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 signals from the formation of a black hole: A probe of the equation of state of dense matter

The gravitational collapse of a nonrotating, black-hole-forming massive star is studied by nu-radiation-hydrodynamical simulations for two different sets of realistic equation of state of dense matter. We show that the event will produce as many neutrinos as the ordinary supernova, but with distinctive characteristics in luminosities and spectra that will be an unmistakable indication of black hole formation. More importantly, the neutrino signals are quite sensitive to the difference of equation of state and can be used as a useful probe into the properties of dense matter. The event will be unique in that they will be shining only by neutrinos (and, possibly, gravitational waves) but not by photons, and hence they should be an important target of neutrino astronomy.     

Effect on Jarlskog Determinant Above the GUT Scale Within Four Flavor Neutrino Framework

We study the Planck scale effects on Jarlskog determiant in the four flavor framework. On electroweak symmetry breaking, quantum gravitational effects lead to an effective SU(2) × U(1) invariant dimension-5 Lagrangian including neutrino and Higgs forces, which perturbed the neutrino mass term and produce an extra terms in the neutrino mass matrix. We consider that gravitational interaction is independent from flavor and compute the Jarlskog determiant due to Planck scale effects. In the case of leptonic sector, the strentgh of CP violation is measured by Jarlskog determiant. We applied our approach to study Jarlskog determinant in the four flavor neutrino mixing above the GUT scale.

     

Three Flavor Neutrino Mixing and Dark Energy Above GUT Scale

Neutrino mixing lead to a non zero contribution to the dark energy of the universe. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. The mechanism of neutrino mixing is a possible candidate to contribute the cosmological dark energy. Quantum gravitational (Planck scale) effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavor. In this paper, we discuss the three flavor neutrino mixing and cosmological dark energy contributes due to Planck scale effects.     

Neutrino Oscillations in the de Sitter and the Anti-de Sitter Space-Time

General expressions of the neutrino oscillation phase in the generally static space-time with spherical symmetry are given. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. We find that a blue shift of the oscillation length takes place when the neutrino travels out of the gravitational field. Then, we discuss the variation of the oscillation length influenced by the cosmological constant. In the de Sitter space-time, the positive cosmological constant prolongs the oscillation length. And, in the anti-de Sitter space-time, the negative cosmological constant shortens it as expected.     

LETTER: Some Remarks on the Neutrino Oscillation Phase in a Gravitational Field

The weak gravitational field expansion method to account for the gravitationally induced neutrino oscillation effect is critically examined, then it is shown that the splitting of the neutrino phase into a "kinematic" and a "gravitational" phase is not always possible because the relativistic factor modifies the particle interference phase splitting condition in a gravitational field.     

Does CP Phase Exist Above the GUT Scale

We consider non-reormalizable interaction term as a perturbation of the conventional neutrino mass matrix. Quantum gravitational (Planck scale )effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. In particular, for the $\theta_{13}'$ range 0.00005–0.28, indicates the existence of CP violating phase above the GUT scale. We assume that the gravitational interaction is flavor blind. In this paper, we further investigate the possibility of CP phase exist from Quantum gravity.     

Using Hamilton-Jacobi Equation to Study the Neutrino Oscillations in the Stationary Space-Time

We study the mass neutrino oscillation by solving Hamilton-Jacobi equation in the Kerr-Newman-Kasuya space-time, as an important example of the stationary space-time, and give the general expression of the oscillation phase. A special case, the geodesic with L=aE is considered. Then, the proper oscillation length is studied carefully. The effects of the gravitational field, the rotating parameter a, the electric charge and magnetic charge on the oscillation length are given. It is worth noting that a blue shift of the oscillation length rather than a red shift takes place as the neutrino travels out of the gravitational field.     

Neutrinos in general relativity: Four(?) levels of approach

The three subsequent levels of approach to the problem of the neutrino in general relativity which have been exploited till now, are:

1. ‘classical particle’ approach, i.e. a study on the neutrino as a classical particle in a classical, given gravitational field;
2. ‘quantum particle’ approach, i.e. considering the Dirac equation for the neutrino in a given gravitational field;
3. ‘classical field’ approach comprising the study of combined neutrino-gravitational fields.

Many results obtained along these lines are presented, with emphasis upon the geometrical theory of two-component neutrino-gravitational fields. A synthesis of the particle and fields aspects of the neutrino could provide a possible fourth, till now non-existing, ‘quantum field’ level of approach. This should deal with a guantized neutrino field in a curved space-time (which might be also quantized, but perhaps this should belong already to a next, fifth level of approach). Studies on the neutrino physics in gravitational fields reveal not only a series of results which are of interest in se, and which may be used as the basis to a unified theory of neutrino and gravitational fields (the Rainich problem for the neutrino). They provide in addition the necessary material for astrophysical and cosmological applications; some of these are outlined in relation to the results presented.     

Neutrino oscillations in the gravitational field

We calculate the gravitational correction to the phase difference between neutrino mass eigenstates for the spherically symmetric gravitational field described by the Schwarzschild metric. This correction was calculated in a number of works, but the results of these works differ from each other. Our result does not coincide with the results ever published. In this work, we make calculations in the simplest way and verify our result by several tests.     

Addendum to: Gen. Rel. Grav. 28 (1996) 1161, First Prize Essay for 1996: Neutrino Oscillations and Supernovae

In a 1996 JRO Fellowship Research Proposal (Los Alamos), the author suggested that neutrino oscillations may provide a powerful indirect energy transport mechanism to supernovae explosions. The principal aim of this addendum is to present the relevant unedited text of Section 1 of that proposal. We then briefly remind, (a) of an early suggestion of Mazurek on vacuum neutrino oscillations and their relevance to supernovae explosion, and (b) Wolfenstein's result on suppression of the effect by matter effects. We conclude that whether or not neutrino oscillations play a significant role in supernovae explosions shall depend if there are shells/regions of space in stellar collapse where matter effects play no essential role. Should such regions exist in actual astrophysical situations, the final outcome of neutrino oscillations on supernovae explosions shall depend, in part, on whether or not the LNSD signal is confirmed. Importantly, the reader is reminded that neutrino oscillations form a set of flavor-oscillation clocks and these clock suffer gravitational redshift which can be as large as 20 percent. This effect must be incorporated fully into any calculation of supernova explosion.     

Probing the violation of equivalence principle at a muon storage ring via neutrino oscillation

We examine the possible tests of violation of the gravitational equivalence principle (VEP) at a muon storage ring via neutrino oscillation experiments. If the gravitational interactions of the neutrinos are not diagonal in the flavour basis and the gravitational interaction eigenstates have different couplings to the gravitational field, this leads to the neutrino oscillation. If one starts with μ⁺ beam then appearance of τ^±, e⁺ and μ⁻ in the final state are the signals for neutrino oscillation. We have estimated the number of μ⁻ events in this scenario in ν_μ–N deep inelastic scattering. Final state lepton energy distribution can be used to distinguish the VEP scenario from the others. A large area of VEP parameter space can be explored at a future muon storage ring facility with moderate beam energy.     

Angular momentum non-conserving decays in isotropic media

Various processes that are forbidden in vacuum due to angular momentum conservation can occur in a medium that is isotropic and does not carry any angular momentum. We illustrate this by considering explicitly two examples. The first one is the decay of a spin-0 particle into a photon and another spin-0 particle, using a model involving the Yukawa interactions of the scalar particles with a charged fermion field. The second one involves the decay of a neutrino into another neutrino and a graviton, in the standard model of particle interactions augmented with the linearized gravitational couplings.     

Neutrino oscillations in the general spherically symmetric gravitational field

The results for neutrino oscillations in the gravitational field described by the Schwarzschild metric are generalized to the general spherically symmetric gravitational field.     

Neutrino—antineutrino asymmetry around rotating black holes

Propagation of fermion in curved space-time generates gravitational interaction due to the coupling between spin of the fermion and space-time curvature. This gravitational interaction appears as a CPT violating term in the Lagrangian. It is seen that this space-time interaction can generate neutrino asymmetry in the Universe. If the background metric is spherically asymmetric, say, of a rotating black hole, this interaction is non-zero, thus the net difference to the number density of the neutrino and anti-neutrino is non-zero.     

Neutrino mass and dark energy from weak lensing

Weak gravitational lensing of background galaxies by intervening matter directly probes the mass distribution in the Universe. This distribution is sensitive to both the dark energy and neutrino mass. We examine the potential of lensing experiments to measure features of both simultaneously. Focusing on the radial information contained in a future deep 4000 deg(2) survey, we find that the expected (1-sigma) error on a neutrino mass is 0.1 eV, if the dark-energy parameters are allowed to vary. The constraints on dark-energy parameters are similarly restrictive, with errors on w of 0.09.     

The Evolution for Various Matter Perturbations in the Expanding Universe

We present a systematic treatment of the linear theory of scalar gravitational perturbations of various matter (including baryons, cold dark matter, photons, massless neutrinos,and massive neutrino) for the flat, open and close universes, concentrating on the treatment of the massive neutrino component which has been either ignored or approximated crudely for the nonflat universe in previous literatures.     

Neutrino helicity flip in a curved space-time

In Minkowskian spaces, the helicity of a massless fermion is a conserved quantity. In principle, this property may not hold when gravitational effects are not neglected. In this context, this work proves that the helicity of a massless neutrino is not conserved in curved spaces. In order to show this fact, the time variation of the helicity in the Heisenberg picture is calculated. Also, we verify that the differential cross-section due to helicity flip of a massless neutrino in a curved space does not vanish as a result of the coupling between the spin and the curvature of space-time.     

Neutrino radiation in spherically-symmetric gravitational fields II. The structure of the radiation field

It is shown that the neutrino radiation field emitted by a star may be described by Vaidya's radiating Schwarzschild metric. The gravitational energy shift of the neutrino field is also considered, both in terms of an exact solution and in the weak field approximation.     

A MODEL OF NEUTRINO STELLAR SYSTEM AND THE UPPER BOUND OF NEUTRINO MASS OBTAINED FROM THE RCTATION CURVES OF SOME GALAXIES

We discuss in this paper a stellar model of degenerate massive neutrinos with a core made of heavy matter. Dimension of the core is much smaller than the scale of neutrino star. The Oppenheimer-Volkoff equation is solved for such a system. Our calculation shows that under certain conditions, this neutrino halo will resemble a pure neutrino star. We have further obtained insides the neutrino star (or halo) the rdtation curve and the gravitational red shifts. It is interesting to note that the relative rotation velocity v(r)EV(r)/V(R) (R is the radius of the neutrino star) depends only on the relative coordinate ξ=r/R in the nonrelativistic cases. Therefore, all nonrelativistically degenerate neutrino systems will have a universa1 relative rotation curve(v versus ξ). Within the accuracy of numeri calcalculation, we have also obtained a useful relation connecting the maximum velocity V_m and the corresponding coordinate R_m as V_mR_m2=0.231. By comparing this relation with the observed rotation data at large distances for some galaxies, we have obtained an upper bound for neutrino mass of about 6-9eV.