Chiral Oscillations Research Articles

Majorana phase and matter effects in neutrino chiral oscillation

Due to finite masses and mixing, for neutrinos propagation in space-time, there is a chiral oscillation between left- and right- chiral neutrinos, besides the usual oscillation between different generations. The probability of chiral oscillation is suppressed by a factor of m2/E2 making the effect small for relativistic neutrinos. However, for non-relativistic neutrinos, this effect can be significant. In matter, the equation of motion is modified. When neutrinos produced in weak interaction pass through the matter, the eigen-energies are split into two different ones depending on the helicity of the neutrino. This results in different oscillation behavior for neutrinos with different helicity, in particular there is a new resonant effect related to the helicity state of neutrino different than the usual MSW effect. For Majorana neutrinos, chiral oscillation also depends on Majorana phases.

Symmetry and reduction for second order degenerate Lagrangians

For the chiral oscillator described by a second order and degenerate Lagrangian with special Euclidean group of symmetries, we show, by cotangent bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of oscillator algebra, the central extension of special Euclidean algebra in two dimensions.

Spacetime evolution of lepton number densities and wave-packet-like effects for neutrino flavor and chiral oscillations in quantum field theory

Spacetime evolution of lepton number densities and wave-packet-like effects for neutrino flavor and chiral oscillations in quantum field theory

Chiral oscillations

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.

Odd dynamics of living chiral crystals.

Active crystals are highly ordered structures that emerge from the self-organization of motile objects, and have been widely studied in synthetic1,2 and bacterial3,4 active matter. Whether persistent crystalline ordercan emerge in groups of autonomously developing multicellular organisms is currently unknown. Here we show that swimming starfish embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiments, theory and simulations, we demonstrate that the formation, dynamics and dissolution of these living crystals are controlled by the hydrodynamic properties and the natural development of embryos. Remarkably, living chiral crystals exhibit self-sustained chiral oscillations as well as various unconventional deformation response behaviours recently predicted for odd elastic materials5,6. Our results provide direct experimental evidence for how non-reciprocal interactions between autonomous multicellular components may facilitate non-equilibrium phases of chiral active matter.

Dirac’s analysis and Ostrogradskii’s theorem for a class of second-order degenerate Lagrangians

This paper analyzes the constraint structure of a class of degenerate second-order particle Lagrangian that includes chiral oscillator, noncommutative oscillator, and two examples from reduced topologically massive gravity. For even-dimensional configuration spaces with maximal nondegeneracy, Dirac bracket is defined solely by coefficient field of highest derivative whereas for odd dimensions almost all fields may contribute. Ostrogradskii’s theorem on energy instability is discussed. Results of Dirac analysis are used to identify ghost degrees of freedom. Translational symmetries are used to construct first-order variational formalisms for oscillator examples, thereby making them ghost-free.

Lepton-Antineutrino Entanglement and Chiral Oscillations

Dirac bispinors belong to an irreducible representation of the complete Lorentz group, which includes parity as a symmetry yielding two intrinsic discrete degrees of freedom: chirality and spin. For massive particles, chirality is not dynamically conserved, which leads to chiral oscillations. In this contribution, we describe the effects of this intrinsic structure of Dirac bispinors on the quantum entanglement encoded in a lepton-antineutrino pair. We consider that the pair is generated through weak interactions, which are intrinsically chiral, such that in the initial state the lepton and the antineutrino have definite chirality but their spins are entangled. We show that chiral oscillations induce spin entanglement oscillations and redistribute the spin entanglement to chirality-spin correlations. Such a phenomenon is prominent if the momentum of the lepton is comparable with or smaller than its mass. We further show that a Bell-like spin observable exhibits the same behavior of the spin entanglement. Such correlations do not require the knowledge of the full density matrix. Our results show novel effects of the intrinsic bispinor structure and can be used as a basis for designing experiments to probe chiral oscillations via spin correlation measurements.

Chiral oscillations in the non-relativistic regime

Massive Dirac particles are a superposition of left and right chiral components. Since chirality is not a conserved quantity, the free Dirac Hamiltonian evolution induces chiral quantum oscillations, a phenomenon related to the Zitterbewegung, the trembling motion of free propagating particles. While not observable for particles in relativistic dynamical regimes, chiral oscillations become relevant when the particle’s rest energy is comparable to its momentum. In this paper, we quantify the effect of chiral oscillations on the non-relativistic evolution of a particle state described as a Dirac bispinor and specialize our results to describe the interplay between chiral and flavor oscillations of non-relativistic neutrinos: we compute the time-averaged survival probability and observe an energy-dependent depletion of the quantity when compared to the standard oscillation formula. In the non-relativistic regime, this depletion due to chiral oscillations can be as large as 40%. Finally, we discuss the relevance of chiral oscillations in upcoming experiments which will probe the cosmic neutrino background.

Parity violation and chiral oscillation of cosmological relic neutrinos

The conventional derivation of neutrino oscillation treats neutrino mass eigenstate as plane wave with an overall evolution phase. Nevertheless, due to the intrinsic parity-violating nature of weak interactions, only the left-chiral neutrino can be produced as initial condition. On the other hand, the neutrino mass term connects the left-chiral component to the right-chiral one and unavoidably leads to generation of the later through oscillation. This chiral oscillation has significant consequences on the detection of the cosmological relic neutrinos. The event rate is reduced by a factor of 2 than the conventional prediction.

Chiral oscillations in electronic transport through graphene nanoribbons induced by pseudospin filters

We show here that the application of potential barriers that induce contributions of hyperboloid subbands (pseudospin filters) in graphene nanoribbons locally breaks the chiral symmetry of the Dirac state, in the sides of the barrier, with the consequent transition from Klein to anti-Klein behavior. With the increased filter potential applied, resonances of Fabry-P\'erot type with line widths that are decreasing are generated in the conductance, which is associated with a pseudospin precession located on the sides of the barrier. Interestingly, throughout this process the chiral symmetry of the state is conserved, and pseudospin oscillations (opposite) that increase in intensity are observed on the sides of the filter. This is associated with a gradual loss of the electron-hole correlation, with the increased filter potential, which ends with the formation of a transport gap when the electron-hole symmetry is completely broken. This is an example of how the chiral symmetry can evolve and still be conserved, during a tunneling process. All this leads to the generation of energy gaps, associated with anti-Klein tunneling, which can be controlled using certain spatial configurations of the applied filters. The inclusion of a new type of asymmetry (roughness in the filters) makes it possible to recover Klein's tunneling in the region of induced gaps. The interaction of the hyperboloid subbands with the Dirac band can be observed in density-of-states maps using the pseudospin filters, following the behavior of the van Hove singularities as a function of the filter potential.

Chiral Oscillations and Spontaneous Mirror Symmetry Breaking in a Simple Polymerization Model

The origin of biological homochirality—defined as the preference of biological systems for only one enantiomer—has widespread implications in the study of chemical evolution and the origin of life. The activation—polymerization—epimerization—depolymerization (APED) model is a theoretical model originally proposed to describe chiral symmetry breaking in a simple dimerization system. It is known that the model produces chiral and chemical oscillations for certain system parameters, in particular, the preferential formation of heterochiral polymers. In order to investigate the effect of higher oligomers, our model adds trimers, tetramers, and pentamers. We report sustained oscillations of all chemical species and the enantiomeric excess for a wide range of parameter sets as well as the periodic chiral amplification of a small initial enantiomeric excess to a nearly homochiral state.

Chiral and chemical oscillations in a simple dimerization model

We consider the APED model (activation-polymerization-epimerization-depolymerization) for describing the emergence of chiral solutions within a non-catalytic framework for chiral polymerization. The minimal APED model for dimerization can lead to the spontaneous appearance of chiral oscillations and we describe in detail the nature of these oscillations in the enantiomeric excess, and which are the consequence of oscillations of the concentrations of the associated chemical species.

Quantum flavor oscillations extended to the Dirac theory

AbstractFlavor oscillations by itself and its coupling with chiral oscillations and/or spin‐flipping are the most relevant quantum phenomena of neutrino physics. This report deals with the quantum theory of flavor oscillations in vacuum, extended to fermionic particles in the several subtle aspects of the first quantization and second quantization theories. At first, the basic controversies regarding quantum‐mechanical derivations of the flavor conversion formulas are reviewed based on the internal wave packet (IWP) framework. In this scenario, the use of the Dirac equation is required for a satisfactory evolution of fermionic mass‐eigenstates since in the standard treatment of oscillations the mass‐eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. Within first quantized theories, besides flavor oscillations, chiral oscillations automatically appear when we set the dynamic equations for a fermionic Dirac‐type particle. It is also observed that there is no constraint between chiral oscillations, when it takes place in vacuum, and the process of spin‐flipping related to the helicity quantum number, which does not take place in vacuum. The left‐handed chiral nature of created and detected neutrinos can be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left‐handed neutrinos to the undetected right‐handed neutrinos can be obtained in analytic form. These modifications introduce correction factors proportional to mν2/Eν2 that are very difficult to be quantified by the current phenomenological analysis. All these effects can also be identified when the non‐minimal coupling with an external (electro)magnetic field in the neutrino interacting Lagrangian is taken into account. In the context of a causal relativistic theory of a free particle, one of the two effects should be present in flavor oscillations: (a) rapid oscillations or (b) initial flavor violation. Concerning second quantized approaches, a simple second quantized treatment exhibits a tiny but inevitable initial flavor violation without the possibility of rapid oscillations. Such effect is a consequence of an intrinsically indefinite but approximately well defined neutrino flavor. Within a realistic calculation in pion decay, including the quantum field treatment of the creation process with finite decay width, it is possible to quantify such violation. The violation effects are shown to be much larger than loop induced lepton flavor violation processes, already present in the standard model in the presence of massive neutrinos with mixing. For the implicitly assumed fermionic nature of the Dirac theory, the conclusions of this report lead to lessons concerning flavor mixing, chiral oscillations, interference between positive and negative frequency components of Dirac equation solutions, and the field formulation of quantum oscillations.

Chiral polymerization: symmetry breaking and entropy production in closed systems

We solve numerically a kinetic model of chiral polymerization in systems closed to matter and energy flow, paying special emphasis to its ability to amplify the small initial enantiomeric excesses due to the internal and unavoidable statistical fluctuations. The reaction steps are assumed to be reversible, implying a thermodynamic constraint among some of the rate constants. Absolute asymmetric synthesis is achieved in this scheme. The system can persist for long times in quasi- stationary chiral asymmetric states before racemizing. Strong inhibition leads to long-period chiral oscillations in the enantiomeric excesses of the longest homopolymer chains. We also calculate the entropy production {\sigma} per unit volume and show that {\sigma} increases to a peak value either before or in the vicinity of the chiral symmetry breaking transition.

Noncommutativity and Duality through the Symplectic Embedding Formalism

This work is devoted to review the gauge embedding of either commutative and noncommutative (NC) theories using the symplectic formalism framework. To sum up the main features of the method, during the process of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and brings some light on the so-called "arbitrariness problem". This alternative embedding formalism also presents a way to obtain a set of dynamically dual equivalent embedded Lagrangian densities which is obtained after a finite number of steps in the iterative symplectic process, oppositely to the result proposed using the BFFT formalism. On the other hand, we will see precisely that the symplectic embedding formalism can be seen as an alternative and an efficient procedure to the standard introduction of the Moyal product in order to produce in a natural way a NC theory. In order to construct a pedagogical explanation of the method to the nonspecialist we exemplify the formalism showing that the massive NC U(1) theory is embedded in a gauge theory using this alternative systematic path based on the symplectic framework. Further, as other applications of the method, we describe exactly how to obtain a Lagrangian description for the NC version of some systems reproducing well known theories. Naming some of them, we use the procedure in the Proca model, the irrotational fluid model and the noncommutative self-dual model in order to obtain dual equivalent actions for these theories. To illustrate the process of noncommutativity introduction we use the chiral oscillator and the nondegenerate mechanics.

THEORETICAL CORRELATION BETWEEN POSSIBLE EVIDENCES OF NEUTRINO CHIRAL OSCILLATIONS AND POLARIZATION MEASUREMENTS

Reporting about the formalism with the Dirac equation we describe the dynamics of chiral oscillations for a fermionic particle non-minimally coupling with an external magnetic field. For massive particles, the chirality and helicity quantum numbers represent different physical quantities of representative importance in the study of chiral interactions, in particular, in the context of neutrino physics. After solving the interacting Hamiltonian (Dirac) equation for the corresponding fermionic Dirac-type particle (neutrino) and quantifying chiral oscillations in the Dirac wave packet framework, we avail the possibility of determining realistic neutrino chirality conversion rates by means of (helicity) polarization measurements. We notice that it can become feasible for some particular magnetic field configurations with large values of B orthogonal to the direction of the propagating particle.

Chiral oscillations in terms of the zitterbewegung effect

We seek the immediate description of chiral oscillations in terms of the trembling motion described by the velocity (Dirac) operator α. By taking into account the complete set of Dirac equation solutions, which results in a free propagating Dirac wave packet composed by positive and negative frequency components, we report about the well-established zitterbewegung results and indicate how chiral oscillations can be expressed in terms of the well-known quantum oscillating variables. We conclude with the interpretation of chiral oscillations as very rapid position oscillation projections onto the longitudinally decomposed direction of the motion.

The Construction of Dirac Wave Packets for a Fermionic Particle Non-Minimally Coupling with an External Magnetic Field

We shall proceed with the construction of normalizable Dirac wave packets for {\em fermionic} particles (neutrinos) with dynamics governed by a ``modified'' Dirac equation with a non-minimal coupling with an external magnetic field. We are not only interested on the analytic solutions of the ``modified'' Dirac wave equation but also on the construction of Dirac wave packets which can be used for describing the dynamics of some observable physical quantities which are relevant in the context of the quantum oscillation phenomena. To conclude, we discuss qualitatively the applicability of this formal construction in the treatment of chiral (and flavor) oscillations in the theoretical context of neutrino physics.

Chirality dynamics for a fermionic particle non-minimally coupling with an external magnetic field

We proceed with the construction of normalizable Dirac wave packets for treating chiral oscillations in the presence of an external magnetic field. Both chirality and helicity quantum numbers correspond to variables of fundamental importance in the study of chiral interactions, in particular, in the context of neutrino physics. In order to clarify a subtle aspect in the confront of such concepts which, for massive particles, represent different physical quantities, we are specifically interested in quantifying chiral oscillations for a {\em fermionic} Dirac-{\em type} particle (neutrino) non-minimally coupling with an external magnetic field {\boldmath$B$} by solving the correspondent interacting Hamiltonian (Dirac) equation. The viability of the intermediate wave packet treatment becomes clear when we assume {\boldmath$B$} orthogonal/parallel to the direction of the propagating particle.

Flavor coupled with chiral oscillations in the presence of an external magnetic field

By reporting to the Dirac wave-packet prescription where it is formally assumed the {\em fermionic} nature of the particles, we shall demonstrate that chiral oscillations implicitly aggregated to the interference between positive and negative frequency components of mass-eigenstate wave-packets introduce some small modifications to the standard neutrino flavor conversion formula. Assuming the correspondent spinorial solutions of a ``modified'' Dirac equation, we are specifically interested in quantifying flavor coupled with chiral oscillations for a {\em fermionic} Dirac-{\em type} particle (neutrino) non-minimally coupling with an external magnetic field {\boldmath$B$}. The viability of the intermediate wave-packet treatment becomes clear when we assume {\boldmath$B$} orthogonal/parallel to the direction of the propagating particle.