For cosmic neutrinos we study the conditions and the effects of the coherence loss as well as coherent broadening of the spectrum. We evaluate the width of the neutrino wavepacket produced by charged particles under various circumstances: in an interaction-free environment, in a radiation-dominated medium (typical of the sources of the gamma ray bursts) and in the presence of a magnetic field. The effect of the magnetic field on the wavepacket size appears to be more important than the scattering. If the magnetic field at the source is larger than $\sim$10 Gauss, the coherence of neutrinos will be lost while traveling over cosmological distances. Various applications of these results have been considered. We find that for large magnetic fields ($B> 10^9$ Gauss) and high energies ($E_ν>{\rm PeV}$), "coherent broadening" can modify the energy spectrum of neutrinos. In the coherent case, averaging out the oscillatory terms of the probabilities does not induce any statistical uncertainty beyond what expected in the absence of these terms. A deviation from the standard quantum mechanics that preserves average energy and unitarity cannot alter the picture.
The apparent symmetry between energy and momentum found in all covariant descriptions of neutrino oscillations is destroyed in the neutrino detector, a quantum mechanical system described by a density matrix diagonal in energy but not in momentum. The off diagonal matrix elements between states of different momenta and the same energy produce the coherence and interference between mass eigenstates having the same energy and different momenta that produce oscillations.
The definition of `lepton flavour eigenstates' introduced in a recent paper hep-ph/0302045 is in disagreement with the Standard Model prediction for the structure of the leptonic charged current and implies the absence of neutrino oscillations following pion decay, in contradiction to experimental data
The temporal and spatial coherence widths of the microscopic process by which a neutrino is detected are incorporated in the quantum mechanical wave packet treatment of neutrino oscillations, confirming the observation of Kiers, Nussinov and Weiss that an accurate measurement of the energies of the particles participating in the detection process can increase the coherence length. However, the wave packet treatment presented here shows that the coherence length has an upper bound, determined by the neutrino energy and the mass-squared difference, beyond which the coherence of the oscillation p…
General arguments in favor of the necessity of a wave packet description of neutrino oscillations are presented, drawing from analogies with other wave phenomena. We present a wave packet description of neutrino oscillations in stationary beams using the density matrix formalism. Recent claims of the necessity of an equal energy of different massive neutrinos are refuted.
It is pointed out that an agreement of the one particle energy spectrum of the cosmic background radiation (CMBR) with Plank distribution of 2.725 [K] does not give a strong constraint on the coherence length of CMBR if the mean free path of CMBR is very long. The coherence length in this situation is estimated as a few times of $k_BT$. Due to this finite coherence length, the attenuation length of ultra-high energy cosmic rays (UHECR) is reduced in the $Δ$ resonance region,i.e., around $10^{20}$ [eV]. The small attenuation length makes the suppression of the flux of cosmic rays in this energy…
The radical departure from classical physics implies quantum coherence, i.e., coherent superposition of eigenstates of Hermitian operators with a discrete spectrum. In resource theory, quantum coherence is a resource for quantum operations. Typically the stochastic phenomenon induces decoherence effects. However, in the present work, we prove that nonunitary evolution leads to the generation of quantum coherence in some cases. Specifically, we consider the neutrino propagation in the dissipative environment, namely in a magnetic field with a stochastic component, and focus on neutrino flavor, …
In charged current weak interaction processes, neutrinos are produced in an entangled state with the charged lepton. This correlated state is disentangled by the measurement of the charged lepton in a detector at the production site. We study the dynamical aspects of disentanglement, propagation and detection, in particular the conditions under which the disentangled state is a coherent superposition of mass eigenstates. The appearance and disappearance far-detection processes are described from the time evolution of this disentangled "collapsed" state. The familiar quantum mechanical interpre…
The experimental observation of neutron - antineutron oscillations is one of the oldest problems of elementary-particle physics. However, the search for these processes in the laboratories on the Earth have thus far yielded no results. In this paper, we consider the possibility of finding $n - \tilde n$ oscillations in the solar cosmic rays at flare increases. There are two arguments in favour of such an approach to this problem: a long distance for a neutron run and a weak magnetic field in the solar cosmic-ray environment. Therefore, the presence of antinucleons in solar cosmic rays may be a…
I discuss the effects of neutrino oscillations on high energy cosmic neutrinos which come from cosmologically distant astrophysical sources. I incorporate all the up-to-date constraints from the solar, atmospheric, reactor, accelerator data and give the possible pattern for the ratio of the high energy cosmic neutrinos in the cases of three and four neutrino schemes.
In this paper, we consider the quantum correlations, coherence and entanglement, in neutrino oscillation. We find that the $l_{1}$-norm as a coherence measure is equal to sum of the three possible concurrences for measuring the entanglement among different flavor modes which were calculated in the paper by (M. Blasone et al., Europhys. Lett., {\bf 112}, 20007). Our result shows that the origin of the flavor entanglement in neutrino oscillation is the same as that of quantum coherence. Furthermore, in the wave packet framework, the variation of $l_{1}$-norm is investigated by varying the wave p…
We present a prescription for consistently constructing non-Fock coherent flavour neutrino states within the framework of the seesaw mechanism, and establish that the physical vacuum of massive neutrinos is a condensate of Standard Model massless neutrino states. The coherent states, involving a finite number of massive states, are derived by constructing their creation operator. Such a construction is the key requirement so that the oscillations of particles indeed occur. We comment on the inherent non-unitarity of the oscillation probability induced by the requirement of coherence.
We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They can be classified by a number N of linearly independent functions that describe all neutrino modes as linear superpositions. What is more, the dynamics is equivalent to another ensemble with the same effective density, consisting of N modes with discrete energies E_i with i=1, ..., N. We use this equivalence to derive the analytic solution for two-mode (bimo…
A Feynman path integral analysis of a two-neutrino-flavour electron appearence experiment following pion decay at rest recovers the standard oscillation phase, revealing an important contribution from the decay amplitude of the pion as well as an error in previous similar calculations by the present author. In the calculation, path amplitudes for different neutrino mass eigenstates add coherently, but no putative `neutrino flavour eigenstates' are invoked. It is shown that the coherent production of the latter states is incompatible with the measured values of $Γ(π\rightarrow {\rm e}ν)/Γ(π\rig…
We study the conditions for the existence of neutrino oscillations in the field-theoretical approach which combines neutrino production and detection processes in a single Feynman graph. The ``oscillating neutrino'' is represented by an inner line of this graph where, due to the macroscopic distance L between source and detector, the neutrino propagators for neutrinos with definite mass are replaced by the projection operators unto the neutrino states on mass shell. We use as a concrete model reaction the neutrino source and detector as given in the LSND experiment and we carefully take into a…
The natural parameterization of vacuum oscillations in three neutrino flavors is studied. Compact and exact relations of its three parameters with the ordinary three mixing angles and CP violating phase are obtained. Its usefulness is illustrated by considering various applications: the study of the flavor ratio and of its uncertainties, the comparison of expectations and observations in the flavor triangle, the intensity of the signal due to Glashow resonance. The results in the literature are easily reproduced and in particular the recently obtained agreement of the observations of IceCube w…
We study the effect of coherent and incoherent broadening on neutrino oscillations both in vacuum and in the presence of matter (the MSW effect). We show under very general assumptions that it is not possible to distinguish experimentally neutrinos produced in some region of space as wave packets from those produced in the same region of space as plane waves with the same energy distribution.
Simple rigorous quantum mechanics with no hand waving nor loopholes clarifies the confusion between three contradictory descriptions of neutrino oscillations: (1)The time oscillations shown in standard textbooks produced by neutrino eigenstates with different masses and different energies. (2) That time oscillations and interference between states having different energies cannot be observed in realistic experiments. (3) That interference between different neutrino mass eigenstates is not observable in "missing mass" experiments where information determining the neutrino mass is available from…
Leggett-Garg Inequality~(LGI) is a time analogue of Bell's inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett-Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of …
Several measures of quantum correlations such as Leggett-Garg and Bell-type inequalities have been extensively studied in the context of neutrino oscillations. However these analyses are performed under the assumption of standard model (SM) interactions of neutrinos. In this work we study new physics effects on $l_1$-norm based measure of quantum coherence which quantifies the quantumness embedded in the system and is also intrinsically related to various measures of quantum correlations. Moreover, it is considered to be a resource theoretical tool which can be utilized in quantum algorithms a…
Cosmic strings provide a radically different paradigm for the formation of structure to the prevailing inflationary one. They afford some extra technical complications: for example, the calculation of the power spectrum of matter and radiation perturbations requires the knowledge of the history of the evolution of the defects in the form of two-time correlation functions. We describe some numerical simulations of string networks, designed to measure the two-time correlations during their evolution.
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 wi…
The dynamics of neutrino mixing and oscillations are studied directly in finite real time in a model that effectively describes charged current weak interactions. Finite time corrections to the S-matrix result for the appearance and disappearance probabilities are obtained. It is observed that these effects may be of the same order of the S-matrix result in long-baseline appearance experiments. We argue that fundamentally, the S-matrix is ill-suited to describe long-baseline events due to the fact that the neutrino is produced in an entangled state with the charged lepton, which can be disenta…
We study the propagation coherence for neutrino oscillations in media with different density profiles. For each profile, we find the dependence of the coherence length, $L_{coh}$, on neutrino energy and address the issue of correspondence of results in the distance and energy-momentum representations. The key new feature in matter is existence of energy ranges with enhanced coherence around the energies $E_0$ of "infinite coherence" at which $L_{coh} \rightarrow \infty$. In the configuration space, the infinite coherence corresponds to equality of the (effective) group velocities of the eigens…
The quantum field theoretical description of coherence in the oscillations of particles, especially neutrinos, is a standing problem in particle physics. In this talk, several inconsistencies of the standard approach to particle oscillations will be explained, and how they are resolved in a process-independent manner, by a novel approach inspired by the Bardeen--Cooper--Schrieffer theory of superconductivity and the Nambu--Jona-Lasinio model. The formalism leads to corrections to the neutrino oscillation probability originally written by Pontecorvo and Gribov, however the standard probability …
In this paper, we investigate the quantum coherence for two flavor neutrinos propagating in a Schwarzschild metric. In fact, this issue is explored both qualitatively via calculating the parameter $K_{3}$ in Leggett-Garg inequality (LGI) and also quantitatively by evaluating the $l_{1}$-norm, ${\cal C}(ρ)$. Using the weak field approximations, we show that the gravitational effects decrease the maximum value of $K_{3}$ for some intervals of energy such a way that there is no violation, while it leaves the maximum amount of the quantum coherence, ${\cal C}(ρ)$ unchanged.
We study the $ν_μ- ν_s$ oscillation effects in the near detector of the MINOS experiment. Conceptually, the MINOS search for sterile neutrinos with mass $\sim 1$ eV realizes an interesting situation of partial decoherence of the neutrino state at the production. This corresponds to a difference of energies of the two mass eigenstates that is comparable with or bigger than the width of the initial state (pion). We show that these effects modify the MINOS bound on mixing of sterile neutrino for $Δm^2_{41} \aprge 0.5$ eV$^2$ and make the experiment insensitive to oscillations with $Δm^2_{41} \gtr…
We consider a novel quantum field-theoretical approach to the description of processes passing at finite space-time intervals based on the Feynman diagram technique in the coordinate representation. The most known processes of this type are neutrino and neutral kaon oscillations. The experimental setting of these processes requires one to adjust the rules of passing to the momentum representation in the Feynman diagram technique in accordance with it, which leads to a modification of the Feynman propagator in the momentum representation. The approach does not make use of wave packets, both ini…
Neutrino oscillation represents an intriguing physical phenomenon where the quantumness can be maintained and detected over a long distance. Previously, the non-classical character of neutrino oscillation was tested with the Leggett-Garg inequality, where a clear violation of the classical bound was observed [J. A. Formaggio et al., Phys. Rev. Lett. 117, 050402 (2016)]. However, there are several limitations in testing neutrino oscillations with the Leggett-Garg inequality. In particular, the degree of violation of the Leggett-Garg inequality cannot be taken as a "measure of quantumness". Here…
If there exists the mirror world, a parallel hidden sector of particles with exactly the same microphysics as that of the observable particles, then the primordial nucleosynthesis constraints require that the temperature of the cosmic background of mirror relic photons should be smaller than that of the ordinary relic photons, T'/T < 0.5 or so. On the other hand, the present experimental and astrophysical limits allow a rather fast neutron - mirror neutron oscillation in vacuum, with an oscillation time $τ\sim 1$ s, much smaller than the neutron lifetime. We show that this could provide a very…
Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking π\to μν\ decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different …
The unimpeded relativistic propagation of cosmological neutrinos prior to recombination of the baryon-photon plasma alters gravitational potentials and therefore the details of the time-dependent gravitational driving of acoustic oscillations. We report here a first detection of the resulting shifts in the temporal phase of the oscillations, which we infer from their signature in the Cosmic Microwave Background (CMB) temperature power spectrum.
It is shown that F(R)-modified gravitational theories lead to curvature oscillations in astrophysical systems with rising energy density. The frequency and the amplitude of such oscillations could be very high and would lead to noticeable production of energetic cosmic ray particles.
The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and non-adiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g. matter) potentials. Neglecting effects of ensemble decoherence for now we study the evolution of a neutrino ensemble governed by the associated Quantum Kinetic Equations, which …
We analyze quantum correlations and quantum coherence in neutrino oscillations. To this end, we exploit complete complementarity relations (CCR) that fully characterize the interplay between different correlations encoded in a quantum system both for pure and mixed states. We consider the CCR for neutrino oscillations both in the case of plane-waves (pure state) and of wave packets (mixed state). In this last case we find a complex structure of correlations depending on the mixing angle, and we show the connection with the non local advantage of quantum coherence, a relevant quantifier of cohe…
In this talk, we will demonstrate some concepts of a simultaneous treatment of neutrino decays and neutrino oscillations in an illustrative manner. This includes topics such as phase coherence discussions and time delay effects of massive supernova neutrinos.
In this essay we extend the standard discussion of neutrino oscillations to astrophysical neutrinos propagating through expanding space. This extension introduces a new cosmological parameter $I$ into the oscillation phase. The new parameter records cosmic history in much the same manner as the redshift z or the apparent luminosity D_L. Measuring $I$ through neutrino oscillations could help determine cosmological parameters and discriminate among different cosmologies.
For neutrino oscillations to take place the entangled quantum state of a neutrino and a charged lepton produced via charged current interactions must be disentangled. Implementing a non-perturbative Wigner-Weisskopf method we obtain the correct \emph{entangled} quantum state of neutrinos and charged leptons from the (two-body) decay of a parent particle. The source lifetime and disentanglement length scale lead to a suppression of the oscillation probabilities in short-baseline experiments. The suppression is determined by $π\, L_s/L_{osc}$ where $L_s$ is the \emph{smallest} of the decay lengt…
Present experimental data do not exclude fast oscillation of the neutron $n$ to its degenerate twin from a hypothetical parallel sector, the so called mirror neutron $n'$. We show that this effect brings to a remarkable modifications of the ultrahigh-energy cosmic ray spectrum testable by the present Pierre Auger Observatory (PAO) and Telescope Array (TA) detector, and the future JEM-EUSO experiment. In particular, the baryon non-conservation during UHECR propagation at large cosmological distances shifts the beginning of the GZK cutoff to lower energies, while in presence of mirror sources it…
Response of Hellinger-distance based coherence to weak decoherence in two-flavor neutrino oscillations
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）；LPC Caen, Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3（卡昂粒子与核物理实验室，诺曼底大学，ENSICAEN，UNICAEN，CNRS/IN2P3）
The ultra high energy (UHE) cosmic neutrinos are expected to play a pivotal role in the disquisition of physics beyond the standard model of particle physics as well as serve as an ideal cosmic messengers. This epitomizes the selling point of several currently running or planned neutrino telescopes. The UHE cosmic neutrinos usually perambulate gargantuan scales in the extragalactic universe having a magnetic field. If neutrinos have a finite magnetic moment ($μ_ν$) owing to quantum loop corrections, this may result in spin-flavor oscillations, which can affect the cosmic neutrino flux. Using t…
Supernova neutrinos have several exceptional features which can lead to interesting physical consequences. At the production point their wave packets have an extremely small size $σ_x \sim 10^{-11}$ cm; hence the energy uncertainty can be as large as the energy itself, $σ_E \sim E$, and the coherence length is short. On the way to the Earth the wave packets of mass eigenstates spread to macroscopic sizes and separate. Inside the Earth the mass eigenstates split into eigenstates in matter and oscillate again. The coherence length in the Earth is comparable with the radius of the Earth. We explo…
We analyse the MOdified Gravity (MOG) theory, proposed by Moffat, in a cosmological context. We use data from Type Ia Supernovae (SNe Ia), Baryon Acoustic Oscillations (BAO) and Cosmic Chronometers (CC) to test MOG predictions. For this, we perform $χ^2$ tests considering fixed values of $H_0$ and $V_G$, the self-interaction potential of one of the scalar fields in the theory. Our results show that the MOG theory is in agreement with all data sets for some particular values of $H_0$ and $V_G$, being the BAO data set the most powerful tool to test MOG predictions, due to its constraining power.
A theoretical analysis of possible influence of neutrino magnetic moments on the propagation of ultrahigh-energy cosmic neutrinos in the interstellar space is carried out under the assumption of two-neutrino mixing. The exact solution of the effective equation for neutrino evolution in the presence of a magnetic field and matter is obtained, which accounts for four neutrino species corresponding to two different flavor states with positive and negative helicities. Using most stringent astrophysical bounds on the putative neutrino magnetic moment, probabilities of neutrino flavor and spin oscil…
The Starobinsky model of modified gravity suggested to explain dark energy may be also considered in the astrophysical context. Recently it has been pointed out that in contracting regions curvature oscillations around the GR value may lead to the production of high energy particles which contribute to the cosmic ray flux. We revisit these calculations in the Einstein frame and show that the continuous approximation for the matter density used in the original calculations is not valid. We show that this problem is generic in $F(R)$-gravity models introduced to describe the dark energy. We go b…
In this paper we consider the coherence properties of neutrinos produced by the decays of pions in conventional neutrino beams. Using a multi-particle density matrix formalism we derive the oscillation probability for neutrinos emitted by a decaying pion in an arbitrary quantum state. Then, using methods from decoherence theory we calculate the pion state which evolves through interaction with decay-pipe gases in a typical accelerator neutrino experiment. These two ingredients are used to obtain the distance scales for neutrino beam coherence loss. We find that for the known neutrino mass spli…
We show that, under general assumptions, in six-dimensional brane-world models with compactified large extra dimensions, the energy density of brane oscillations scales as that of cold dark matter and its present value is compatible with observations. Such value is obtained from the only dimensional scale in the theory, namely, the fundamental scale of gravity in six dimensions $M_6\sim 1$ TeV, without any fine-tuning or the introduction of additional mass scales apart from the large size of the extra dimensions. It has been suggested that the same kind of models could provide also the correct…
Inflationary scenarios motivated by high-energy physics generically contain a plethora of degrees of freedom beyond the primordial curvature perturbation. The latter interacts in a simple way with what we name "inflationary flavor eigenstates", which differ, in general, from freely propagating "mass eigenstates". We show that the mixing between these misaligned states results in new striking behaviors in the squeezed limit of the curvature perturbation three-point function, depending not only on the mass spectrum but also on the "mixing angles" of the theory. These results bring about a new pe…
Based on a newly proposed mirror-matter model of neutron-mirror neutron ($n-n'$) oscillations, the puzzles related to ultrahigh-energy cosmic rays (UHECRs) are explained. In particular, the phenomena around the Greisen-Zatsepin-Kuzmin (GZK) cutoff for UHECRs can be well understood under the new mirror matter model assuming a mirror-to-ordinary temperature ratio of $T'/T \sim 0.3$. The suppression factor of the GZK effect due to the opacity of cosmic microwave background is calculated and agrees with the observations well. Most of the super-GZK events (i.e., above the GZK cutoff), as predicted …
Baryon Acoustic Oscillations (BAO) involve measuring the spatial distribution of galaxies to determine the growth rate of cosmic structure. We derive constraints on cosmological parameters from $17$ uncorrelated BAO measurements that were collected from $333$ published data points in the effective redshift range $0.106 \leq z \leq 2.36$. We test the correlation of the subset using random covariance matrix. The $Λ$CDM model fit yields the cosmological parameters: $Ω_m = 0.261 \pm 0.028$ and $Ω_Λ= 0.733 \pm 0.021$. Combining the BAO data with the Cosmic Chronometers data, the Pantheon Type Ia su…
Using an analogy with the well-known double-slit experiment, we show that the standard phase of neutrino oscillations is correct, refuting recent claims of a factor of two correction. We also improve the wave packet treatment of neutrino oscillations taking into account explicitly the finite coherence time of the detection process.
IceCube has observed a flux of cosmic neutrinos, with a "bump" in the energy range $10 \lesssim E/{\rm TeV} \lesssim 100$ that creates a $3σ$ tension with gamma-ray data from the Fermi satellite. This has been interpreted as evidence for a population of hidden cosmic-ray accelerators. We propose an alternative explanation of this conundrum on the basis of cold dark matter which decays into sterile neutrinos that after oscillations produce the bump in the cosmic neutrino spectrum.
Analytical solutions are obtained to the nonlinear equations describing neutrino oscillations when explicit neutrino-antineutrino asymmetries are present. Such a system occurs in the early Universe if neutrinos have a non-zero chemical potential. Solutions to the equations lead to a new type of coherent behavior governed by two modes. These bimodal solutions provide new insights into dense neutrino gases and into neutrino oscillations in the early Universe, thereby allowing one to surmise the flavor behavior of neutrinos with a non-zero chemical potential.
