Model-independent diagnostic of self-induced spectral equalization versus ordinary matter effects in supernova neutrinos

Self-induced flavor conversions near the supernova (SN) core can make the fluxes for different neutrino species become almost equal, potentially altering the dynamics of the SN explosion and washing out all further neutrino oscillation effects. We present a new model-independent analysis strategy for the next galactic SN signal that will distinguish this flavor equalization scenario from a matter-effects-only scenario during the SN accretion phase. Our method does not rely on fitting or modeling the energy-dependent fluences of the different species to a known function, but rather uses a model-independent comparison of charged-current and neutral-current events at large next-generation underground detectors. Specifically, we advocate that the events due to elastic scattering on protons in a scintillator detector, which is insensitive to oscillation effects and can be used as a model-independent normalization, should be compared with the events due to inverse beta decay of ${\overline{\nu }}_e$ in a water Cherenkov detector and/or the events due to charged-current interactions of ${\nu }_e$ in an argon detector. The ratio of events in these different detection channels allow one to distinguish a complete flavor equalization from a pure matter effect, for either of the neutrino mass orderings, as long as the spectral differences among the different species are not too small.

Figure 1

Wroclaw model: Neutrino fluence spectra for the different flavors, unoscillated (top panels) and for different oscillation scenarios (bottom panels).

Figure 2

Garching model: Neutrino fluence spectra for the different flavors, unoscillated (top panels) and for different oscillation scenarios (bottom panels).

Figure 3

Observed spectrum from proton elastic scattering in JUNO, for the Wroclaw (left) and Garching (right) models. The red curve represents the contribution of ${\nu }_e$, the blue curve is for ${\overline{\nu }}_e$, and the green for ${\nu }_x$.

Figure 4

Observed spectrum from inverse beta decay in Hyper-Kamiokande for the Wroclaw (left) and Garching (right) models. The green (blue) curve represents matter effects only in NO (IO), while the red curve refers to complete flavor equalization.

Figure 5

Observed event spectrum from a charged current on argon in DUNE for the Wroclaw (left) and Garching (right) models. The green (blue) curve represents matter effects only in NO (IO), while the red curve refers to complete flavor equalization.

Figure 6

Reconstructed neutrino energy spectrum ${\tilde{F}}_{\text{PES}}$ from proton elastic scattering in JUNO for the Wroclaw (left panel) and Garching (right panel) models. Dashed curves represent the true neutrino flux $F_{\text{PES}}$ in Eq. (10).

Figure 7

Reconstructed neutrino energy spectrum ${\tilde{F}}_{\mathrm{IBD}}$ from inverse beta decay in Hyper-Kamiokande, assuming the Wroclaw (left panel) and Garching (right panel) models. The green (blue) curve represents matter effects only in NO (IO), while the red curve refers to complete flavor equalization. Dashed curves refer to the true neutrino flux $F_{\mathrm{IBD}}$ in Eq. (14).

Figure 8

Reconstructed neutrino energy spectrum ${\tilde{F}}_{\text{ArCC}}$ from charged current on argon in DUNE, assuming the Wroclaw (left panel) and Garching (right panel) models. The green (blue) curve represents matter effects only in NO (IO), while the red curve refers to complete flavor equalization. Dashed curves refer to the true neutrino flux $F_{\text{ArCC}}$ in Eq. (18).

Figure 9

Ratio $R$ (upper panels) and $\overline{R}$ (lower panels) in NO. Left panels refer to the matter-effects-only scenario, while right panels are for complete flavor equalization. The dot refers to the Wroclaw model, while the triangle is for the Garching one. The physical region in the high-energy spectral tails is below the dashed line corresponding to $x=\overline{x}$. (See text for details.)

Figure 10

Upper panels: Ratio $\overline{R}$ in NO for different values of ${\overline{P}}_{ee}$. Histograms represent the results obtained from the inversion procedure, while dashed curves are obtained calculating $\overline{R}$ directly from the oscillated $\nu$ fluxes. The horizontal dashed line at $\overline{R}=6$ represents our threshold value: $\overline{R}>6$ excludes complete flavor equalization. Middle panels: Statistical errors for the case of complete flavor equalization. Lower panels: Statistical errors for the case with only matter effects. Left panels refer to the W model, while right panels are for the G model.

Figure 11

Ratio $R$ in NO in the same format as in Fig. 10. Values of $R>6$ exclude pure matter effects, while $R<6$ excludes complete flavor equalization.

Figure 12

Ratio of events in NO for the Garching model for a SN at $d=1\mathrm{kpc}$. Upper panels: Ratio $R$ (left) and $\overline{R}$ (right) for different values of ${\overline{P}}_{ee}$. Middle panels: Statistical errors for the case of complete flavor equalization. Lower panels: Statistical errors for the case of pure matter effects.

Figure 13

Ratio $R$ (upper panels) and $\overline{R}$ (lower panels) in IO. Left panels refer to the pure matter effects scenario, while right panels are for complete flavor equalization. The dot refers to the Wroclaw model, while the triangle is for the Garching one. The physical region in the high-energy spectral tails is below the dashed line corresponding to $x=\overline{x}$. (See text for details)

Figure 14

Ratio $\overline{R}$ in IO in the same format as in Fig. 10. In this case our threshold value is $\overline{R}=5$. $\overline{R}<5$ excludes complete flavor equalization.