to the Schrodinger equation for the Hamiltonian that describes neutrino interaction with a constant and a rotating (in space) magnetic field are given. It is shown that the approximate analytic formula obtained in the present study for the probability of neutrino transitions is consistent with the respective numerical solution to the evolution equation at high frequencies of the rotating magnetic fields.

Quantum theory of neutrino oscillations for pedestrians: simple answers to confusing questions

Why are different mass states coherent? What is the correct formula for the oscillation phase? How can textbook formulas for oscillations in time describe experiments which never measure time? How can we treat the different velocities and different transit times of different mass eigenstates and avoid incorrect factors of two? How can textbook forumulas which describe coherence between energy states be justified when Stodolsky's theorem states there is no coherence between different energies? Is covariant relativistic quantum field theory necessary to describe neutrino oscillations? How important is the detector, which is at rest in the laboratory and cannot be Lorentz tranformed to other frames? These questions are answered by a simple rigorous calculation which includes the quantum fluctuations in the position of the detector and in the transit time between source and detector. The commonly used standard formula for neutrino oscillation phases is confirmed. An "ideal" detector which measures precisely the energy and momentum of the neutrino destroys all phases in the initial wave packet and cannot observe oscillations. A realistic detector preserves the phase differences between neutrinos having the same energy and different momenta and confirms the standard formula. Whether phase differences between neutrinos with different energies are observable or destroyed by the detector is irrelevant.

Mass neutrino oscillations in Robertson–Walker space–time

We try to understand flavor oscillations and to develop the formulae for describing neutrino oscillations in de Sitter space-time. First, the covariant Dirac equation is investigated under the conformally flat coordinates of de Sitter geometry. Then, we obtain the exact solutions of the Dirac equation and indicate the explicit form of the phase of wave function. Next, the concise formulae for calculating the neutrino oscillation probabilities in de Sitter space-time are given. Finally, The difference between our formulae and the standard result in Minkowski space-time is pointed out.

Active-sterile neutrino oscillations and pulsar kicks

We develop a thorough description of neutrino oscillations in a magnetized protoneutron star, based on a resonance layer for neutrinos with different momentum directions. We apply our approach to the calculation of the asymmetry in the neutrino emission during the birth of a neutron star and the pulsar acceleration in the case of an active-sterile neutrino resonant conversion. The observed velocities can be obtained with the magnetic fields expected in the interior of a protoneutron star, for sterile neutrino masses of the order of KeV and small mixing angles.

Neutrinos in electromagnetic fields and moving media

The history of the development of the theory of neutrino-flavor and neutrino-spin oscillations in electromagnetic fields and in a medium is briefly surveyed. A new Lorentz-invariant approach to describing neutrino oscillations in a medium is formulated in such a way that it makes it possible to consider the motion of a medium at an arbitrary velocity, including relativistic ones. This approach permits studying neutrinospin oscillations under the effect of an arbitrary external electromagnetic field. In particular, it is predicted that, in the field of an electromagnetic wave, new resonances may exist in neutrino oscillations. In the case of spin oscillations in various electromagnetic fields, the concept of a critical magnetic-field-component strength is introduced above which the oscillations become sizable. In considering neutrino oscillations in moving matter, it is shown within the Lorentz-invariant formalism that the relativistic motion of matter significantly affects the character of neutrino oscillations and can radically change the conditions under which the oscillations are resonantly enhanced. Possible new effects in neutrino oscillations are discussed for the case of neutrino propagation in relativistic fluxes of matter.

RareKdecays in a model of quark and lepton masses

An extension of a model of neutrino masses to the quark sector provides an interesting link between these two sectors. A parameter which is important to describe neutrino oscillations and masses is found to be a crucial one appearing in various ``penguin'' operators, in particular the so-called Z penguin. This parameter is severely constrained by the rare decay process $K_{L} \to \mu^{+} \mu^{-}$. This in turn has interesting implications on the decay rates of other rare processes such as $K_{L} \to \mu e$, etc..., as well as on the masses of the neutrinos and the masses of the vector-like quarks and leptons which appear in our model.

Neutrino propagation in matter

The enhancement of neutrino oscillations in matter is briefly reviewed. Exact and approximate solutions of the equations describing neutrino oscillations in matter are discussed. The role of stochasticity of the media that the neutrinos propagate through is elucidated.

Do muons oscillate?

We develop a theory of the EPR-like effects due to neutrino oscillations in the φ → μν decays. Its experimental implications are space-time correlations of the neutrino and muon when they are both detected, while the pion decay point is not fixed. However, the more radical possibility of μ-coscillations in experiments where only muons are detected (as suggested in hep-ph/9509261), is ruled out. We start by discussing decays of monochromatic pions, and point out a few “paradoxes”. Then we consider pion wave packets, solve the “paradoxes”, and show that the formulas for μv correlations can be transformed into the usual expressions, describing neutrino oscillations, as soon as the pion decay point is fixed.