Neutrino Oscillations In Matter Research Articles

Understanding gravitationally induced decoherence parameters in neutrino oscillations using a microscopic quantum mechanical model

In this work, a microscopic quantum mechanical model for gravitationally induced decoherence introduced by Blencowe and Xu is investigated in the context of neutrino oscillations. The focus is on the comparison with existing phenomenological models and the physical interpretation of the decoherence parameters in such models. The results show that for neutrino oscillations in vacuum gravitationally induced decoherence can be matched with phenomenological models with decoherence parameters of the form Γ ij ∼ Δ m 4 ij E -2. When matter effects are included, the decoherence parameters exhibit a dependence on the varying matter density across the Earth layers. This behavior can be explained by the nature of the coupling between neutrinos and the gravitational wave environment, as suggested by linearised gravity. On a theoretical level, these different models can be characterised by a different choice of Lindblad operators, with the model with decoherence parameters that do not include matter effects being less suitable from the point of view of linearised gravity. Consequently, in the case of neutrino oscillations in matter, the microscopic model does not agree with many existing phenomenological models that assume constant decoherence parameters in matter. Nonetheless, we identify the KamLAND experimental setup as particularly well-suited to establish the first experimental constraints on the model parameters, namely the neutrino coupling to the gravitational wave environment and its temperature, based on a prior analysis using the phenomenological model.

Neutrino oscillations in matter using the adjugate of the Hamiltonian

We revisit neutrino oscillations in constant matter density for a number of different scenarios: three flavors with the standard Wolfenstein matter potential, four flavors with standard matter potential and three flavors with non-standard matter potentials. To calculate the oscillation probabilities for these scenarios one must determine the eigenvalues and eigenvectors of the Hamiltonians. We use a method for calculating the eigenvalues that is well known, determination of the zeros of determinant of matrix (λI-H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\lambda I -H)$$\\end{document}, where H is the Hamiltonian, I the identity matrix and λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} is a scalar. To calculate the associated eigenvectors we use a method that is little known in the particle physics community, the calculation of the adjugate (transpose of the cofactor matrix) of the same matrix, (λI-H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\lambda I -H)$$\\end{document}. This method can be applied to any Hamiltonian, but provides a very simple way to determine the eigenvectors for neutrino oscillation in matter, independent of the complexity of the matter potential. This method can be trivially automated using the Faddeev–LeVerrier algorithm for numerical calculations. For the above scenarios we derive a number of quantities that are invariant of the matter potential, many are new such as the generalization of the Naumov–Harrison–Scott identity for four or more flavors of neutrinos. We also show how these matter potential independent quantities become matter potential dependent when off-diagonal non-standard matter effects are included.

Hermitian Matrix Diagonalization and Its Symmetry Properties

A Hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These equations are simple in structure and manifestly invariant in form under the symmetry operations of dilatation, translation, rephasing, and permutation. When applied to the problem of neutrino oscillation in matter, they produced two new “matter invariants” which are confirmed by available data.

Quantum coherence and entanglement in neutral-current neutrino oscillation in matter

Although neutrino–antineutrino states originating from neutral-current interactions are blind concerning the flavor state, an oscillation pattern is predicted provided that both neutrino and antineutrino are detected. This issue arises from both the coherence and entanglement of the neutrino–antineutrino states. Based on quantum resource theory, we use the l_1-norm and concurrence to quantify quantum coherence and entanglement, respectively. Considering the localization properties by the wave packet approach and a matter potential which appears when neutrino and antineutrino propagate in a material medium, we obtain the l_1-norm and concurrence. We see that the neutrino and antineutrino remain entangled for larger baseline lengths when they propagate in a material medium. In the case of the coherence property, the l_1-norm decreases in comparison to the corresponding one in vacuum. However, its damping occurs for larger distances.

Exploring non standard interactions effects in T2HK and DUNE

Neutrino oscillations in matter offer a novel path to investigate new physics. One of the main goals of neutrino experiments is to determine the CP phase, and the presence of new physics can alter the scenario. We assume that the observed difference, if any, in the CP phase is due to the possible non-standard interactions. We derive the relevant coupling strengths using the results of NOnu A and T2K and study their effects in the next generation of long-baseline experiments: T2HK and DUNE. Our analysis reveals a significant impact on the sensitivity of atmospheric mixing angle theta _{23} in the normal and inverted orderings. Furthermore, we observe discernible differences in probabilities for both experiments when non-standard interaction from e-mu and e-tau sectors are included.

Symmetry in Neutrino Oscillation in Matter: New Picture and the νSM–Non-Unitarity Interplay

We update and summarize the present status of our understanding of the reparametrization symmetry with an i↔j state exchange in neutrino oscillation in matter. We introduce a systematic method called “Symmetry Finder” (SF) to uncover such symmetries, demonstrate its efficient hunting capability, and examine their characteristic features. Apparently they have a local nature: the 1–2 and 1–3 state exchange symmetries exist at around the solar and atmospheric resonances, respectively, with the level-crossing states exchanged. However, this view is not supported, to date, in the globally valid Denton et al. (DMP) perturbation theory, which possesses the 1–2, but not the 1–3, exchange symmetry. This is probably due to our lack of understanding, and we find a clue for a larger symmetry structure than we know of. In the latter part of this article, we introduce non-unitarity, or unitarity violation (UV), into the νSM neutrino paradigm, a low-energy description of beyond νSM new physics at a high (or low) scale. Based on the analyses of UV extended versions of the atmospheric resonance and the DMP perturbation theories, we argue that the reparametrization symmetry has a diagnostic capability for the theory with the νSM and UV sectors. Speculation is given on the topological nature of the identity, which determines the transformation property of the UV α parameters.

Toward diagnosing neutrino non-unitarity through CP phase correlations

Abstract We discuss correlations between the neutrino-mass-embedded Standard Model CP phase δ and the phases that originate from new physics which cause neutrino-sector unitarity violation (UV) at low energies. This study aims to provide one of the building blocks for machinery to diagnose non-unitarity, our ultimate goal. We extend the perturbation theory of neutrino oscillation in matter proposed by Denton et al. (DMP) to include the UV effect expressed by the α parametrization. By analyzing the DMP-UV perturbation theory to first order, we are able to draw a complete picture of the δ–UV phase correlations in the whole kinematical region covered by terrestrial neutrino experiments. Two regions exist with characteristically different patterns of the correlations: (i) the chiral-type $[e^{- i \delta } \alpha _{\mu e}, \, e^{ - i \delta } \alpha _{\tau e}, \, \alpha _{\tau \mu }]$ (Particle Data Group convention) correlation in the entire high-energy region $\vert \rho E \vert \gtrsim 6 \, (\text{g/cm}^3)$ GeV, and (ii) (blobs of the α parameters)–e±iδ correlation anywhere else. Some relevant aspects for the measurement of the UV parameters, such as the necessity of determining all the αβγ elements at once, are also pointed out. Subject Index: B52, B54

T violation without complex entries in the lepton mixing matrix

We demonstrate that $T$ invariance can be violated even when the Pontecorvo-Maki-Nakagawa-Sakata lepton mixing matrix is real. We obtain a sufficient condition of $T$ violation in neutrino oscillations in matter and electromagnetic field. In the two-flavor model we derive the $T$-violating spin-flavor transition probabilities. Then we prove that the transition probabilities for neutrino in a moving medium in electromagnetic field differ from those for antineutrino in matter composed of antiparticles and electromagnetic field only in the sign of the $T$-violating term.

Quantum coherence in neutrino oscillation in matter

A closer and more detailed study of neutrino oscillation, in addition to assisting us in founding physics beyond the standard model, can potentially be used to understand the fundamental aspects of quantum mechanics. In particular, we know that the neutrino oscillation occurs because the quantum states of the produced and detected neutrinos are a coherent superposition of the mass eigenstates, and this coherency is maintained during the propagation due to the small mass difference of neutrinos. In this paper, we consider the decoherence due to the neutrino interaction in the material medium with constant density in addition to the decoherence coming from the localization properties. For this purpose, we use $l_1\text{-norm}$ in order to quantify the coherence and investigate its dependence on the matter density. According to our results, in general, the coherence in material medium is less than vacuum. However, there exist exceptions; for some matter densities, the localization coherence lengths become infinite. So, for these cases, $l_1\text{-norm}$ in matter is more than the vacuum.

Continuous and discrete symmetries of renormalization group equations for neutrino oscillations in matter

Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses (for i = 1, 2, 3) and the effective mixing matrix V αi (for α = e,μ, τ and i = 1, 2, 3). When the matter parameter is taken as an independent variable, a complete set of first-order ordinary differential equations for and |V αi |2 have been derived in the previous works. In the present paper, we point out that such a system of differential equations possesses both the continuous symmetries characterized by one-parameter Lie groups and the discrete symmetry associated with the permutations of three neutrino mass eigenstates. The implications of these symmetries for solving the differential equations and looking for differential invariants are discussed.

Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes

Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries of the oscillation parameters. We elucidate the ${2}^{7}$ parameter symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an additional set of ${2}^{7}$ parameter symmetries of the matter parameters exists. Due to the complexity of the exact expressions for neutrino oscillations in matter, numerous approximations have been developed; we show that under certain assumptions approximate expressions have at most ${2}^{6}$ additional parameter symmetries of the matter parameters. We also include one parameter symmetry related to the large mixing angle (LMA)-dark degeneracy that holds under the assumption of $CPT$ invariance; this adds one additional factor of 2 to all of the above cases. Explicit, nontrivial examples are given of how physical observables in neutrino oscillations, such as the probabilities, $CP$ violation, the position of the solar and atmospheric resonance, and the effective $\mathrm{\ensuremath{\Delta}}{m}^{2}$'s for disappearance probabilities, are invariant under all of the above symmetries. We investigate which of these parameter symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.

Symmetry Finder applied to the 1\u20133 mass eigenstate exchange symmetry

In a previous paper, Symmetry Finder (SF) method is proposed to find the reparametrization symmetry of the state-exchange type in neutrino oscillation in matter. It has been applied successfully to the 1–2 state exchange symmetry in the DMP perturbation theory, yielding the eight symmetries. In this paper, we apply the SF method to the atmospheric-resonance perturbation theory to uncover the 1–3 state relabeling symmetries. The pure 1–3 state symmetry takes the unique position that it is practically impossible to formulate in vacuum under the conventional choice of the flavor mixing matrix. In contrast, our SF method produces the sixteen 1–3 state exchange symmetries in matter. The relationship between the symmetries in the original (vacuum plus matter) Hamiltonian and the ones in the diagonalized system is discussed.

Interplay between the factorization of the Jarlskog invariant and location of the solar and atmospheric resonances for neutrino oscillations in matter

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 the 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. They are not identical but the fractional differences are both found to be less than 0.1%. In addition, we explain why symmetry polynomials of the square of the mass of the neutrino eigenvalues in matter, such as inverse of the square of the Jarlskog invariant in matter, can be given as polynomials in the matter potential.

CP-Violating Neutrino Nonstandard Interactions in Long-Baseline-Accelerator Data.

Neutrino oscillations in matter provide a unique probe of new physics. Leveraging the advent of neutrino appearance data from NOvA and T2K in recent years, we investigate the presence of CP-violating neutrino nonstandard interactions in the oscillation data. We first show how to very simply approximate the expected NSI parameters to resolve differences between two long-baseline appearance experiments analytically. Then, by combining recent NOvA and T2K data, we find a tantalizing hint of CP-violating NSI preferring a new complex phase that is close to maximal: ϕ_{eμ} or ϕ_{eτ}≈3π/2 with |ε_{eμ}| or |ε_{eτ}|∼0.2. We then compare the results from long-baseline data to constraints from IceCube and COHERENT.

Neutrino oscillations in matter: from microscopic to macroscopic description

Neutrino flavour transmutations in nonuniform matter are described by a Schrödinger-like evolution equation with coordinate-dependent potential. In all the derivations of this equation it is assumed that the potential, which is due to coherent forward scattering of neutrinos on matter constituents, is a continuous function of coordinate that changes slowly over the distances of the order of the neutrino de Broglie wavelength. This tacitly assumes that some averaging of the microscopic potential (which takes into account the discrete nature of the scatterers) has been performed. The averaging, however, must be applied to the microscopic evolution equation as a whole and not just to the potential. Such an averaging has never been explicitly carried out. We fill this gap by considering the transition from the microscopic to macroscopic neutrino evolution equation through a proper averaging procedure. We discuss some subtleties related to this procedure and establish the applicability domain of the standard macroscopic evolution equation. This, in particular, allows us to answer the question of when neutrino propagation in rarefied media (such as e.g. low-density gases or interstellar or intergalactic media) can be considered within the standard theory of neutrino flavour evolution in matter.

A compact analytical approximation for a light sterile neutrino oscillation in matter * * Jiajie Ling acknowledges the support from National Key R&D program of China (2018YFA0404103) and National Natural Science Foundation of China (11775315). F. Xu is supported partially by NSFC (11605076), as well as the FRFCU (Fundamental Research Funds for the Central Universities in China) (21616309)

The existence of light sterile neutrinos is a long-standing question in particle physics. Several experimental “anomalies” might be explained by introducing eV mass scaled light sterile neutrinos. Many experiments are actively searching for such light sterile neutrinos through neutrino oscillation. For long baseline experiments, the matter effect should be treated carefully for precise calculation of the neutrino oscillation probabilities. However, this is usually time-consuming or analytically complex. In this manuscript, we adopt a Jacobi-like method to diagonalize the Hermitian Hamiltonian matrix and derive analytically simplified neutrino oscillation probabilities for 3 (active) + 1 (sterile)-neutrino mixing for a constant matter density. These approximations can reach a considerably high numerical accuracy while retaining their analytical simplicity and fast computing speed. This would be useful for current and future long baseline neutrino oscillation experiments.

Fibonacci fast convergence for neutrino oscillations in matter

Understanding neutrino oscillations in matter requires a non-trivial diagonalization of the Hamiltonian. As the exact solution is very complicated, many approximation schemes have been pursued. Here we show that one scheme, systematically applying rotations to change to a better basis, converges exponentially fast wherein the rate of convergence follows the Fibonacci sequence. We find that the convergence rate of this procedure depends very sensitively on the initial choices of the rotations as well as the mechanism of selecting the pivots. We then apply this scheme for neutrino oscillations in matter and discover that the optimal convergence rate is found using the following simple strategy: first apply the vacuum (2-3) rotation and then use the largest off-diagonal element as the pivot for each of the following rotations. The Fibonacci convergence rate presented here may be extendable to systems beyond neutrino oscillations.

Oscillation of high-energy neutrinos from choked jets in stellar and merger ejecta

We present a comprehensive study on oscillation of high-energy neutrinos from two different environments: blue supergiant progenitors that may harbor low-power gamma-ray burst (GRB) jets and neutron star merger ejecta that would be associated with short gamma-ray bursts. We incorporate the radiation constraint that gives a necessary condition for nonthermal neutrino production, and account for the time evolution of the jet, which allows us to treat neutrino oscillation in matter more accurately. For massive star progenitors, neutrino injection inside the star can lead to nonadiabatic oscillation patterns in the 1 TeV - 10 TeV and is also visible in the flavor ratio. For neutron star merger ejecta, we find a similar behavior in the 100 GeV - 10 TeV region and the oscillation may result in a $\nu_e$ excess around 1 TeV. These features, which enable us to probe the progenitors of long and short GRBs, could be seen by future neutrino detectors with precise flavor ratio measurements. We also discuss potential contributions to the diffuse neutrino flux measured by IceCube, and find parameter sets allowing choked low-power GRB jets to account for the neutrino flux in the 10 TeV - 100 TeV range without violating the existing constraints.

Standard versus non-standard CP phases in neutrino oscillation in matter with non-unitarity

Abstract We formulate a perturbative framework for the flavor transformation of the standard active three neutrinos but with a non-unitary flavor mixing matrix, a system which may be relevant for the leptonic unitarity test. We use the $\alpha$ parametrization of the non-unitary matrix and take its elements $\alpha_{\beta \gamma}$ ($\beta,\gamma = e,\mu,\tau$) and the ratio $\epsilon \simeq \Delta m^2_{21} / \Delta m^2_{31}$ as the small expansion parameters. Two qualitatively new features that hold in all the oscillation channels are uncovered in the probability formula obtained to first order in the expansion: (1) The phases of the complex $\alpha$ elements always come into the observable in the particular combination with the $\nu$SM CP phase $\delta$ in the form $[e^{- i \delta } \bar{\alpha}_{\mu e}, ~e^{ - i \delta} \bar{\alpha}_{\tau e}, ~\bar{\alpha}_{\tau \mu}]$ under the Particle Data Group convention of a unitary $\nu$SM mixing matrix. (2) The diagonal $\alpha$ parameters appear in particular combinations $\left( a/b - 1 \right) \alpha_{ee} + \alpha_{\mu \mu}$ and $\alpha_{\mu \mu} - \alpha_{\tau \tau}$, where $a$ and $b$ denote, respectively, the matter potential due to charged current and neutral current reactions. This property holds only in the unitary evolution part of the probability, and there is no such feature in the genuine non-unitary part, while the $\delta$–$\alpha$ parameter phase correlation exists for both. The reason for such remarkable stability of the phase correlation is discussed.

Neutrino oscillation in dense matter

As the increasing of neutrino energy or matter density, the neutrino oscillation in matter may undergo ``vacuum-dominated,'' ``resonance,'' and ``matter-dominated'' three different stages successively. Neutrinos endure very different matter effects, and therefore present very different oscillation behaviors in these three different cases. In this paper, we focus on the less discussed matter-dominated case (i.e., $|{A}_{\mathrm{CC}}|\ensuremath{\gg}|\mathrm{\ensuremath{\Delta}}{m}_{31}^{2}|$), study the effective neutrino mass and mixing parameters as well as neutrino oscillation probabilities in dense matter using the perturbation theory. We find that as the matter parameter $|{A}_{\mathrm{CC}}|$ growing larger, the effective mixing matrix in matter $\stackrel{\texttildelow{}}{V}$ evolves approaching a fixed $3\ifmmode\times\else\texttimes\fi{}3$ constant real matrix which is free of $CP$ violation and can be described using only one simple mixing angle $\stackrel{\texttildelow{}}{\ensuremath{\theta}}$ which is independent of ${A}_{\mathrm{CC}}$. As for the neutrino oscillation behavior, ${\ensuremath{\nu}}_{e}$ decoupled in the matter-dominated case due to its intense charged-current interaction with electrons while a two-flavor oscillation are still presented between ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\ensuremath{\nu}}_{\ensuremath{\tau}}$. Numerical analysis are carried on to help understanding the salient features of neutrino oscillation in matter as well as testing the validity of those concise approximate formulas we obtained. At the end of this paper, we make a very bold comparison of the oscillation behaviors between neutrinos passing through the Earth and passing through a typical white dwarf to give some embryonic thoughts on under what circumstances these studies will be applied and put forward the interesting idea of possible ``neutrino lensing'' effect.