Testing decay of astrophysical neutrinos with incomplete information

Neutrinos mix and have mass differences, so decays from one to another must occur. But how fast? The best direct limits on nonradiative decays, based on solar and atmospheric neutrinos, are weak, $\tau \gtrsim {10}^{-3}\mathrm{s}$ ($m/\mathrm{eV}$) or much worse. Greatly improved sensitivity, $\tau \sim 10^3\mathrm{s}$ ($m/\mathrm{eV}$), will eventually be obtained using neutrinos from distant astrophysical sources, but large uncertainties—in neutrino properties, source properties, and detection aspects—do not allow this yet. However, there is a way forward now. We show that IceCube diffuse neutrino measurements, supplemented by improvements expected in the near term, can increase sensitivity to $\tau \sim 10\mathrm{s}$ ($m/\mathrm{eV}$) for all neutrino mass eigenstates. We provide a road map for the necessary analyses and show how to manage the many uncertainties. If limits are set, this would definitively rule out the long-considered possibility that neutrino decay affects solar, atmospheric, or terrestrial neutrino experiments.

Figure 1

Constraints on neutrino masses and lifetimes, as labeled and discussed in the text, with hatched gray disallowed, hatched white allowed only for some eigenstates, and unhatched white allowed for all. Solid lines are lower limits. The thick red dashed lines indicate the sensitivity estimates of this paper. Left: Normal hierarchy. Right: Inverted hierarchy.

Figure 2

Flavor content of mass eigenstates ${\nu }_1$, ${\nu }_2$, and ${\nu }_3$, in the NH (results for the IH are very similar [24]). The regions are generated using the best-fit value of the mixing parameters (light yellow), and their $1\sigma$ (darker) and $3\sigma$ (darkest) uncertainty ranges from Ref. [31]. IceCube astrophysical flavor composition measurements [8] are shown. Values are read parallel to their ticks. Figure modified from Fig. 1 in Ref. [24].

Figure 3

Decay damping $D$ as a function of redshift, for a fixed received neutrino energy $E_0=1\mathrm{PeV}$ and different values of lifetime $\tau /m$. The background shading is darker the higher the differential diffuse flux, assuming $\gamma =2.50$ (see Fig. 9).

Figure 4

Decay damping $D$ as a function of neutrino lifetime, for different values of neutrino energy. The bands are generated by varying the redshift between 0.5 and 6.

Figure 5

Diffuse neutrino fluxes ${\mathrm{\Phi }}_{\alpha }$ ($\alpha =e$, $\mu$, $\tau$) as functions of energy, without and with decay. The fluxes of antineutrinos are identical. The flavor ratios at the sources are ${(\frac{1}{6}:\frac{2}{6}:0)}_{\mathrm{S}}$ separately for neutrinos and antineutrinos. Mixing parameters are fixed to their best-fit values [31]. A lifetime of $\tau /m=10\mathrm{s}{\mathrm{eV}}^{-1}$ applies to ${\nu }_2$, ${\nu }_3$ (NH), and ${\nu }_1$, ${\nu }_2$ (IH). The “no decay” lines for ${\nu }_{\mu }$ and ${\nu }_{\tau }$ cover each other. See text for details.

Figure 6

Allowed ${\nu }_{\alpha }+{\overline{\nu }}_{\alpha }$ flavor ratios at Earth with decay to ${\nu }_1$ (NH). For each value of the decay damping $D$, the region is generated by scanning over all possible flavor ratios at the source and mixing parameters within $3\sigma$ [31]. The flavor-content region of ${\nu }_1$ is outlined in dashed yellow [24].

Figure 7

Shower spectrum at IceCube, assuming five years of exposure. The detector energy resolution is set to $\delta E_{\mathrm{sh}}/E_{\mathrm{sh}}=0.1$ [126]. Left: Using a flux $\propto E^{-2.50}$ [8]. Right: Using a flux $\propto E^{-2.13}$ [11]. Note the change in scale. Contributions of ${\nu }_{\tau }$-initiated showers are not added. See text for details.

Figure 8

Number of showers in IceCube in the range 5–8 PeV, as a function of the common lifetime of the two heavier mass eigenstates, assuming five years of exposure. Left: Using a flux $\propto E^{-2.50}$ [8]. Right: Using a flux $\propto E^{-2.13}$ [11]. Note the change in scale. The probability $P_{n\ge 1}$ of detecting one or more events under complete decay in the IH is only $\sim 16\%$ (left) or $\sim 31\%$ (right). Therefore, if even a single event is detected in the energy range of the Glashow resonance, that will disfavor complete decay in the IH. With higher statistics, the significance will increase rapidly. See text for details.

Figure 9

Differential neutrino diffuse flux $d\mathrm{\Phi }/dz$, from Eq. (b6), as a function of redshift, for two choices of spectral index $\gamma$, following IceCube results. Each curve is individually normalized to its maximum value.

Figure 10

Components of the shower spectrum at IceCube, assuming a flux $\propto E^{-2.13}$ [11] and five years of exposure. The detector energy resolution is set to $\delta E_{\mathrm{sh}}/E_{\mathrm{sh}}=0.1$ [126]. See text for details.