Neutrino-neutrino Interactions Research Articles

Boltzmann hierarchy for interacting neutrinos I: formalism

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (ceff2,cvis2)-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles.

Significance of neutrino-neutrino interaction in neutrino oscillation in core-collapse supernova

We study the possibility of neutrino-neutrino interaction inside the neutrino core of supernova (ρ ≥ 1010 g/cc) and outside the neutrinosphere. The angular dependence of the neutrino-neutrino interaction Hamiltonian causes multi-angle effects that can lead either to oscillation or free streaming of neutrinos. If the angle between interactions is π/2, the neutrinos are trapped inside neutrino core and chances of oscillation increases due to interaction. As the angle gradually changes, the chance of oscillation decreases and free streaming of neutrino can be observed out of core of supernova as shock waves.DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11780 BIBECHANA 12 (2015) 89-95

Neutrino magnetic moment,CPviolation, and flavor oscillations in matter

We consider collective oscillations of neutrinos, which are emergent nonlinear flavor evolution phenomena instigated by neutrino-neutrino interactions in astrophysical environments with sufficiently high neutrino densities. We investigate the symmetries of the problem in the full three flavor mixing scheme and in the exact many-body formulation by including the effects of CP violation and neutrino magnetic moment. We show that, similar to the two flavor scheme, several dynamical symmetries exist for three flavors in the single-angle approximation if the net electron background in the environment and the effects of the neutrino magnetic moment are negligible. Moreover, we show that these dynamical symmetries are present even when the CP symmetry is violated in neutrino oscillations. We explicitly write down the constants of motion through which these dynamical symmetries manifest themselves in terms of the generators of the SU(3) flavor transformations. We also show that the effects due to the CP-violating Dirac phase factor out of the many-body evolution operator and evolve independently of nonlinear flavor transformations if neutrino electromagnetic interactions are ignored. In the presence of a strong magnetic field, CP-violating effects can still be considered independently provided that an effective definition for neutrino magnetic moment is used.

Multi-azimuthal-angle instability for different supernova neutrino fluxes

It has been recently discovered that removing the axial symmetry in the "multi-angle effects" associated with the neutrino-neutrino interactions for supernova (SN) neutrinos, a new multi-azimuthal-angle (MAA) instability would trigger flavor conversions in addition to the ones caused by the bimodal and multi-zenith-angle (MZA) instabilities. We investigate the dependence of the MAA instability on the original SN neutrino fluxes, performing a stability analysis of the linearized neutrino equations of motion. We compare these results with the numerical evolution of the SN neutrino non-linear equations, looking at a local solution along a specific line of sight, under the assumption that the transverse variations of the global solution are small. We also assume that self-induced conversions are not suppressed by large matter effects. We show that the pattern of the spectral crossings (energies where F_{\nu_e} = F_{\nu_x}, and F_{\bar\nu_e} = F_{\bar\nu_x}) is crucial in determining the impact of MAA effects on the flavor evolution. For neutrino spectra with a strong excess of \nu_e over \bar\nu_e, presenting only a single-crossing, MAA instabilities would trigger new flavor conversions in normal mass hierarchy. In our simplified flavor evolution scheme, these would lead to spectral swaps and splits analogous to what produced in inverted hierarchy by the bimodal instability. Conversely, in the presence of spectra with a moderate flavor hierarchy, having multiple crossing energies, MZA effects would produce a sizable delay in the onset of the flavor conversions, inhibiting the growth of the MAA instability. In this case the splitting features for the oscillated spectra in both the mass hierarchies are the ones induced by the only bimodal and MZA effects.

Suppression of the multi-azimuthal-angle instability in dense neutrino gas during supernova accretion phase

It has been recently pointed out that by removing the axial symmetry in the ``multi-angle effects'' associated with the neutrino-neutrino interactions for supernova (SN) neutrinos a new multi-azimuthal-angle (MAA) instability would arise. In particular, for a flux ordering ${F}_{{\ensuremath{\nu}}_{e}}>{F}_{{\overline{\ensuremath{\nu}}}_{e}}>{F}_{{\ensuremath{\nu}}_{x}}$, as expected during the SN accretion phase, this instability occurs in the normal neutrino mass hierarchy. However, during this phase, the ordinary matter density can be larger than the neutrino one, suppressing the self-induced conversions. In this regard, we investigate the matter suppression of the MAA effects, performing a linearized stability analysis of the neutrino equations of motion, in the presence of realistic SN density profiles. We compare these results with the numerical solution of the SN neutrino nonlinear evolution equations. Assuming axially symmetric distributions of neutrino momenta, we find that the large matter term strongly inhibits the MAA effects. In particular, the hindrance becomes stronger including realistic forward-peaked neutrino angular distributions. As a result, in our model for a $10.8\text{ }{M}_{\ensuremath{\bigodot}}$ iron-core SNe, MAA instability does not trigger any flavor conversion during the accretion phase. Instead, for a $8.8\text{ }{M}_{\ensuremath{\bigodot}}$ O-Ne-Mg core SN model, with lower matter density profile and less forward-peaked angular distributions, flavor conversions are possible also at early times.

Multi-azimuthal-angle effects in self-induced supernova neutrino flavor conversions without axial symmetry

The flavor evolution of neutrinos emitted by a supernova (SN) core is strongly affected by the refractive effects associated with the neutrino-neutrino interactions in the deepest stellar regions. Till now, all numerical studies have assumed the axial symmetry for the "multi-angle effects" associated with the neutrino-neutrino interactions. Recently, it has been pointed out in \cite{Raffelt:2013rqa} that removing this assumption, a new multi-azimuthal-angle (MAA) instability would emerge in the flavor evolution of the dense SN neutrino gas in addition to the one caused by multi-zenith-angle (MZA) effects. Inspired by this result, for the first time we numerically solve the non-linear neutrino propagation equations in SN, introducing the azimuthal angle as angular variable in addition to the usual zenith angle. We consider simple energy spectra with an excess of \nu_e over anti-\nu_e. In these cases, we find that even starting with a complete axial symmetric neutrino emission, the MAA effects would lead to significant flavor conversions in normal mass hierarchy, in cases otherwise stable under the only MZA effects. The final outcome of the flavor conversions, triggered by the MAA instability, depends on the initial asymmetry between \nu_e and anti-\nu_e spectra. If it is sufficiently large, final spectra would show an ordered behavior with spectral swaps and splits. Conversely, for small flavor asymmetries flavor decoherence among angular modes develops, affecting the flavor evolution also in inverted mass hierarchy.

Flavor Oscillations in Core-Collapse Supernovae

Core collapse supernovae are unique laboratories to study many aspects of neutrino physics. The vicinity of the proto-neutron star in a core-collapse supernova is characterized by large matter and neutrino densities. A salient feature of this region is the impact of neutrino-neutrino interactions. Properties of the ensuing non-linear many-neutrino system are examined with a particular emphasis on its collective behavior and its symmetries. The impact of neutrino properties and interactions on the r-process nucleosynthesis that may take place in the supernova environment is discussed.

Flavor stability analysis of dense supernova neutrinos with flavor-dependent angular distributions

Numerical simulations of the supernova (SN) neutrino self-induced flavor conversions, associated with the neutrino-neutrino interactions in the deepest stellar regions, have been typically carried out assuming the "bulb-model". In this approximation, neutrinos are taken to be emitted half-isotropically by a common neutrinosphere. In the recent Ref. \cite{Mirizzi:2011tu} we have removed this assumption by introducing flavor-dependent angular distributions for SN neutrinos, as suggested by core-collapse simulations. We have found that in this case a novel multi-angle instability in the self-induced flavor transitions can arise. In this work we perform an extensive study of this effect, carrying out a linearized flavor stability analysis for different SN neutrino energy fluxes and angular distributions, in both normal and inverted neutrino mass hierarchy. We confirm that spectra of different nu species which cross in angular space (where F_{\nu_e}=F_{\nu_x} and F_{\bar\nu_e}=F_{\bar\nu_x}) present a significant enhancement of the flavor instability, and a shift of the onset of the flavor conversions at smaller radii with respect to the case of an isotropic neutrino emission. We also illustrate how a qualitative (and sometimes quantitative) understanding of the dynamics of these systems follows from a stability analysis.

Flavor oscillations of supernova neutrinos

Neutrinos emitted by core-collapse supernovae (SNe) represent an important laboratory for both particle physics and astrophysics. While propagating in the dense SN environment, they can feel not only the presence of background matter (via ordinary Mikheev-Smirnov-Wolfenstein effects) but also of the gas of neutrinos and antineutrinos (via neutrino-neutrino interaction effects). The MSW effect would imprint on SN neutrinos a track of the shock-wave propagation and of the matter turbulences in the stellar envelope. Moreover, the neutrino-neutrino interactions appear to modify the flavor evolution of SN neutrinos in a collective way, completely different from the ordinary matter effects. In these conditions, the flavor evolution equations become highly nonlinear, sometimes resulting in surprising phenomena when the entire neutrino system oscillates coherently as a single collective mode. In this talk, I will present the recent results on supernova neutrino flavor conversions and I will discuss about the sensitivity of these effects to the ordering of the neutrino mass spectrum.

Role of collective neutrino flavor oscillations in core-collapse supernova shock revival

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 (two-dimensional) radiation-hydrodynamic core-collapse supernova simulations, tracking the first 400 ms of the post-core-bounce evolution in $11.2\mathrm{\text{\ensuremath{-}}}{M}_{\ensuremath{\bigodot}}$ and $15\mathrm{\text{\ensuremath{-}}}{M}_{\ensuremath{\bigodot}}$ progenitor stars. Using inputs from these two-dimensional simulations, we perform neutrino flavor oscillation calculations in multienergy single-angle and multiangle single-energy approximations. Our results show that flavor conversions do not set in until close to or outside the stalled shock, enhancing heating by not more than a few percent in the most optimistic case. Consequently, we conclude that the postbounce preexplosion dynamics of standard core-collapse supernovae remains unaffected by neutrino oscillations. Multiangle effects in regions of high electron density can further inhibit collective oscillations, strengthening our conclusion.

Neutrino spectral split in core-collapse supernovae: A magnetic resonance phenomenon

A variety of neutrino flavour conversion phenomena occur in core-collapse supernova, due to the large neutrino density close to the neutrinosphere, and the importance of the neutrino-neutrino interaction. Three different regimes have been identified so far, usually called the synchronization, the bipolar oscillations and the spectral split. Using the formalism of polarization vectors, within two-flavours, we focus on the spectral split phenomenon and we show for the first time that the physical mechanism underlying the neutrino spectral split is a magnetic resonance phenomenon. In particular, we show that the precession frequencies fulfill the magnetic resonance conditions. Our numerical calculations show that the neutrino energies and the location at which the resonance takes place in the supernova coincide well with the neutrino energies at which a spectral swap occurs. The corresponding adiabaticity parameters present spikes at the resonance location.

No Collective Neutrino Flavor Conversions during the Supernova Accretion Phase

We perform a dedicated study of the supernova (SN) neutrino flavor evolution during the accretion phase, using results from recent neutrino radiation hydrodynamics simulations. In contrast to what was expected in the presence of only neutrino-neutrino interactions, we find that the multiangle effects associated with the dense ordinary matter suppress collective oscillations. The matter suppression implies that neutrino oscillations will start outside the neutrino decoupling region and therefore will have a negligible impact on the neutrino heating and the explosion dynamics. Furthermore, the possible detection of the next galactic SN neutrino signal from the accretion phase, based on the usual Mikheyev-Smirnov-Wolfenstein effect in the SN mantle and Earth matter effects, can reveal the neutrino mass hierarchy in the case that the mixing angle θ(13) is not very small.

The neutrino signal at HALO: learning about the primary supernova neutrino fluxes and neutrino properties

Core-collapse supernova neutrinos undergo a variety of phenomena when they travel from the high neutrino density region and large matter densities to the Earth. We perform analytical calculations of the supernova neutrino fluxes including collective effects due to the neutrino-neutrino interactions, the Mikheev-Smirnov-Wolfenstein (MSW) effect due to the neutrino interactions with the background matter and decoherence of the wave packets as they propagate in space. We predict the numbers of one- and two-neutron charged and neutral-current electron-neutrino scattering on lead events. We show that, due to the energy thresholds, the ratios of one- to two-neutron events are sensitive to the pinching parameters of neutrino fluxes at the neutrinosphere, almost independently of the presently unknown neutrino properties. Besides, such events have an interesting sensitivity to the spectral split features that depend upon the presence/absence of energy equipartition among neutrino flavors. Our calculations show that a lead-based observatory like the Helium And Lead Observatory (HALO) has the potential to pin down important characteristics of the neutrino fluxes at the neutrinosphere, and provide us with information on the neutrino transport in the supernova core.

Linearized flavor-stability analysis of dense neutrino streams

Neutrino-neutrino interactions in dense neutrino streams, like those emitted by a core-collapse supernova, can lead to self-induced neutrino flavor conversions. While this is a nonlinear phenomenon, the onset of these conversions can be examined through a standard stability analysis of the linearized equations of motion. The problem is reduced to a linear eigenvalue equation that involves the neutrino density, energy spectrum, angular distribution, and matter density. In the single-angle case, we reproduce previous results and use them to identify two generic instabilities: The system is stable above a cutoff density ("cutoff mode"), or can approach an asymptotic instability for increasing density ("saturation mode"). We analyze multi-angle effects on these generic types of instabilities and find that even the saturation mode is suppressed at large densities. For both types of modes, a given multi-angle spectrum typically is unstable when the neutrino and electron densities are comparable, but stable when the neutrino density is much smaller or much larger than the electron density. The role of an instability in the SN context depends on the available growth time and on the range of affected modes. At large matter density, most modes are off-resonance even when the system is unstable.

Multiangle effects in self-induced oscillations for different supernova neutrino fluxes

The non-isotropic nature of the neutrino emission from a supernova (SN) core might potentially affect the flavor evolution of the neutrino ensemble, via neutrino-neutrino interactions in the deepest SN regions. We investigate the dependence of these "multi-angle effects" on the original SN neutrino fluxes in a three-flavor framework. We show that the pattern of the spectral crossings (energies where F_\nu_e= F_\nu_x, and F_\bar\nu_e= F_\bar\nu_x) is crucial in determining the impact of multi-angle effects on the flavor evolution. For neutrino spectra presenting only a single-crossing, synchronization of different angular modes prevails over multi-angle effects, producing the known "quasi single-angle" evolution. Conversely, in the presence of spectra with multiple crossing energies, synchronization is not stable. In this situation, multi-angle effects would produce a sizable delay in the onset of the flavor conversions, as recently observed. We show that, due to the only partial adiabaticity of the evolution at large radii, the multi-angle suppression can be so strong to dramatically affect the final oscillated neutrino spectra. In particular three-flavor effects, associated with the solar parameters, could be washed-out in multi-angle simulations.

N-mode coherence in collective neutrino oscillations

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 (bimodal) coherence, relevant for spectral-split formation in supernova neutrinos.

Self-Induced Suppression of Collective Neutrino Oscillations in a Supernova

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 neutrino-neutrino interactions and the vacuum oscillation term.

Collective flavor oscillations of supernova neutrinos and r-process nucleosynthesis

Neutrino-neutrino interactions inside core-collapse supernovae may give riseto collective flavor oscillations resulting in swap between flavors. These oscillations depend on the initial energy spectra, and relative fluxes or relative luminosities of the neutrinos.It has been observed that departure from energy equipartition among different flavors can give rise to one or more sharp spectral swap over energy, termed as splits. We study the occurrence of splits in the neutrino and antineutrinospectra, varying the initial relative fluxes for different models of initial energy spectrum, in both normal and inverted hierarchy. These initialrelative flux variations give rise to several possible split patterns whereasvariation over different models of energy spectra give similar results. We explore the effect of these spectral splits on the electron fraction, Ye,that governs r-process nucleosynthesis inside supernovae. Since spectral splits modify the electron neutrino and antineutrino spectra in the region where r-process is postulated to happen, and since the pattern of spectral splits depends on the initial conditions of the spectra and the neutrino mass hierarchy, we show that the condition Ye < 0.5 required for successfulr-process nucleosynthesis will lead to constraints on the initial spectral conditions, for a given neutrino mass hierarchy.

One-loop correction effects on supernova neutrino fluxes: a new possible probe for Beyond Standard Models

We present the consequences of a large radiative correction term coming from Supersymmetry (SUSY) upon the electron neutrino fluxes streaming off a core-collapse supernova using a 3-flavour neutrino-neutrino interaction code. We explore the interplay between the neutrino-neutrino interaction and the effects of the resonance associated with the μ−τ neutrino index of refraction. We find that sizeable effects may be visible in the flux on Earth and, consequently, on the number of events upon the energy signal of electron neutrinos in a liquid argon detector. Such effects could lead to a probe for Beyond Standard Model (BSM) physics and, ideally, to constraints in the SUSY parameter space.

Triggering collective oscillations by three-flavor effects

Collective flavor transformations in supernovae, caused by neutrino-neutrino interactions, are essentially a two-flavor phenomenon driven by the atmospheric mass difference and the small mixing angle ${\ensuremath{\theta}}_{13}$. In the two-flavor approximation, the initial evolution depends logarithmically on ${\ensuremath{\theta}}_{13}$ and the system remains trapped in an unstable fixed point for ${\ensuremath{\theta}}_{13}=0$. However, any effect breaking exact ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ equivalence triggers the conversion. Such three-flavor perturbations include radiative corrections to weak interactions, small differences between the ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ fluxes, or nonstandard interactions. Therefore, extremely small values of ${\ensuremath{\theta}}_{13}$ are in practice equivalent, the fate of the system depending only on the neutrino spectra and their mass ordering.