Neutrino Oscillation Length Research Articles

Locating the core-mantle boundary using oscillations of atmospheric neutrinos

Atmospheric neutrinos provide a unique avenue to explore the internal structure of Earth based on weak interactions, which is complementary to seismic studies and gravitational measurements. In this work, we demonstrate that the atmospheric neutrino oscillations in the presence of Earth matter can serve as an important tool to locate the core-mantle boundary (CMB). An atmospheric neutrino detector like the proposed 50 kt magnetized ICAL at INO can observe the core-passing neutrinos efficiently. These neutrinos would have experienced the MSW resonance and the parametric or neutrino oscillation length resonance. The net effect of these resonances on neutrino flavor conversions depends upon the location of CMB and the density jump at that radius. We quantify the capability of ICAL to measure the location of CMB in the context of multiple three-layered models of Earth. For the model where the density and the radius of core are kept flexible while the mass and radius of Earth as well as the densities of outer and inner mantle are fixed, ICAL can determine the location of CMB with a 1σ precision of about 250 km with an exposure of 1000 kt yr. With the 81-layered PREM profile, this 1σ precision would be about 350 km. The charge identification capability of ICAL plays an important role in achieving this precision.

Time-energy uncertainty relation for neutrino oscillations in curved spacetime

We derive the Mandelstam–Tamm time–energy uncertainty relation for neutrino oscillations in a generic stationary curved spacetime. In particular, by resorting to Stodolsky covariant formula of the quantum mechanical phase, we estimate gravity effects on the neutrino energy uncertainty. Deviations from the standard Minkowski result are explicitly evaluated in Schwarzschild, Lense–Thirring and Rindler (uniformly accelerated) geometries. Finally, we discuss how spacetime could affect the characteristic neutrino oscillation length in connection with the recent view of flavor neutrinos as unstable particles.

Liouville term for neutrinos: flavor structure and wave interpretation

Neutrino production, absorption, transport, and flavor evolution in astrophysical environments is described by a kinetic equation Dϱ=−i[H,ϱ]+\U0001d49e[ϱ]. Its basic elements are generalized occupation numbers ϱ, matrices in flavor space, that depend on time t, space x, and momentum p. The commutator expression encodes flavor conversion in terms of a matrix H of oscillation frequencies, whereas \U0001d49e[ϱ] represents source and sink terms as well as collisions. The Liouville operator on the left hand side involves linear derivatives in t, x and p. The simplified expression D=∂t+p̂⋅∂x for ultra-relativistic neutrinos was recently questioned in that flavor-dependent velocities should appear instead of the unit vector p̂. Moreover, a new damping term was postulated as a result. We here derive the full flavor-dependent velocity structure of the Liouville term although it appears to cause only higher-order corrections. Moreover, we argue that on the scale of the neutrino oscillation length, the kinetic equation can be seen as a first-order wave equation.

Turbulence patterns and neutrino flavor transitions in high-resolution supernova models

During the shock-wave propagation in a core-collapse supernova (SN), matter turbulence may affect neutrino flavor conversion probabilities. Such effects have been usually studied by adding parametrized small-scale random fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric matter density profiles. Recently, however, two-dimensional (2D) SN models have reached a space resolution high enough to directly trace anisotropic density profiles, down to scales smaller than the typical neutrino oscillation length. In this context, we analyze the statistical properties of a large set of SN matter density profiles obtained in a high-resolution 2D simulation, focusing on a post-bounce time (2 s) suited to study shock-wave effects on neutrino propagation on scales as small as O(100) km and possibly below. We clearly find the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as generically expected in 2D turbulence spectra. We then compute the flavor evolution of SN neutrinos along representative realizations of the turbulent matter density profiles, and observe no or modest damping of the neutrino crossing probabilities on their way through the shock wave. In order to check the effect of possibly unresolved fluctuations at scales below O(100) km, we also apply a randomization procedure anchored to the power spectrum calculated from the simulation, and find consistent results within ± 1σ fluctuations. These results show the importance of anchoring turbulence effects on SN neutrinos to realistic, fine-grained SN models.

Neutrino Oscillations Founded on Tachyon Theory of Neutrino

De Broglie's neutrino relations have been derived in this paper in the spirit of tachyon neutrino theory. The analysis of the physical characteristics of the neutrino as the tachyon particle has been done and a formula derived for the oscillation length. By analyzing phase angle of the plane wave, we came to the conclusion that the oscillations of neutrinos could be performed by speeds greater than the speed of light. Starting off from the application of Heisenberg's uncertainty relation in the micro-world , the postulate of neutrino confinement was introduced in the macroscopic area defined by the neutrino oscillation length. It is shown that the neutrino mass which belongs to the tachyon four-dimension space-time and the neutrino mass of the four-dimension space-time of the theory of relativity are not mutually equal by value, but the corresponding energy and momentum are unchanging.

On the question of the magnitude of day-night asymmetry for solar neutrinos

The effect of flavor day-night asymmetry is considered for solar neutrinos of energy about 1 MeV under the assumption that the electron-density distribution within the Earth is approximately piecewise continuous on the scale of the neutrino-oscillation length. In this approximation, the resulting asymmetry factor for beryllium neutrinos does not depend on the structure of the inner Earth’s layers or on the properties of the detector used. Its numerical estimate is on the order of −4 × 10−4, which is far beyond the reach of present-day experiments.

Quantum Gravity on Neutrino Oscillation Length

The oscillation length of neutrino oscillation could be discussed in the frame work of quantum gravity. Quantum gravity (Planck scale effects) leads to an effective SU(2) L ×U(1) invariant dimension-5 Lagrangian involving, neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the neutrino masses and mixing. We compute the neutrino oscillation length due to Planck scale effects. The gravitational interaction (M X =M pl ) demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino oscillation length, namely modified dispersion relation for neutrino oscillation phases.

R-Charged Black Hole and Neutrino Oscillation

In this paper we consider neutrino oscillation in general curved space-times. Then we calculate neutrino oscillation length in the R-charged black hole background, which is a five dimensional space-time, and compare it with the results of various backgrounds. We obtain effect of the electrical charge corresponding to the chemical potential on the oscillation length.

Neutrino production coherence and oscillation experiments

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 \pi\to \mu \nu \ 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 approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length.

Neutrino Oscillations in the Robertson-Walker Metric and the Cosmological Blue Shift of the Oscillation Length

The Doppler effect of the neutrino oscillation length in the flat space is discussed. When the observer travels away from the source, the oscillation length decreases. Moreover, the mass neutrino oscillation in the Robertson-Walker metric is studied, and the general equations of the oscillation phases are given. We obtain the relation between the phase and the scale factor. The expansion of the universe leads to the reduction of the oscillation length (blue shift), which is contrary to the red shift of the light ray.

Can Gravity Distinguish between Dirac and Majorana Neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and the gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavor system, as shown explicitly for SN 1987A.

Neutrino wave packet propagation in gravitational fields

We discuss the propagation of neutrino wave packets in a Lense–Thirring metric using a gravitational phase approach. We show that the neutrino oscillation length is altered by gravitational corrections and that neutrinos are subject to helicity flip induced by stellar rotation. For the case of a rapidly rotating neutron star, we show that absolute neutrino masses can be derived, in principle, from rotational contributions to the mass-induced energy shift, without recourse to mass generation models presently discussed in the literature.

Pulsar motions from neutrino oscillations induced by a violation of the equivalence principle

We analyze a possible explanation of the pulsar motions in terms of resonant neutrino transitions induced by a violation of the equivalence principle (VEP). Our approach, based on a parametrized post-Newtonian (PPN) expansion, shows that VEP effects give rise to highly directional contributions to the neutrino oscillation length. These terms induce anisotropies in the linear and angular momentum of the emitted neutrinos, which can account for both the observed translational and rotational pulsar motions. The violation needed to produce the actual motions is completely compatible with the existing bounds.

Enhancing mechanisms of neutrino transitions in a medium of nonperiodic constant-density layers and in the Earth

The enhancement of the transitions ${\ensuremath{\nu}}_{\ensuremath{\mu}}({\ensuremath{\nu}}_{e})\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}({\ensuremath{\nu}}_{\ensuremath{\mu};\ensuremath{\tau}}),$ ${\ensuremath{\nu}}_{2}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e},$ ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{s},$ ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s},$ etc. of neutrinos passing through a medium of nonperiodic density distribution, consisting of (i) two layers of different constant densities (e.g., Earth core and mantle), or (ii) three layers of constant density with the first and the third layers having identical densities and widths which differ from those of the second layer (e.g., mantle-core-mantle in the Earth), is studied. We find that, in addition to the known local maxima associated with the MSW effect and the neutrino oscillation length resonance (NOLR), the relevant two-neutrino transition probabilities have new resonance-like absolute maxima. The latter correspond to a new effect of total neutrino conversion and are absolute maxima in any independent variable: the neutrino energy, the layers widths, etc. We find the complete set of such maxima. We prove that the NOLR and the new absolute maxima are caused by a maximal constructive interference between the amplitudes of the neutrino transitions in the different density layers. We show that the strong resonance-like enhancement of the transitions in the Earth of the Earth-core-crossing solar and atmospheric neutrinos is due to the effect of total neutrino conversion.

Quantum gravity corrections to neutrino propagation

Massive spin-1/2 fields are studied in the framework of loop quantum gravity by considering a state approximating, at a length scale L much greater than Planck length l(P), a spin-1/2 field in flat spacetime. The discrete structure of spacetime at l(P) yields corrections to the field propagation at scale L. Neutrino bursts ( &pmacr; approximately 10(5) GeV) accompanying gamma ray bursts that have traveled cosmological distances L are considered. The dominant correction is helicity independent and leads to a time delay of order (&pmacr;l(P))L/c approximately 10(4) s. To next order in &pmacr;l(P), the correction has the form of the Gambini and Pullin effect for photons. A dependence L(-1)(os) approximately &pmacr;(2)l(P) is found for a two-flavor neutrino oscillation length.

New enhancement mechanism of the transitions in the earth of the solar and atmospheric neutrinos crossing the earth core

It is shown that the ν 2 → ν e and ν μ → ν e ( ν e → ν μ( τ) ) transitions respectively of the solar and atmospheric neutrinos in the Earth in the case of ν e − ν μ( τ) mixing in vacuum, are strongly enhanced by a new type of resonance when the neutrinos cross the Earth core. The resonance is operative at small mixing angles but differs from the MSW one. It is in many respects similar to the electron paramagnetic resonance taking place in a specific configuration of two magnetic fields. The conditions for existence of the new resonance include, in particular, specific constraints on the neutrino oscillation lengths in the Earth mantle and in the Earth core, thus the resonance is a “neutrino oscillation length resonance”. It leads also to enhancement of the ν 2 → ν e and ν e → ν s transitions in the case of ν e − ν s mixing and of the ν μ → ν s (or ν μ → ν s ) transitions at small mixing angles. The presence of the neutrino oscillation length resonance in the transitions of solar and atmospheric neutrinos traversing the Earth core has important implications for current and future solar and atmospheric neutrino experiments, and more specifically, for the interpretation of the results of the Super-Kamiokande experiment.

Diffractive-like (or parametric-resonance-like?) enhancement of the Earth (day-night) effect for solar neutrinos crossing the Earth core

It is shown that the strong enhancement of the Earth (day-night) effect for solar neutrinos crossing the Earth core in the case of the small mixing angle MSW ν e → ν μ( τ) transition solution of the solar neutrino problem is due to a new resonance effect in the solar neutrino transitions in the Earth and not just to the MSW effect in the core. The effect is in many respects similar to the electron paramagnetic resonance. The conditions for existence of this new resonance effect are discussed. They include specific constraints on the neutrino oscillation lengths in the Earth mantle and in the Earth core, thus the resonance is a “neutrino oscillation length resonance”. The effect exhibits strong dependence on the neutrino energy. Analytic expression for the probability accounting for the solar neutrino transitions in the Earth, which provides a high precision description of the transitions, including the new resonance effect, is derived. The implications of our results for the searches of the day-night asymmetry in the solar neutrino experiments are also briefly discussed. The new resonance effect is operative also in the ν μ → ν e ( ν e → ν μ ) transitions of atmospheric neutrinos crossing the Earth core.

Neutrino tomography of the Earth

Neutrino oscillations inside matter are very sensitive to the density of the medium traversed by the neutrinos. If the neutrino mixing angle (so far unknown) is not very small, then the neutrino oscillation length is of the size of the Earth, and we can use the phenomenon of neutrino matter oscillations to study the Earth's density distribution. Although neutrino attenuation data have already been proposed as a means to infer the density structure of the Earth, we show that neutrino oscillation data could also be used to make a density tomograph of the Earth. A numerical experiment in which neutrino beams from an accelerator are sent across the Earth, and are detected at six different locations on the Earth's surface, shows the feasibility of using neutrino oscillation data, with the advantage of using only currently available neutrino energies.

Neutrinos for geophysics

The Mikheyev-Smirnov-Wolfenstein solution to the solar-neutrino deficit provides a range for the acceptable neutrino parameters (Δm2 and sin 2θ0). If the vacuum mixing angle θ0 is not too small, the resulting neutrino oscillation length in matter is comparable to the radius of the earth. For such appropriate neutrino parameters we study neutrino oscillations inside the earth. The core of the earth is taken as a sphere with constant density 11 g/cm3, while the mantle, surrounding the core, is taken to be a spherically symmetric shell of constant density 4.4 g/cm3. We obtain an exact, analytic expression for the probability that an electron-neutrino after traversing the earth, emerges as an electron-neutrino. Our results indicate that the neutrinos might serve as the ideal tools for earth tomography.

Fermion masses and mixing angles in anSU(2) L ×U(1) model with horizontal interactions

AnSU(2) L ×U(1) horizontal model is presented, in which fermions mass splitting, quark and lepton family mixing is attributed to the presence of the horizontal interactions. In the quark sector, the Cabibbo angle and the Cabibbo-like angles are evaluated. In the lepton sector, the neutrinos mixing angles, which orginate from the charged leptons mixing, are calculated, the scale of the horizontal interactions is related to the neutrino oscillation length.