We identify a generic new form of collective flavor oscillations in dense neutrino gases that amounts to a self-induced parametric resonance. It occurs in a homogeneous and isotropic ensemble when a range of neutrino modes is prepared in a different flavor than the neighboring modes with lower and higher energies. The flavor content of the intermediate spectral part librates relative to the other parts with a frequency corresponding to a typical Delta m^2/2E. This libration persists in the limit of an arbitrarily large neutrino density where one would have expected synchronized flavor oscillations.
When neutrinos travel through matter with a periodic density profile, the neutrino oscillation probability can be enhanced if certain conditions are satisfied. In a two-neutrino framework, the condition for parametric resonance is known. Herein, we consider the analogous parametric resonance condition within the context of a full three-neutrino framework with two oscillation scales. For energies in the range of hundreds of MeV to a few GeV, we find that neutrino oscillation can be parametrically enhanced if two approximate relations are satisfied. The first is similar to the two-neutrino param…
Within the Lorentz invariant formalizm for description of neutrino evolution in electromagnetic fields and matter we consider neutrino spin oscillations in the electromagnetic wave with varying amplitude and in "castle wall" magnetic field. It is shown for the first time that the parametric resonances of neutrino oscillations in such systems can occur.
The time-evolution of quantum meson fields in O(4)-linear sigma model is treated approximately. It is shown that the amplification of the amplitudes of pion modes with low momenta occurs by means of both the parametric resonance and the forced oscillation.
Within the Lorentz invariant formalizm for description of neutrino evolution in electromagnetic fields and matter we consider neutrino spin oscillations in the circular polarized electromagnetic wave, the amplitude of which is a modulated function of time. It is shown for the first time that the parametric resonance of neutrino oscillations can occur in such a system.
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscilla…
We study the parametric resonance of the neutrino oscillation through the matter whose density varies spatially. The Fourier analysis of the matter effect enables us to clarify the parametric resonance condition, which is summarized in a frequency matching between the neutrino oscillation and the spatial variation of the matter density. As a result, the n-th Fourier mode of a matter density profile modifies the energy spectrum of the nu_mu -> nu_e appearance probability at around the n-th dip.
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 study two-flavor collective neutrino oscillations in the dense-neutrino region above the neutrino sphere in a supernova (SN). The angular dependence of the neutrino-neutrino interaction potential causes "multi-angle" effects that can lead either to complete kinematical decoherence in flavor space or only to small differences between different trajectories. This nonlinear system switches abruptly between "self-maintained coherence" and "self-induced decoherence" among the angular modes, depending on the strength of the deleptonization flux. For a realistic SN the quasi single-angle behavior …
We discuss the relationship between a symmetry in the neutrino flavour evolution equations and neutrino flavour oscillations in the collective precession mode. This collective precession mode can give rise to spectral swaps (splits) when conditions can be approximated as homogeneous and isotropic. Multi-angle numerical simulations of supernova neutrino flavour transformation show that when this approximation breaks down, non-collective neutrino oscillation modes decohere kinematically, but the collective precession mode still is expected to stand out. We provide a criterion for significant fla…
We present an exact analytic solution to the neutrino evolution equation in matter with periodic step-function density profile and discuss in detail the parametric resonance of neutrino oscillations that can occur in such a system. Solar and atmospheric neutrinos traversing the earth pass through layers of alternating density and can therefore experience parametric resonance of their oscillations. Atmospheric neutrinos can undergo parametrically enhanced oscillations in the earth when their trajectories deviate from the vertical by about $26^\circ - 32^\circ$. Solar neutrinos traversing the ea…
We review the rich phenomena associated with neutrino flavor transformation in the presence of neutrino self-coupling. Our exposition centers on three collective neutrino oscillation scenarios: a simple bipolar neutrino system that initially consists of mono-energetic electron neutrinos and antineutrinos; a homogeneous and isotropic neutrino gas with multiple neutrino/antineutrino species and continuous energy spectra; and a generic neutrino gas in an anisotropic environment. We use each of these scenarios to illustrate key facets of collective neutrino oscillations. We discuss the implication…
We investigate collective flavor oscillations of supernova neutrinos at late stages of the explosion. We first show that the frequently used single-angle (averaged coupling) approximation predicts oscillations close to, or perhaps even inside, the neutrinosphere, potentially invalidating the basic neutrino transport paradigm. Fortunately, we also find that the single-angle approximation breaks down in this regime; in the full multiangle calculation, the oscillations start safely outside the transport region. The new suppression effect is traced to the interplay between the dispersion in the ne…
We extend the multi-angle computational framework and investigate the time evolution of the neutrino halo on collective neutrino oscillation in the core collapse of an iron core progenitor. We find that in the case of the $9.6\, \rm M_\odot$ progenitor adopted in this work, there are windows of time when the effects of neutrino halo and collective neutrino oscillation are not simultaneously large. Inside the shock, the impact of the inward-scattered halo neutrino cannot in general be neglected compared to the outward-propagating neutrino flux. However, during early epochs, collective neutrino …
Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem t…
Neutrino oscillations in matter can exhibit a specific resonance enhancement -- parametric resonance, which is different from the MSW resonance. Oscillations of atmospheric and solar neutrinos inside the earth can undergo parametric enhancement when neutrino trajectories cross the core of the earth. In this paper we review the parametric resonance of neutrino oscillations in matter. In particular, physical interpretation of the effect and the prospects of its experimental observation in oscillations of solar and atmospheric neutrinos in the earth are discussed.
Neutrino oscillations in matter can exhibit a specific resonance enhancement -- parametric resonance, which is different from the MSW resonance. Recently it has been shown that the oscillations of atmospheric and solar neutrinos inside the earth can undergo parametric enhancement when neutrino trajectories cross the core of the earth. In this paper we continue the study of the parametric resonance of neutrino oscillations in the earth. The following issues are discussed: stability of the resonance with respect to the variations of the zenith angle of the neutrino source; higher-order resonance…
We perform a self-consistent calculation of collective neutrino oscillations including the effect of back scattered neutrinos (Halo effect) in the `single-angle' approximation, within a spherically symmetric supernova model. We find that due to the Halo effect the onset of flavor transformations is pushed to smaller radii, by a few kilometers. The celebrated phenomenon of the spectral split is found to be robust under the present inclusion of the Halo effect.
Collective neutrino oscillations are critical to determine the neutrino flavor content, which has striking impacts on core-collapse supernovae or compact binary merger remnants. It is a challenging many-body problem that so far has been mainly studied at the mean-field approximation. We use a setup that captures the relevant physics and allows exact solution for a large number of neutrinos. We, for the first time, find quantitative deviation from the mean-field evolution due to many-body decoherence in flavor space. Similar features have been observed in a spin-1 Bose-Einstein condensate, whic…
Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings, such as supernovae, where the neutrino density is large. In this regime, neutrino-neutrino interactions are important and simulations in the mean-field approximation show evidence for collective oscillations occurring at time scales much larger than those associated with vacuum oscillations. In this work, we study the out-of-equilibrium dynamics of a corresponding spin model using Matrix Product States and show how collective bipolar oscillations can be triggered by many-body correlati…
Neutrinos and antineutrinos emitted from a core collapse supernova interact among themselves, giving rise to collective flavor conversion effects that are significant near the neutrinosphere. We develop a formalism to analyze these collective effects in the complete three-flavor framework. It naturally generalizes the spin-precession analogy to three flavors and is capable of analytically describing phenomena like vacuum/MSW oscillations, synchronized oscillations, bipolar oscillations and spectral split. Using the formalism, we demonstrate that the flavor conversions may be "factorized" into …
We demonstrate the non-negligible effect of transition magnetic moments on three-flavor collective oscillations of Majorana neutrinos in the core of type-II supernovae, within the single-angle approximation. We argue that data from a galactic supernova in conjunction with terrestrial experiments can potentially give us clues about the non-zero nature of neutrino transition magnetic moments if these are Majorana fermions, even if their values are as small as those predicted by the Standard Model augmented by nonzero neutrino Majorana masses.
We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They can be classified by a number N of linearly independent functions that describe all neutrino modes as linear superpositions. What is more, the dynamics is equivalent to another ensemble with the same effective density, consisting of N modes with discrete energies E_i with i=1, ..., N. We use this equivalence to derive the analytic solution for two-mode (bimo…
Recently, it has been demonstrated that neutrinos in a supernova oscillate collectively. This process occurs much deeper than the conventional matter-induced MSW effect and hence may have an impact on nucleosynthesis. In this paper we explore the effects of collective neutrino oscillations on the r-process, using representative late-time neutrino spectra and outflow models. We find that accurate modeling of the collective oscillations is essential for this analysis. As an illustration, the often-used "single-angle" approximation makes grossly inaccurate predictions for the yields in our setup.…
We consider neutrino evolution master equations in dense moving and polarized matter consisted of electrons, neutrons, protons and neutrinos. We also take into account the neutrino magnetic moment interaction with a magnetic field. We point out the mechanisms responsible for the neutrino spin precession and provide the expressions for the corresponding interaction Hamiltonians that should be taken into account in theoretical treatments of collective neutrino oscillations.
If ultra-light dark matter (ULDM) exists and couples to neutrinos, the neutrino oscillation probability might be significantly altered by a parametric resonance. This resonance can occur if the typical frequency of neutrino flavor-oscillations $Δm^2/(2E)$, where $Δm^2$ is the mass-squared difference of the neutrinos and $E$ is the neutrino energy, matches the oscillation frequency of the ULDM field, determined by its mass, $m_ϕ$. The resonance could lead to observable effects even if the ULDM coupling is very small, and even if its typical oscillation period, given by $τ_ϕ=2π/m_ϕ$, is much sho…
The vp process is a primary nucleosynthesis process which occurs in core collapse supernovae. An essential role in this process is being played by electron antineutrinos. They generate, by absorption on protons, a supply of neutrons which, by (n,p) reactions, allow to overcome waiting point nuclei with rather long beta-decay and proton-capture lifetimes. The synthesis of heavy elements by the vp process depends sensitively on the \barν_e luminosity and spectrum. As has been shown recently, the latter are affected by collective neutrino flavor oscillations which can swap the \barν_e and \barν_{…
In dense neutrino backgrounds present in supernovae and in the early Universe, neutrino oscillations may exhibit complex collective phenomena, such as synchronized oscillations, bipolar oscillations and spectral splits and swaps. In this Letter we consider for the first time the effects of decoherence by wave packet separation on these phenomena. We derive the evolution equations that govern neutrino oscillations in a dense medium in the presence of decoherence and consider the evolution of several simple neutrino systems in detail. We show that decoherence may modify the oscillation pattern s…
We consider a solution of the atmospheric neutrino problem based on oscillations of muon neutrinos to sterile neutrinos: $ν_μ$ $\leftrightarrow$ $ν_s$. The zenith angle ($Θ$) dependences of the neutrino and upward-going muon fluxes in presence of these oscillations are studied. The dependences have characteristic form with two dips: at $\cos Θ= -0.6 ÷-0.2$ and $\cos Θ= -1.0 ÷-0.8$. The latter dip is due to parametric resonance in oscillations of neutrinos which cross the core of the earth. A comparison of predictions with data from the MACRO, Baksan and Super-Kamiokande experiments is given.
We study the effect of Majorana transition magnetic moments on the flavor evolution of neutrinos and antineutrinos inside the core of Type-II supernova explosions. We find non-trivial collective oscillation effects relating neutrinos and antineutrinos of different flavors, even if one restricts the discussion to Majorana transition electromagnetic moment values that are not much larger than those expected from standard model interactions and nonzero neutrino Majorana masses. This appears to be, to the best of our knowledge, the only potentially observable phenomenon sensitive to such small val…
We derive the effective Hamiltonian describing collective oscillations of Majorana neutrinos with a transition magnetic moment, allowing for the presence of scalar and pseudoscalar nonstandard neutrino self-interactions (NSSIs). Using this Hamiltonian, we analyze new flavor instability channels of collective oscillations in a core-collapse supernova environment that open up in the presence of a small but nonzero neutrino magnetic moment. It turns out that, contrary to certain claims in the literature, within the minimally extended Standard Model (i.e., without NSSIs), no new instabilities aris…
Collective oscillations of supernova neutrinos above the neutrino sphere can be completely described by the propagation of individual neutrinos in external potentials and are in this sense a linear phenomenon. An effective theory of collective oscillations can be developed based on certain assumptions about time dependence of these potentials. General conditions for strong flavor transformations are formulated and these transformations can be interpreted as parametric resonance effects induced by periodic modulations of the potentials. We study a simplified and solvable example, where a probe …
In this proceeding, we study time evolution of a complex scalar field, in symmetry broken phase, in presence of oscillating spacetime metric background. We show that spacetime oscillations lead to parametric resonance of the field. This generates excitations in the field for a wide range of frequency of spacetime oscillations which ultimately lead to the formation of topological vortices. The lowest frequency cut-off to induce this phenomena is set by system size due to finite size effects.
We explore the effects of collective neutrino flavor oscillations due to neutrino-neutrino interactions on the neutrino heating behind a stalled core-collapse supernova shock. We carry out axisymmetric (2D) radiation-hydrodynamic core-collapse supernova simulations, tracking the first 400 ms of the post-core-bounce evolution in 11.2 solar mass and 15 solar mass progenitor stars. Using inputs from these 2D simulations, we perform neutrino flavor oscillation calculations in multi-energy single-angle and multi-angle single-energy approximations. Our results show that flavor conversions do not set…
In supernovae neutrinos are emitted from a region with a width $r_{\rm eff}$ of a few kilometers (rather than from a surface of infinitesimal width). We study the effect of integration (averaging) over such an extended emission region on collective oscillations. The averaging leads to additional suppression of the correlation (off-diagonal element of the density matrix) by a factor $ \sim 1/r_{\rm eff} V_e \sim 10^{-10}$, where $V_e$ is the matter potential. This factor enters the initial condition for further collective oscillations and, consequently, leads to a delay of the strong flavour tr…
Extreme conditions present in the interiors of the core-collapse supernovae make neutrino-neutrino interactions not only feasible but dominant in specific regions, leading to the non-linear evolution of the neutrino flavor. Results obtained when such collective neutrino oscillations are treated in the mean-field approximation deviate from the results using the many-body picture because of the ignored quantum correlations. We present the first three flavor many-body calculations of the collective neutrino oscillations. The entanglement is quantified in terms of the entanglement entropy and the …
We investigate the importance of going beyond the mean-field approximation in the dynamics of collective neutrino oscillations. To expand our understanding of the coherent neutrino oscillation problem, we apply concepts from many-body physics and quantum information theory. Specifically, we use measures of nontrivial correlations (otherwise known as "entanglement") between the constituent neutrinos of the many-body system, such as the entanglement entropy and the Bloch vector of the reduced density matrix. The relevance of going beyond the mean field is demonstrated by comparisons between the …
Collective neutrino oscillations can potentially play an important role in transporting lepton flavor in astrophysical scenarios where the neutrino density is large, typical examples are the early universe and supernova explosions. It has been argued in the past that simple models of the neutrino Hamiltonian designed to describe forward scattering can support substantial flavor evolution on very short time scales $t\approx\log(N)/(G_Fρ_ν)$, with $N$ the number of neutrinos, $G_F$ the Fermi constant and $ρ_ν$ the neutrino density. This finding is in tension with results for similar but exactly …
We present a formalism for precise description of oscillation phenomena in matter at high energies or high densities, V > Δm^2/2E, where V is the matter-induced potential of neutrinos. The accuracy of the approximation is determined by the quantity \sin^2 2θ_m ΔV/2πV, where θ_m is the mixing angle in matter and ΔV is a typical change of the potential over the oscillation length (l \sim 2π/V). We derive simple and physically transparent formulas for the oscillation probabilities, which are valid for arbitrary matter density profiles. They can be applied to oscillations of high energy (E > 10 Ge…
Collective flavor oscillations driven by neutrino-neutrino self interaction inside core-collapse supernovae have now been shown to bring drastic changes in the resultant neutrino fluxes. This would in turn significantly affect the diffuse supernova neutrino background (DSNB), created by all core-collapse supernovae that have exploded in the past. In view of these collective effects, we re-analyze the potential of detecting the DSNB in currently running and planned large-scale detectors meant for detecting both electron neutrinos and antineutrinos. The next generation detectors should be able t…
Effects of decoherence by wave packet separation on collective neutrino oscillations in dense neutrino gases are considered. We estimate the length of the wave packets of neutrinos produced in core collapse supernovae and the expected neutrino coherence length, and then proceed to consider the decoherence effects within the density matrix formalism of neutrino flavour transitions. First, we demonstrate that for neutrino oscillations in vacuum the decoherence effects are described by a damping term in the equation of motion of the density matrix of a neutrino as a whole (as contrasted to that o…
The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the non-spherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the ``single…
Solar-System Abundances of $p$-Nuclides Probe Collective Neutrino Oscillations in Supernovae
SLAC National Accelerator Laboratory, Stanford University（斯坦福大学斯坦福直线加速器中心）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）；Department of Physics, University of California Berkeley（加州大学伯克利分校物理系）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Department of Physics, University of California San Diego（加州大学圣地亚哥分校物理系）；School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学院）；Department of Physics, New York Institute of Technology（纽约理工学院物理系）；Reed College（里德学院）
