Using the Mandelstam-Tamm method we derive time-energy uncertainty relations for neutrino oscillations. We demonstrate that the small energy uncertainty of antineutrinos in a recently considered experiment with recoilless resonant (Mössbauer) production and absorption of tritium antineutrinos is in conflict with the energy uncertainty which, according to the time-energy uncertainty relation, is necessary for neutrino oscillations to happen. A Mössbauer neutrino experiment could provide a unique possibility to test the applicability of the time-energy uncertainty relation to neutrino oscillations and to reveal the true nature of neutrino oscillations.
Neutrino oscillations is a phenomenon which is characterized by a finite oscillation time (length). For such phenomena time-energy uncertainty relation is valid. This means that energy uncertainty is needed for oscillations to occur. We consider neutrino oscillations from this point of view. We demonstrate that for mixed neutrino states, which describe flavor neutrinos $ν_{e}$, $ν_μ$ and $ν_τ$, translational invariance does not take place.
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.
We consider neutrino oscillations as non stationary phenomenon based on Schrodinger evolution equation and mixed neutrino states with definite flavor. We demonstrate that for such states invariance under translations in time does not take place. We show that time-energy uncertainty relation plays a crucial role in neutrino oscillations. We compare neutrino oscillations with $K^{0}\leftrightarrows\bar K^{0}$, $B_{d}^{0}\leftrightarrows\bar B_{d}^{0}$ etc oscillations.
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 …
That muon neutrinos $ν_μ$ oscillating into the mixture of tau neutrinos $ν_τ$ and sterile neutrinos $ν_{s}$ has been studied to explain the atmospheric $ν_μ$ disappearance. In this scenario, the effect of Earth matter is a key to determine the fraction of $ν_{s}$. Considering that the Earth matter density has uncertainty and this uncertainty has significant effects in some neutrino oscillation cases, such as the CP violation in very long baseline neutrino oscillations and the day-night asymmetry for solar neutrinos, we study the effects caused by this uncertainty in the above atmospheric $ν_μ$…
We discuss the implications of the time-energy uncertainty relation to recoillessly emitted and captured neutrinos (Mossbauer neutrinos) and show that it does not preclude oscillations of these neutrinos, contrary to a recent claim (J. Phys. G35 (2008) 095003, arXiv:0803.0527).
We show that coherent flavor neutrino states are produced (and detected) due to the momentum-coordinate Heisenberg uncertainty relation. The Mandelstam-Tamm time-energy uncertainty relation requires non-stationary neutrino states for oscillations to happen and determines the time interval (propagation length) which is necessary for that. We compare different approaches to neutrino oscillations which are based on different physical assumptions but lead to the same expression for the neutrino transition probability in standard neutrino oscillation experiments. We show that a Moessbauer neutrino …
We discuss neutrino oscillations in an experiment with Mössbauer recoilless resonance absorbtion of tritium antineutrinos, proposed recently by Raghavan. We demonstrate that small energy uncertainty of antineutrinos which ensures a large resonance absorption cross section is in a conflict with the energy uncertainty which, according to the time-energy uncertainty relation, is necessary for neutrino oscillations to happen. The search for neutrino oscillations in the Mössbauer neutrino experiment would be an important test of the applicability of the time-energy uncertainty relation to a newly d…
A brief review of the status of neutrino oscillations is given. The phenomenology of neutrino mixing and the standard seesaw mechanism of neutrino mass generation is discussed. Different approaches to neutrino oscillations are considered and compared. The role of the Heisenberg space-momentum uncertainty relation and the Mandelstam-Tamm time-energy uncertainty relation in neutrino oscillations is discussed in some detail.
We investigate the effect induced by variations in the density profile of the Earth's interior using a long-baseline neutrino oscillation experiment. At first, we point out two facts. (i) The most essential part of the matter profile is the first Fourier mode of the matter profile function; and (ii) The Earth models based on the study of seismology include a large uncertainty for the first Fourier mode. Next, we show that there is a strong correlation between the average density value and the first Fourier coefficient in the analysis of oscillation probability. This means that the matter profi…
We discuss different schemes of neutrino oscillations and the time-energy uncertainty relation. From the results of the K2K and MINOS accelerator experiments follows that neutrino oscillations are a non-stationary phenomenon and that the standard time-energy uncertainty relation is satisfied. Are these properties a general feature of neutrino oscillations? In this paper we demonstrate that a recently proposed tritium/helium-3 Moessbauer neutrino-experiment could answer this question.
Neutrino scillations cannot arise from an initial isolated one particle state if four-momentum is conserved. The transition matrix element is generally squared and summed over all final states with no interference between orthogonal final states. Lorentz covariant descriptions based on relativistic quantum field theory cannot describe interference between orthogonal states with different $ν$ masses producing neutrino oscillations. Simplified model presents rigorous derivation of handwaving argument about "energy-time uncertainty". Standard time-dependent perturbation theory for decays shows ho…
We comment on the paper "On application of the time-energy uncertainty relation to Mössbauer neutrino experiments" (see arXiv: 0803.1424) in which our paper "Time-energy uncertainty relations for neutrino oscillation and Mössbauer neutrino experiment" (see arXiv: 0803.0527) has been criticized. We argue that this critique is a result of misinterpretation: The authors of (arXiv: 0803.1424) do not take into account (or do not accept) the fact that at present there exist different schemes of neutrino oscillations which can not be distinguished in usual neutrino oscillation experiments. We stress …
Basics of neutrino oscillations is discussed. Importance of time-energy uncertainty relation is stressed. Neutrino oscillations in the leading approximation and evidence for neutrino oscillations are briefly summarized.
In this work, we investigate the role of multi-nucleon (MN) effects (mainly 2p-2h and RPA) on the sensitivity measurement of various neutrino oscillation parameters, in the disappearance channel of NO$ν$A (USA) experiment. Short-range correlations and detector effects have also been included in the analysis. We use the kinematical method of reconstruction of the incoming neutrino energy, both at the near and far detectors. The extrapolation technique has been used to estimate oscillated events at the far detector. The latest global best fit values of various light neutrino oscillation paramete…
Neutrino and anti-neutrino states coming from the neutral current or $Z_0$ decay are blind with respect to the flavor. The neutrino oscillation is observed and formulated when its flavor is known. However, it has been shown that we can see neutrino oscillation pattern for $Z_0$ decay neutrinos provided that both neutrino and anti-neutrino are detected. In this paper, we restudy this oscillation via quantum field theory approach. Through this approach, we find that the oscillation pattern ceases if the distance between the detectors is larger than the coherence length, while both neutrino and a…
While oscillations of solar neutrinos are usually studied using the single-particle quantum-mechanical approach, flavor conversions of supernovae neutrinos are typically analyzed using the kinetic equation for the matrix of densities due to the necessity of including also the scattering processes. Using the Wigner formulation of quantum mechanics we show the equivalence of the quantum-mechanical and kinetic approaches in the limit of collisionless neutrino propagation (in a background medium). Based on this observation we also argue that solutions of the kinetic equation account for the Heisen…
We point out that determination of the MNS matrix element |U_{e3}| = s_{13} in long-baseline ν_μ \to ν_e neutrino oscillation experiments suffers from large intrinsic uncertainty due to the unknown CP violating phase δand sign of Δm^2_{13}. We propose a new strategy for accurate determination of $θ_{13}$; tune the beam energy at the oscillation maximum and do the measurement both in neutrino and antineutrino channels. We show that it automatically resolves the problem of parameter ambiguities which involves δ, θ_{13}, and the sign of Δm^2_{13}.
Effects of the inhomogeneous matter density on the three-generation neutrino oscillation probability are analyzed. Realistic profile of the matter density is expanded into a Fourier series. Taking in the Fourier modes one by one, we demonstrate that each mode has its corresponding target energy. The high Fourier mode selectively modifies the oscillation probability of the low-energy region. This rule is well described by the parametric resonance between the neutrino oscillation and the matter effect. The Fourier analysis gives a simple guideline to systematically control the uncertainty of the…
We derive the neutrino flavor transition probabilities with the neutrino treated as a wave packet. The decoherence and dispersion effects from the wave-packet treatment show up as damping and phase-shifting of the plane-wave neutrino oscillation patterns. If the energy uncertainty in the initial neutrino wave packet is larger than around 0.01 of the neutrino energy, the decoherence and dispersion effects would degrade the sensitivity of reactor neutrino experiments to mass hierarchy measurement to lower than 3 $σ$ confidence level.
The role of simple quantum mechanics in understanding neutrino oscillation experiments is pointed out by comparison with two-slit and Bragg scattering experiments. The importance of considering the beam and the detector as a correlated quantum system is emphasized. Quantum mechanics alone shows that the difference observed in the same neutrino detector at Super-Kamiokande between upward and downward going neutrinos requires the existence of a neutrino mass difference. The localization of the source and detector in space in the laboratory system for long times leads to an uncertainty in the mom…
We study the effects of neutrino oscillation on supernova neutrino in the case of the inverted mass hierarchy ($m_{3} \ll m_{1} < m_{2}$) as well as the normal mass hierarchy ($m_{1} < m_{2} \ll m_{3}$). Numerical analysis using a realistic supernova and presupernova model allows us to discuss quantitatively a possibility to probe neutrino oscillation parameters. We show that information about the mass hierarchy can be obtained if $θ_{13}$ is rather large ($\sin^{2}{2 θ_{13}} > 10^{-3}$) and that $θ_{13}$ can be well probed by SuperKamiokande if the neutrino mass hierarchy is the inverted case…
As a result of a non-trivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton …
We study the impact of the dynamical Lorentz symmetry breaking induced by the auxiliary gauge fields of neutrino on the oscillations probability at DUNE. The DLSB introduces an alternative energy-momentum relation of the neutrinos and thus results in a new oscillation probability. We extend the previously proposed four-Majorana fermion model that gives rise to DLSB after the type II seesaw mechanism by considering the electron neutrino forward scattering when passing through a medium. Moreover, we incorporate the three-flavor neutrino states, which introduce the CP-violation term inside the os…
Long baseline (LBL) neutrino experiments aim to measure the neutrino oscillation parameters to high precision. These experiments use nuclear targets for neutrino scattering and hence are inflicted with complexities of nuclear effects. Nuclear effects and their percolation into sensitivity measurement of neutrino oscillations parameters are not yet fully understood and therefore need to be dealt with carefully. In a recent work [1], we reported some results on this for NO$ν$A experiment using the kinematic method of neutrino energy reconstruction, where it was observed that the nuclear effects …
We study the feasibility of using neutrino-electron elastic scattering to measure the neutrino flux in the DUNE neutrino oscillation experiment. The neutrino-electron scattering cross section is precisely known, and the kinematics of the reaction allow determination of the incoming neutrino energy by precise measurement of the energy and angle of the recoiling electron. For several possible near detectors, we perform an analysis of their ability to measure neutrino flux in the presence of backgrounds and uncertainties. With realistic assumptions about detector masses, we find that a liquid arg…
CP phase determination for the near future long baseline experiments, T2HK and DUNE, will require precise measurements of the oscillation probabilities. However, the uncertainty in the Earth's density must be considered in determining these oscillation probabilities. Therefore, in this study, we update the individual sensitivities of these experiments for determining the current unknowns in the standard three flavor scenario considering the latest configuration and also the complementarity between them while considering the uncertainty in the density. Our study showed that this uncertainty has…
The quantitative description of the effects of nuclear dynamics on the measured neutrino-nucleus cross sections -- needed to reduce the systematic uncertainty of long baseline neutrino oscillation experiments -- involves severe difficulties. Owing to the uncertainty on the incoming neutrino energy, different reaction mechanisms contribute to the cross section measured at fixed energy and scattering angle of the outgoing lepton, and must therefore be consistently taken into account within a unified model. We review the theoretical approach based on the impulse approximation and the use of reali…
It is well known that neutrino oscillations may damp due to decoherence caused by the separation of mass eigenstate wave packets or by a baseline uncertainty of order the oscillation wave length. In this note we show that if the particles created together with the neutrino are not measured and do not interact with the environment, then the first source of decoherence is not present. This demonstration uses the saddle point approximation and also assumes that the experiment lasts longer than a certain threshold. We independently derive this result using the external wave packet model and also u…
We present results of a combined analysis in neutrino oscillations without unitarity assumption in the $3ν$ mixing picture. Constraints on neutrino mixing matrix elements are based on recent data from the reactor, solar and long-baseline accelerator neutrino oscillation experiments. The current data are consistent with the standard $3ν$ scheme. The precision on different matrix elements can be as good as a few percent at $3σ$ CL, and is mainly limited by the experimental statistical uncertainty. The $ν_e$ related elements are the most precisely measured among all sectors with the uncertainties…
It is shown that several ratios of neutral to charged current cross sections are determined accurately, because the largest contribution is determined by isospin symmetry and the smaller terms are estimated from data or theoretical calculations. This way the theoretical uncertainty is very small. It is further discussed that the ratios can be measured at various distances from the origin of the neutrino beams, because an increase with distance will be indication for neutrino oscillations and will allow a precise determination of the oscillation parameters. Finally, coherent scattering is discu…
Sensitivities to sin^2{2theta_{13}} without statistical errors (``systematic limit'') are investigated in neutrino oscillation experiments with multiple reactors. Using an analytical approach, we show that the systematic limit on sin^2{2theta_{13}} is dominated by the uncorrelated systematic error sigma_u of the detector. Even in an experiment with multi-detectors and multi-reactors, it turns out that most of the systematic errors including the one due to the nature of multiple sources is canceled as in the case with a single reactor plus two detectors, if the near detectors are placed suitabl…
Terrestrial Matter Effects on Reactor Antineutrino Oscillations: Constant vs. Fluctuated Density Profiles
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；East China University of Technology（华东理工大学）；Institute of Geology and Geophysics, Chinese academy of sciences（中国科学院地质与地球物理研究所）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Simultaneous treatment of neutrino oscillations and collisions in astrophysical environments requires the use of (quantum) kinetic equations. Despite major advances in the field of quantum kinetics, the structure of the kinetic equations and their consistency with the uncertainty principle are still debated. The goals of the present work are threefold. First, it clarifies the structure of the Liouville term in the presence of mixing. Second, we derive evolution equation for neutrinos propagating in vacuum or matter from the Schrodinger equation and show that in the relativistic limit its form …
In the case of large 1-3 mixing angle as sin^2(2theta13 > 0.03, we investigate the possibility for measuring the leptonic CP phase by using only nu_mu --> nu_mu oscillations independently of nu_mu --> nu_e oscillations. As the result, we find that the CP phase can be measured best around the energy E=0.43 GeV and the baseline length L=5000km without strongly depending on the uncertainties of other parameters. In this region, the CP phase effect remains even after averaging over neutrino energy. We also find that there is the CP sensitivity even in the short baseline length L < 1000 km if Delta…
We investigate the effects of a nonzero leptonic mixing angle $θ_{13}$ on the solar neutrino day-night asymmetry. Using a constant matter density profile for the Earth and well-motivated approximations, we derive analytical expressions for the $ν_e$ survival probabilities for solar neutrinos arriving directly at the detector and for solar neutrinos which have passed through the Earth. Furthermore, we numerically study the effects of a non-zero $θ_{13}$ on the day-night asymmetry at detectors and find that they are small. Finally, we show that if the uncertainties in the parameters $θ_{12}$ and…
We consider neutrino oscillations in vacuum in the framework of quantum field theory in which neutrino production and detection processes are part of a single Feynman diagram and the corresponding cross section is computed in the standard way, i.e. with final states represented by plane waves. We use assumptions which are realized in actual experiments and concentrate on the detection process. Moreover, we also allow for a finite time interval of length $τ$ during which the detector records neutrino events. In this context we are motivated by accelerator-neutrino oscillation experiments where …
Darmstadt $ν$ oscillations in decay of radioactive ion can only come from initial state wave function. Causality forbids any influence on transition probability by detection of $ν$ or final state interference after decay. Energy-time uncertainty allows two initial state components with different energies to decay into combination of two orthogonal states with same energy, different momenta and different $ν$ masses. Final amplitudes completely separated at long times have broadened energy spectra overlapping at short times. Their interference produces oscillations between Dicke superradiant and…
We investigate the initial progenitor mass dependence of the early-phase neutrino signal from supernovae taking neutrino oscillations into account. The early-phase analysis has advantages in that it is not affected by the time evolution of the density structure of the star due to shock propagation or whether the remnant is a neutron star or a black hole. The initial mass affects the evolution of the massive star and its presupernova structure, which is important for two reasons when considering the neutrino signal. First, the density profile of the mantle affects the dynamics of neutrino oscil…
We discuss the status of the solutions of the solar neutrino problem in terms of oscillations of $ν_e$ into active or sterile neutrinos. We present the results of a global fit to the full data set corresponding to the latest data presented at the $ν$-2000 conference. We show the possible solutions in the full parameter space including both MSW and vacuum, as well as quasi-vacuum oscillations (QVO) and matter effects for mixing angles in the second octant (the so called dark side). Our conclusion is that from the statistical point of view, all solutions for oscillations into active neutrinos: L…
We have recently proposed an explanation for the birth velocities of pulsars based on neutrino oscillations (hep-ph/9606428). One of the quantities, dN/dT, was evaluated in the approximation of constant chemical potential for the electrons. An alternative approximation based on the assumption Ye=const, used by Qian (astro-ph/9705055), yields a somewhat higher prediction for the magnetic field inside a neutron star. If the same input parameters are used, the two approximations are in reasonable agreement, given the uncertainty in the geometry of the magnetic field and the simplified picture of …
In neutrino oscillation experiments precise measurement of neutrino oscillation parameters is of prime importance as well as a challenge. To improve the statistics, presently running and proposed experiments are using heavy nuclear targets. These targets introduce nuclear effects and the quantification of these effects on neutrino oscillation parameters will be decisive in the prediction of neutrino oscillation physics. Limited understanding of neutrino nucleus interactions and inaccurate reconstruction of neutrino energy causes uncertainty in the cross section. The error in the determination …
We discuss about effects of the non-standard interaction of neutrinos with matter on the nu_e appearance search in the MINOS experiment. We consider the effects of the complex phase of the interaction and of the uncertainty on theta_23 also. We show that the oscillation probability can be so large that can not be explained by the ordinary oscillation. We show also how much constraints on the non-standard effects can be improved if the experiment does not observe nu_e appearance signal.
We discuss to what extent future precision measurements of neutrino mixing observables will influence the information we can draw from a measurement of (or an improved limit on) neutrinoless double beta decay. Whereas the Delta m^2 corresponding to solar and atmospheric neutrino oscillations are expected to be known with good precision, the parameter theta_{12} will govern large part of the uncertainty. We focus in particular on the possibility of distinguishing the neutrino mass hierarchies and on setting a limit on the neutrino mass. We give the largest allowed values of the neutrino masses …
We study the earth matter effects in the Tokai-to-Kamioka-and-Korea experiment (T2KK), which is a proposed extension of the T2K (Tokai-to-Kamioka) neutrino oscillation experiment between J-PARC at Tokai and Super-Kamiokande (SK) in Kamioka, where an additional detector is placed in Korea along the same neutrino beam line.By using recent geophysical measurements, we examine the earth matter effects on the oscillation probabilities at Kamioka and Korea. The average matter density along the Tokai-to-Kamioka baseline is found to be 2.6 g/cm^3, and that for the Tokai-to-Korea baseline is 2.85, 2.98…
(Abridged.) We present a thorough analysis of the current solar neutrino data, in the context of two-flavor active neutrino oscillations. We aim at performing an accurate and exhaustive statistical treatment of both the input and the output information. Concerning the input, we analyze 81 observables, including the Cl rate, the total Ga rate and its winter-summer difference, the 44 spectrum bins from SK and the 34 spectrum bins from SNO. We carefully evaluate and propagate the effects of 31 correlated systematic uncertainties, including 12 SSM input errors, the 8B neutrino energy spectrum unce…
The first phase of the long-baseline neutrino experiment, LBNE10, will use a broadband, high-energy neutrino beam with a 10-kt liquid argon TPC at 1300 km to study neutrino oscillation. In this paper, we describe potential upgrades to LBNE10 that use Project X to produce high-intensity, low-energy neutrino beams. Simultaneous, high-power operation of 8- and 60-GeV beams with a 200-kt water Cerenkov detector would provide sensitivity to nu_mu to nu_e oscillations at the second oscillation maximum. We find that with ten years of data, it would be possible to measure sin2(2theta_13) with precisio…
Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss, in the framework of the wave packet approach, a number of such issues, including the relevance of the "same energy" and "same momentum" assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the production/detection and propagation coherence conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillatio…
We analyze all available solar and related reactor neutrino experiments, as well as simulated future 7Be, p-p, pep, and ^8B solar neutrino experiments. We treat all solar neutrino fluxes as free parameters subject to the condition that the total luminosity represented by the neutrinos equals the observed solar luminosity (the `luminosity constraint'). Existing experiments show that the p-p solar neutrino flux is 1.02 +- 0.02 (1 sigma) times the flux predicted by the BP00 standard solar model; the 7Be neutrino flux is 0.93^{+0.25}_{-0.63} the predicted flux; and the ^8B flux is 1.01 +- 0.04 the…
