Collective neutrino flavor transitions in supernovae and the role of trajectory averaging

Abstract

Abstract. Non-linear effects on supernova neutrino oscillations, associated with neutrino-neutrino interactions, are known to induce collective flavor transformations near the supernova core for θ 13 = 0. In scenarios with very shallow electron density profiles, these transformations have been shown to couple with ordinary matter effects, jointly producing spectral distortions both in normal and inverted hierarchy. In this work we consider a complementary scenario, characterized by higher electron density, as indicated by shock-wave simulations during a few seconds after bounce. In this case, early collective flavor transitions are decoupled from later, ordinary matter effects. Moreover, such transitions become more amenable to both numerical computations and analytical interpretations in inverted hierarchy, while they basically vanish in normal hierarchy. We numerically evolve the neutrino density matrix in the region relevant for self-interaction effects, using thermal spectra and a representative value sin 2 θ 13 = 10 −4 . In the approximation of averaged intersection angle between neutrino trajectories, our simulations neatly show the collective phenomena of synchronization, bipolar oscillations, and spectral split, with analytically understandable features, as recently discussed in the literature. In the more realistic (but computationally demanding) case of non-averaged neutrino trajectories, our simulations do not show new significant qualitative features, apart from the smearing of "fine structures" such as bipolar nutations. Our results seem to suggest that, at least for non-shallow matter density profiles, averaging over neutrino trajectories plays a minor role in the final outcome. In this case, the swap of ν e and ν µ,τ spectra above a critical energy may represent an unmistakable signature of the inverted neutrino hierarchy, especially for θ 13 small enough to render further (ordinary or even turbulent) matter effects irrelevant.PACS numbers: 14.60. Pq, 13.15.+g, 97.60.Bw Collective neutrino flavor transitions in supernovae and the role of trajectory averaging 2

Resonances driven by a neutrino gyroscope and collective neutrino oscillations in supernovae

“…The parameters governing these phenomena have largely been determined except for the neutrino mass hierarchy, the vacuum mixing angle θ 13 , and the CP-violation phase. For supernova neutrinos, in addition to the MSW effect induced by neutrino forward scattering on electrons in matter [2,3], novel phenomena of flavor transformation can occur (see [4] and references therein) due to neutrino forward scattering on other neutrinos [5][6][7].…”

Self interactions of Supernova neutrinos

“…We investigated the case in which there is only one split for neutrinos and only one split for antineutrinos. Some of the features of the collective oscillations can be understood by means of three global vectors, J, J and D = J − J [3], constructed by opportunely adding the polarization vectors P(E) and P(E), that describe the oscillations of each ν andν energy mode…”

“…In a first approximation, we can simply disregard the LE split: in this case the HE split can be obtained from an integral equation expressing lepton number conservation [3]. The equation of motion of the polarization vector (see [3]) can have a resonance-like behavior in the (anti)neutrino sector if D z < 0 (D z > 0).…”

“…The equation of motion of the polarization vector (see [3]) can have a resonance-like behavior in the (anti)neutrino sector if D z < 0 (D z > 0). The resonance happens when the vacuum frequency of a mode is of the order of the self-interaction potential times D z , i.e.…”

“…Note that the previous equation has two unknowns, the energy of the mode and the radius at which the resonance occurs. When the collective oscillations begin (bipolar regime), all the mode precess with the same frequency ω bipolar ≃ √ µω ave Q z ∼ √ µω ave D z (see [4] for a definition of Q z and [3] for a definition of ω ave ). When ω ω bipolar , even after the start of the collective oscillations, the corresponding mode remains decoupled, while for ω < ω bipolar the mode participate to the collective oscillations.…”