Aspects of gravitational decoherence in neutrino lensing

We study spin and flavor oscillations of astrophysical neutrinos under the influence of external fields in curved spacetime. First, we consider spin oscillations in case of neutrinos gravitationally scattered off a rotating supermassive black hole surrounded by a thin magnetized accretion disk. We find that the gravitational interaction only does not result in the spin-flip of scattered ultrarelativistic neutrinos. Realistic magnetic fields lead to the significant reduction of the observed flux of neutrinos possessing reasonable magnetic moments. Second, we study neutrino flavor oscillations in stochastic gravitational waves (GWs). We derive the effective Hamiltonian for neutrinos interacting with a plane GW having an arbitrary polarization. Then, we consider stochastic GWs with arbitrary correlators of amplitudes. The equation for the density matrix for neutrino oscillations is solved analytically and the probabilities to detect certain neutrino flavors are derived. We find that the interaction of neutrinos, emitted by a core-collapsing supernova, with the stochastic GW background results in the several percent change of the neutrino fluxes. The observability of the predicted effects is discussed.

In this talk, we consider the interplay of fundamental and matter-induced T-violating effects in neutrino oscillations in matter. We present a simple approximative analytical formula for the T-violating probability asymmetry for three flavor neutrino oscillations in matter with an arbitrary density profile. We also discuss some implications of the obtained results. Since there are no T-violating effects in two flavor neutrino case (in the limit of vanshing $\theta_{13}$ or $\Delta m_{21}^2$, the three flavor neutrino oscillations reduces to the two flavor ones), the T-violating probability asymmetry can, in principle, provide a way to measure $\theta_{13}$ and $\Delta m_{21}^2$.

We study the effects of neutrino lensing induced by a Damour–Solodukhin wormhole on the neutrino oscillation. We derive and calculate the flavour transition probabilities in the presence of Damour–Solodukhin factor $$\Lambda $$ Λ as a shift in the massive source to show that the neutrino flavour oscillation is also sensitive not only to the sign of difference between the squared masses but also to the individual mass of neutrinos in both the two-flavour and the three-flavour cases. As a consequence of parameter $$\Lambda $$ Λ within a region, a series of curves of probability function versus the azimuthal angle $$\phi $$ ϕ with definite masses of neutrino can be plotted and their shapes resemble each other in the case of two-flavoured neutrinos and of three-flavoured ones. In view of the probability functions due to the wormhole, we reveal that the contribution of the factor $$\Lambda $$ Λ is novel. Based on our analytical and numerical discussions on the probability expressions, the difference of the neutrino flavour oscillation arising from the shift in the wormhole factor $$\Lambda $$ Λ is detectable. It is crucial that the $$\Lambda $$ Λ as deviation from the black holes can change the shapes of the curves greatly, in the case of three-flavoured neutrinos in particular. The detailed comparisons can be made among our estimations depicted in the figures for neutrino oscillations and the measurements from the detector, which open a new window for judging whether the remote star as lens is black-hole-like wormhole or spherically symmetric black hole and further the wormhole factor $$\Lambda $$ Λ can be estimated.

We numerically solve the evolution equations of neutrino three-flavor density matrices, and show that, even if neutrino oscillations mix neutrino flavors, large lepton number asymmetries are still allowed in certain limits by big bang nucleosynthesis.

T-violating effects in neutrino oscillations with three flavors in matter

A relativistic deep space positioning system has been proposed using four or\nmore pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed\nrepetition period in its rest frame.) The positioning system uses the fact that\nan event in spacetime can be fully described by emission coordinates: the\nproper emission time of each pulse measured at the event. The proper emission\ntime of each pulse from four different pulsars---interpolated as\nnecessary---provides the four spacetime coordinates of the reception event in\nthe emission coordinate system. If more than four pulsars are available, the\nredundancy can improve the accuracy of the determination and/or resolve\ndegeneracies resulting from special geometrical arrangements of the sources and\nthe event.\n We introduce a robust numerical approach to measure the emission coordinates\nof an event in any arbitrary spacetime geometry. Our approach uses a continuous\nsolution of the eikonal equation describing the backward null cone from the\nevent. The pulsar proper time at the instant the null cone intersects the\npulsar world line is one of the four required coordinates. The process is\ncomplete (modulo degeneracies) when four pulsar world lines have been crossed\nby the light cone.\n The numerical method is applied in two different examples: measuring emission\ncoordinates of an event in Minkowski spacetime using pulses from four pulsars\nstationary in the spacetime; and measuring emission coordinates of an event in\nSchwarzschild spacetime using pulses from four pulsars freely falling toward a\nstatic black hole.\n These numerical simulations are merely exploratory, but with improved\nresolution and computational resources the method can be applied to more\npertinent problems. For instance one could measure the emission coordinates,\nand therefore the trajectory, of the Earth.\n

Knitting neutrino mass textures with or without Tri–Bi maximal mixing

The radical departure from classical physics implies quantum coherence, i.e., coherent superposition of eigenstates of Hermitian operators. 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 flavour, spin and spin-flavour oscillations. We present exact analytical results for quantum coherence in neutrino oscillations quantified in terms of the relative entropy. Starting from an initial zero coherence state, we observe persistent oscillations of coherence during the dissipative evolution of an ultra-high energy neutrino in a random interstellar magnetic field. We found that after dissipative evolution, the initial spin-polarized state entirely “thermalizes”, and in the final steady state, the spin-up/down states have the same probabilities. On the other hand, neutrino flavour states also “thermalize”, but the populations of two flavour states do not equate to each other. The initial flavour still dominates in the final steady state.

Using the fluid droplet model of elementary particles, we propose to introduce two spinor fields ϕ and η in order to define two centres. We introduce a new concept of invariance in connection with the possibility that the particle may have a velocity larger than the velocity of light without the need to introduce imaginary proper masses, proper time and proper length. To this new concept, we attach new invariance groups that we interpret physically. In a simple case, we propose a dynamical equation for tachyons.

Using the natural, real units (proper time and proper length) for the definition of the spatial velocity, it is shown that the velocity of light during its propagation through gravitational fields is constant and exactly equal to its value in vacuum. Therefore, according to General Relativity, it is not correct to speak about a variable velocity of light in gravitational fields.

We study the propagation of neutrinos in gravitational fields using wave functions that are exact to first order in the metric deviation. For illustrative purposes, the geometrical background is represented by the Lense-Thirring metric. We derive explicit expressions for neutrino deflection, helicity transitions, flavor oscillations, and oscillation Hamiltonian.

The chapter is concerned with neutrino optics, helicity, and flavour oscillations induced by gravitational fields. It also deals with neutrino lensing, the spin-gravity coupling of neutrinos with primordial gravitational waves and with the phenomenon of pulsar kick.

It has proved convenient to define the effective lepton flavor mixing matrix U˜ and neutrino mass-squared differences Δ˜ji≡m˜j2−m˜i2 (for i,j=1,2,3) to describe the phenomena of neutrino mixing and flavor oscillations in a medium, but the prerequisite is to establish direct and transparent relations between these effective quantities and their fundamental counterparts in vacuum. With the help of two sets of sum rules for U˜ and Δ˜ji, we derive new and exact formulas for moduli of the nine elements of U˜ and the sides of its three Dirac unitarity triangles in the complex plane. The asymptotic behaviors of |U˜αi|2 and Δ˜ji (for α=e,μ,τ and i,j=1,2,3) in very dense matter (namely, allowing the matter parameter A=22GFNeE to mathematically approach infinity) are analytically unraveled for the first time, and in this connection the confusion associated with the parameter redundancy of θ˜12, θ˜13, θ˜23 and δ˜ in the standard parametrization of U˜ is clarified.

We propose a one-loop induced neutrino mass model with hidden U(1) gauge symmetry, in which we successfully involve a bosonic dark matter (DM) candidate propagating inside a loop diagram in neutrino mass generation to explain the e+e− excess recently reported by the DArk Matter Particle Explorer (DAMPE) experiment. In our scenario dark matter annihilates into four leptons through Z′ boson as DM DM → Z′ Z′ (Z′ → ℓ+ ℓ−) and Z′ decays into leptons via one-loop effect. We then investigate branching ratios of Z′ taking into account lepton flavor violations and neutrino oscillation data.

The solutions of the Dirac equation are given in terms of bispinors, four-component objects which include both spin and chirality as internal degrees of freedom. For massive particles, the Dirac equation couples components of the bispinor with different chiralities, yielding chiral oscillations. This phenomenon can be particularly relevant for recent proposals aimed at measuring non-relativistic cosmic neutrinos, and can find analogies in Dirac-like systems, such as graphene. In this paper, a concise review of chiral oscillations is presented, including their description with the Dirac's equation dynamics and the underlying group structure. Two paradigmatic cases of chiral oscillations in physical systems are shown: the effects on lepton-antineutrino spin quantum correlations, and neutrino flavor oscillations. Finally, extensions of recent theoretical investigations as well as future research developments are discussed.