Signs of pseudo-Dirac neutrinos in SN1987A data

Ever since the discovery of neutrinos, we have wondered if neutrinos are their own antiparticles. One remarkable possibility is that neutrinos have a pseudo-Dirac nature, predicting a tiny mass difference between active and sterile states. We analyze the neutrino data from SN1987A in the light of active-sterile oscillations and find a mild preference ($\mathrm{\Delta }{\chi }^2\approx 3$) for $\delta m^2=6.31\times {10}^{-20}{\mathrm{eV}}^2$. Notably, the same data is able to exclude $\delta m^2\sim [2.55,3.01]\times {10}^{-20}{\mathrm{eV}}^2$ with $\mathrm{\Delta }{\chi }^2>9$, the tiniest mass differences constrained so far. We further consider the next-generation of experiments and demonstrate their sensitivity exploring the nature of the neutrino mass.

Figure 1

Characteristic energies and baselines of distinct experiments with reactor (lilac), accelerator (green), atmospheric (light blue), solar (yellow), SN (emerald), DSNB (purple), and high energy (violet) neutrinos. Dotted lines indicate the sensitivity to $\mathrm{\Delta }{m}^2$ via vacuum oscillations; we show three specific values in red for $|\mathrm{\Delta }{m}_{3i}^2|,\mathrm{\Delta }{m}_{21}^2,\delta m^2$, where, in the normal ordering, $\mathrm{\Delta }{m}_{31}^2=2.51\times {10}^{-3}{\mathrm{eV}}^2,\mathrm{\Delta }{m}_{21}^2=7.42\times {10}^{-5}{\mathrm{eV}}^2$ [28], and $\delta m^2=6.31\times {10}^{-20}{\mathrm{eV}}^2$. The particular case for SN1987A is highlighted with the fuchsia rectangle.

Figure 2

Energy averaged neutrino flux times energy squared, $E_{\nu }^{2}d⟨{\mathrm{\Phi }}_{87}⟩/d{E}_{\nu }$, as function of the neutrino energy for the standard case, i.e., including only standard oscillations (green dashed) and introducing active-sterile oscillations (purple). We assumed ${\mathcal{E}}_{\mathrm{tot}}^e=2.9\times {10}^{53}\mathrm{erg}$, $E_{0e}=4\mathrm{MeV}$, $E_{0x}=13\mathrm{MeV}$, and $\delta m^2=6.31\times {10}^{-20}{\mathrm{eV}}^2$ in the PD case (purple), and ${\mathcal{E}}_{\mathrm{tot}}^e=1.2\times {10}^{53}\mathrm{erg}$, $E_{0e}=5\mathrm{MeV}$, $E_{0x}=15\mathrm{MeV}$ for the standard case (green).

Figure 3

Results of our analysis of the SN1987A data in the light of the PD scenario. Left: marginalized $\mathrm{\Delta }{\chi }^2$ as function of the quadratic mass difference $\delta m^2$ for the individual analysis of KII (light-blue dashed), IMB (green dotted), Baksan (orange dot-dashed), and the combined analysis (purple). Right: allowed regions for total energy ${\mathcal{E}}_{\mathrm{tot}}^e$ vs average energy, $E_0\equiv (E_{0e}+E_{0x})/2$. The black dashed is the allowed region without active-sterile oscillations at the $\mathrm{\Delta }{\chi }^2=9$ level.

Figure 4

Measured spectra (gray dashed lines) and individual observed events at KII (top), IMB (middle), and Baksan (bottom) as function of the positron energy $E_i$. We present the predicted spectra in the standard case (green) and including active-sterile oscillations (purple). The assumed parameters correspond to the best fit of the joint analysis, see Table 1.

Figure 5

Expected sensitivity on $\delta m^2$ as a function of ${\sigma }_x$ for DUNE (purple) and HK (green), together with the excluded region from SN1987A (blue) at more than 95% CL We assume that the SN occurs at 10 kpc.

Figure 6

Marginalized $\mathrm{\Delta }{\chi }^2$ for the joint fit of the three distinct datasets coming from KII, IMB, and Baksan as function of $\delta m^2$ for different priors on $⟨E_{0e,0x}⟩$.

Figure 7

Marginalized $\mathrm{\Delta }{\chi }^2$ for the joint fit of the three distinct datasets coming from KII, IMB, and Baksan as function of $\delta m^2$ for different values of $r_{xe}$ as discussed in the text.

Figure 8

Marginalized $\mathrm{\Delta }{\chi }^2$ for the joint fit of the three distinct datasets coming from KII, IMB, and Baksan as a function of $\delta m^2$ for different values of the pinching parameter $\alpha =0$ (orange dashed), 2.3 (purple), and 4 (green dotted).

Figure 9

Marginalized $\mathrm{\Delta }{\chi }^2$ for the joint fit of the three distinct datasets coming from KII, IMB, and Baksan in the plane $\delta m^2$ vs ${\sigma }_x$. The regions with $\mathrm{\Delta }{\chi }^2\le \{1,4,9\}$ correspond to the blue, green, and yellow colors, respectively. The white region is excluded at more than $\mathrm{\Delta }{\chi }^2>9$.

Figure 10

The number of events expected in HK (left) and DUNE (right) for a supernova happening at 10 kpc. For the supernova luminosity, we assume the best-fit value of the SN1987A. We show the number of events for three different scenarios: neutrinos are Dirac fermions, the best-fit point of the SN1987A analysis, and coherence lengths shorter than 10 kpc (decoherence). In particular, in the last case, we use the following parameters: $\delta m^2=5\times {10}^{-21}{\mathrm{eV}}^2,{\sigma }_x={10}^{-15}$ m