Collective oscillations of supernova neutrinos swap the spectra $f_{{\nu }_e}(E)$ and $f_{{\overline{\nu }}_e}(E)$ with those of another flavor in certain energy intervals bounded by sharp spectral splits. This phenomenon is far more general than previously appreciated: typically one finds one or more swaps and accompanying splits in the $\nu$ and $\overline{\nu }$ channels for both inverted and normal neutrino mass hierarchies. Depending on an instability condition, swaps develop around spectral crossings (energies where $f_{{\nu }_e}=f_{{\nu }_x}$, $f_{{\overline{\nu }}_e}=f_{{\overline{\nu }}_x}$ as well as $E\to \infty$ where all fluxes vanish), and the widths of swaps are determined by the spectra and fluxes. Washout by multiangle decoherence varies across the spectrum and splits can survive as sharp spectral features.

The anomalies in the measurements of observables involving b → sμμ decays, namely R _K , R _K*, P ₅ ^′ , and B _s ^ϕ , may be addressed by adding lepton-universality-violating new physics contributions to the effective operators $$ {\mathcal{O}}_{\mathcal{9}},{\mathcal{O}}_{10},{\mathcal{O}}_9^{\prime },{\mathcal{O}}_{10}^{\prime } $$ O 9 , O 10 , O 9 ′ , O 10 ′ . We analyze all the scenarios where the new physics contributes to a pair of these operators at a time. We perform a global fit to all relevant data in the b → s sector to estimate the corresponding new Wilson coefficients, $$ {\mathcal{O}}_9^{\mathrm{NP}},{\mathcal{O}}_{10}^{\mathrm{NP}},{\mathcal{O}}_9^{\prime },{\mathcal{O}}_{10}^{\prime } $$ O 9 N P , O 10 N P , O 9 ′ , O 10 ′ . In the light of the new data on R _K , and R _K*, presented in Moriond 2019, we find that the scenarios with new physics contributions to the $$ \left({\mathcal{O}}_9^{\mathrm{NP}},{\mathcal{O}}_9^{\prime}\right) $$ O 9 N P O 9 ′ or $$ \left({\mathcal{O}}_9^{\mathrm{NP}},{\mathcal{O}}_{10}^{\prime}\right) $$ O 9 N P O 10 ′ pair remain the most favored ones. On the other hand, though the competing scenario $$ \left({\mathcal{O}}_9^{\mathrm{NP}},{\mathcal{O}}_{10}^{\mathrm{NP}}\right) $$ O 9 N P O 10 N P remains attractive, its advantage above the SM reduces significantly due to the tension that emerges between the R _K and R _K* measurements with the new data. The movement of the R _K measurement towards unity would also result in the re-emergence of the one-parameter scenario C ₉ ^NP = − C ₉ ^′ .

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 multiangle 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 multiangle 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.

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/Mikheyev-Smirnov-Wolfenstein (MSW) oscillations, synchronized oscillations, bipolar oscillations, and spectral split. Using the formalism, we demonstrate that the flavor conversions may be “factorized” into two-flavor oscillations with hierarchical frequencies. We explicitly show how the three-flavor solution may be constructed by combining two-flavor solutions. For a typical supernova density profile, we identify an approximate separation of regions where distinctly different flavor conversion mechanisms operate, and demonstrate the interplay between collective and MSW effects. We pictorialize our results in terms of the “${\mathbf{e}}_3\mathrm{\text{−}}{\mathbf{e}}_8$ triangle” diagram, which is a tool that can be used to visualize three-neutrino flavor conversions in general, and offers insights into the analysis of the collective effects in particular.