The Sun and core-collapse supernovae are leading probes of the neutrino lifetime

. The large distances travelled by neutrinos emitted from the Sun and core-collapse supernovae together with the characteristic energy of such neutrinos provide ideal conditions to probe their lifetime, when the decay products evade detection. We investigate the prospects of probing invisible neutrino decay capitalising on the detection of solar and supernova neutrinos as well as the diffuse supernova neutrino background (DSNB) in the next-generation neutrino observatories Hyper-Kamiokande, DUNE, JUNO, DARWIN, and RES-NOVA. We find that future solar neutrino data will be sensitive to values of the lifetime-to-mass ratio τ 1 /m 1 and τ 2 /m 2 of O (10 − 1 –10 − 2 ) s/eV. From a core-collapse super-nova explosion at 10 kpc, lifetime-to-mass ratios of the three mass eigenstates of O (10 5 ) s/eV could be tested. After 20 years of data taking, the DSNB would extend the sensitivity reach of τ 1 /m 1 to 10 8 s/eV. These results promise an improvement of about 6–15 orders of magnitude on the values of the decay parameters with respect to existing limits.

A Statistical analysis and χ 2 -functions 27 1 Introduction The observation of neutrino oscillations provides evidence that neutrinos are massive particles.As a direct implication of non-zero masses, one also finds that at least the two heaviest neutrino mass eigenstates may be unstable. 1Neutrino decay has not been observed yet, but in some extensions of the Standard Model, the predicted neutrino lifetime is larger than the age of the Universe, making neutrinos effectively stable [1].However, the size of the neutrino lifetime predicted varies significantly for different scenarios [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. 1 Since there is a vast number of Standard Model extensions in which neutrinos become unstable, it is useful to introduce the following classification.We denote neutrino decays in which the final-state particles are experimentally accessible as visible decays.Conversely, we refer to decays in which the final products escape detection as invisible decays.Alternatively, decay modes can also be classified into two categories, radiative and non-radiative neutrino decays, depending on whether there is a photon in the final state.
In this paper, we focus on non-radiative invisible decays of neutrinos (i.e.those in which the decay products are not observable).We find it convenient to work in terms of the decay width of the mass eigenstate in its rest frame, Γ i (where the index i indicates the mass eigenstate), instead of the usually adopted ratio between the neutrino lifetime (τ i ) and the mass (m i ).The motivation for this choice is that the absolute neutrino decay width simply results from the sum of the decay width of each channel.Hence, the decay parameter is One could think that neutrinos travelling longer distances would be especially suited to probe the neutrino lifetime.Note, however, that neutrino lifetimes are well-defined in their rest frame.Then, one expects to be sensitive to neutrino lifetimes τ i ∼ t T OF /γ i , where γ i is the Lorentz factor and t T OF is the neutrino time-of-flight.
Invisible neutrino decay can also be constrained through cosmological observables.For instance, Big Bang Nucleosynthesis requires neutrino lifetimes larger than 10 −3 s at 95% C.L. [29].Additionally, the neutrino lifetime and its mass can be explored exploiting the fact that the data from the cosmic microwave background (CMB) agree well with neutrinos free streaming at the temperature of photon decoupling [29][30][31][32][33][34][35].For instance, for a neutrino mass eigenstate ν i decaying into a lighter sterile neutrino ν 4 and a massless scalar particle, ϕ,one can constrain τ ν i →ν 4 +ϕ > (4 × 10 5 → 4 × 10 6 ) s (m ν i /0.05 eV) 5 , depending on the model [34].Furthermore, one can study how the matter power spectrum and lensing of the CMB would be modified if neutrinos decayed invisibly when non-relativistic [36,37].In the near future, data from Euclid, when combined with other cosmological probes, would provide an independent measure of the sum of neutrino masses and lifetime [38].
For what concerns neutrinos of astrophysical origin, one may consider setting limits on neutrino invisible decay from the high-energy neutrinos observed by the IceCube Neutrino Observatory [39][40][41].However, in this case, even though neutrinos travel over cosmic distances, their energy is so large that the effect of neutrino decay on the detectable signal may be suppressed.Better constraints come from a combination of solar datasets [42][43][44].Current limits from invisible neutrino decay take into account information from 7 Be neutrinos at Borexino [45] and KamLAND [46] and 8 B neutrinos at SNO [47], Super-Kamiokande [48], KamLAND [49] and Borexino [50].They also include the analysis of data from the Homestake chlorine detector [51] and from the neutrino capture rate in Gallium at GNO, GALLEX, Figure 1.Excluded regions at 90% C.L. in the plane spanned by the invisible neutrino decay parameters α 1 and α 2 obtained in this work from solar and CCSN neutrinos as well as the DSNB (shown in green, orange and blue, respectively).We also derive limits on neutrino decay from the observation of neutrinos from SN 1987A in red.For details on the derivation of the projected limits, we refer the reader to Secs. 3 to 5. Solar data could set limits about 20 times more stringent than the current ones, whereas from a CCSN at 10 kpc, the sensitivity would improve up to 6-7 orders of magnitude.After 20 years of data taking, the DSNB could improve current bounds on α 1 of about 10 orders of magnitude.
and SAGE [52].At 2σ C.L., the limits read [53,54] α 1 < 1.6 × 10 −13 eV 2 and α 2 < 4.5 × 10 −13 eV 2 , ( or in terms of the ratio between neutrino lifetime and mass, Despite the limited amount of available data, the detection of electron antineutrinos from SN 1987A also provides constraints on invisible neutrino decay.Such limits are generally quoted as the electron-neutrino lifetime: τ νe > 1.7 × 10 5 [m νe /E νe ] [55], where E νe is the electron-neutrino energy and m νe is an effective mass, not properly defined.Current searches for the diffuse supernova neutrino background (DSNB) at Super-Kamiokande are already excluding the most optimistic DSNB models [56].Nonetheless, since the signature of invisible neutrino decay is a reduction of the flux with respect to its theoretical prediction, the lack of data on the DSNB has not provided useful insights into this new physics scenario.This will change soon due to the ongoing enrichment of Super-Kamiokande with Gadolinium [57].
In this work, we explore the prospects for constraining invisible neutrino decay through upcoming large-scale neutrino telescopes relying on neutrinos with energy O(0.1-100) MeV from the Sun and core-collapse supernovae (CCSNe), which seem to hold the optimal combination between neutrino energy and distance from the source.Figure 1 summarises our forecast from solar neutrinos, neutrinos from a galactic CCSN, and the DSNB, together with our recast limits from SN 1987A.Our projected sensitivities take into account uncertainties on the sources for the first time.We can immediately see that the upcoming detection of neutrinos from these sources will provide the most stringent constraints on the invisible neutrino decay parameters α 1 and α 2 through direct neutrino detection.Depending on the value of neutrino masses, the bounds from cosmology could be more stringent than the ones obtained in this work, but they would not be based on the direct detection of neutrinos.
This paper is organised as follows.In Sec. 2, we outline the main features of the next-generation neutrino observatories considered in this work (Hyper-Kamiokande, JUNO, DUNE, DARWIN, and RES-NOVA).Section 3 focuses on the impact of invisible neutrino decay on the signal expected from solar neutrinos, while Sec. 4 presents the forecasted exclusion region of the invisible neutrino decay parameter space obtained relying on CCSN neutrinos, and Sec. 5 investigates the constraining power of the DSNB.Finally, Sec. 6 summarises our main findings.Details on the statistical analysis are provided in Appendix A.

Next-generation neutrino observatories
In this section, we outline the main features of the upcoming neutrino observatories considered to explore the chances to constrain invisible neutrino decay: Hyper-Kamiokande, JUNO, DUNE, DARWIN, and RES-NOVA.We focus on the most relevant detection channels for each detector for the physics case under investigation and the energy range of relevance.

Hyper-Kamiokande
Hyper-Kamiokande [58] is the next-generation underground water Cherenkov detector, and successor of Super-Kamiokande.In its ideal configuration, it will consist of two tanks with a fiducial volume of 187 kt each.The main detection channel for astrophysical neutrinos is inverse beta decay (IBD): νe + p −→ e + + n, with an which depends on the number of targets (N t = 2.5×10 34 for each tank), and the cross-section, σ IBD [59].The response function of the detector, K IBD , relates the true and reconstructed energy of the positron (and, hence, of the neutrinos), which we denote by E ′ e and E e respectively.For the detection channels of interest, we adopt the following parametrisation for the response function where δ(v) is the energy resolution.In particular, for the IBD detection channel in Hyper-Kamiokande, we take δ(E e )/E e = 0.1/ E e [MeV].Assuming a 0.1% loading of both tanks with Gadolinium, the IBD detection efficiency is expected to be ε IBD = 0.67 [58], which includes the efficiency of neutron capture and the detection of 8 MeV photons2 .
Another relevant channel for MeV neutrinos in Hyper-Kamiokande is the elastic scattering on electrons (ES), ν α + e − , with α = e, x, where x denotes the non-electron flavours.Its importance relies on the fact that it provides a measurement of the total flux.The event rate, for a given neutrino flux Φ νe , is which includes the contributions from neutrinos and antineutrinos of the three active flavours.
Here T ′ e denotes the true electron recoil kinetic energy and T e is the reconstructed one.The cross-section σ ES,νx depends on the flavour of the incoming neutrino or antineutrino [59].The response function of the detector, K ES , with the same resolution of Super-Kamiokande-III [61], is with E e = T e + m e .We consider an efficiency ε ES = 0.68 arising from a cut in the angular distribution of the recoil electron [62].Note that the maximum electron recoil kinetic energy depends on the energy of the incoming neutrino, and the number of target electrons is N t = 1.25 × 10 35 per tank.Two other channels can contribute significantly to the number of events expected from a CCSN: ν e + 16 O −→ e − + 16 F * and νe + 16 O −→ e + + 16 N * [63], which however we neglect in this work.This choice is conservative since the inclusion of additional detection channels would increase the collected statistics.

JUNO
The Jiangmen Underground Neutrino Observatory (JUNO) [64] is a next-generation liquid scintillator detector suitable for the observation of electron antineutrinos from astrophysical sources via IBD.The expected event rate is For a fiducial volume of 17 kt, the corresponding number of targets is N t = 1.2 × 10 33 .The other channels of potential relevance for the study of low-energy astrophysical neutrinos, such as neutrino ES on protons, neutral current interactions on 12 C and charged-current interactions of electron neutrinos and antineutrinos on 12 C, are neglected in this work.

DUNE
The upcoming Deep Underground Neutrino Experiment (DUNE) [65] is also suitable for the study of astrophysical neutrinos with energies above O(10) MeV.The main detection channel is charged-current electron-neutrino scattering on argon ( ν e + 40 Ar → e − + 40 K * ).
The event rate from electron neutrino charged-current interactions as a function of the reconstructed neutrino energy is where τ denotes the exposure time and N t = 6.02 × 10 32 is the number of targets, corresponding to a fiducial volume of 40 kt.The cross-section for the detection process (σ νeCC ) is taken from SNOWGLoBES [69] and ε DUNE denotes the detection efficiency.We also account for the response function of the detector, K DUNE , resulting from a Gaussian energy resolution [67,70,71] with δ(E ν )/E ν = 0.2.

DARWIN
Primarily conceived as dark-matter detectors, the physics program of ton-scale Xenon experiments extends to the investigation of astrophysical neutrinos [72].The capability of the DARk matter WImp search with liquid xenoN (DARWIN) [73] to detect low-energy nuclear recoil energy opens the possibility of investigating low-energy astrophysical neutrinos interacting in the detector via Coherent Elastic Neutrino-Nucleus Scattering (CEνNS) [74].The rate of neutrino-induced nuclear recoils is where N t is the number of targets, ε CEνNS is the detection efficiency, E ′ R is the true nuclear recoil energy and E R is the reconstructed one.Notice that this is a flavour-insensitive channel that provides a measurement of the total neutrino flux.DARWIN's 30 tons of Xe correspond to N t = 1.83 × 10 29 targets.We assume perfect detection efficiency and energy resolution defined as [75] δ DARWIN will be sensitive to low-energy electron recoils, enabling the study of neutrino ES on electrons as well.The expected event rate for this channel is the same as in Eq. (2.3), with an energy resolution given by δ(T e ) T e = 0.3171 and an energy threshold of 1 keV [76].Notice that for ES on electrons, the number of target electrons is N t = 9.92 × 10 30 .

RES-NOVA
Similar to DARWIN, astrophysical neutrinos can also be detected by the archaeological-leadbased detector RES-NOVA [77], relying on CEνNS.We consider Phase-III of the planned detector, with a mass of 341 tons of PbWO 4 [78].The interaction rate is the same as the one in Eq. 2.8, but one needs to account for CEνNS on the three elements present in the crystals of PbWO 4 .Besides that, for simplicity, we assume perfect detection efficiency and energy resolution, and a threshold of 1 keV [79].
3 Solar neutrinos in the presence of invisible neutrino decay In this section, we introduce the signal expected from solar neutrinos and explore how such a signal is modified in the presence of invisible neutrino decay.We then present the bounds from solar neutrinos on invisible neutrino decay expected from the next-generation neutrino observatories Hyper-Kamiokande, DUNE, and DARWIN.

Solar neutrino conversion probabilities
Neutrinos are copiously produced in the nuclear reactions powering the Sun [80].A flux of neutrinos with energy up to ∼ 18 MeV results from the effective reaction 4p + 2e − −→ 4 He + 2ν e , consisting of several subprocesses, whose neutrinos are dubbed pp, 7 Be, pep, 8 B and hep neutrinos, depending on the specific production channel.Additionally, neutrinos are also produced in the CNO fusion cycle, as confirmed by Borexino [81,82].
The predicted flux of solar neutrinos is given by the Standard Solar Model (SSM).In this work, we consider the high-metallicity SSM B16-GS98 [83], which is favoured by Borexino data [82].This choice of SSM also determines the uncertainty in the flux normalisation of each reaction chain.For illustrative purposes, we display the contributions to the total solar neutrino flux at Earth in the top panel of Fig. 2.
The Mikheyev-Smirnov-Wolfenstein (MSW) effect [84,85] and the loss of coherence along propagation are responsible for the energy-dependent flavour composition of the solar neutrino flux detected on Earth [86].In the presence of neutrino decay, the picture is slightly modified.Assuming that neutrinos can only decay en route to Earth but not inside the Sun, the expected electron-neutrino oscillation probabilities to the flavour α are given by Here, U αi denotes the elements of the lepton mixing matrix, A(ν e → ν i ) is the amplitude of conversion of ν e into the mass eigenstate ν i at the surface of the Sun for a given neutrino energy E, d ⊙ = 1.5 × 10 8 km is the distance of the Sun from Earth, and α i are the decay parameters introduced in Eq. 1.1.The argument of the exponential in Eq. 3.1 is which allows to estimate the order of magnitude of the decay parameters α i that solar neutrinos can test.We compute flavour conversions numerically and take into account the different production regions for each of the reactions responsible for the solar neutrino flux.For the oscillation parameters, we adopt the best-fit values from Ref. [87].
For simplicity, we neglect electron-neutrino regeneration as a consequence of matter effects on Earth, responsible for the so-called day-night asymmetry [88][89][90].Such matter effects become more prominent as the energy increases and can be neglected below 3 MeV.For comparison, the survival probability in the absence of invisible neutrino decay is displayed (blue dashed line).In all cases, the probability is computed for the SSM GS98-16 and weighted according to the contribution of each chain to the total solar neutrino flux for each neutrino energy.One can see that invisible neutrino decay induces an overall reduction of the survival probability; this effect is inversely proportional to the neutrino energy.
On the other hand, the signature of neutrino decay is more evident as the neutrino energy decreases.Since the most stringent limits on neutrino decay are expected from the study of pp neutrinos, with energy below 0.5 MeV, it is safe to neglect matter effects on Earth.As a result of the reduction in the survival and flavour conversion probabilities, the main signature of invisible neutrino decay in solar neutrino experiments is a reduction of the measured flux.As one can see from Eq. 3.1, the effect is inversely proportional to the neutrino energy.This can be seen in Fig. 2, where the dependence of the ν e survival probability on the decay parameters α 1 and α 2 is illustrated.Note that the fraction of ν 3 that arrives at Earth is approximately sin 2 θ 13 ∼ 0.02 .Then, even if all ν 3 decayed invisibly on their way to Earth, the variation in the total flux would be negligible given the uncertainties from the SSM predictions on the flux normalisation.Therefore, one does not expect any meaningful bound on τ 3 /m 3 from solar neutrino data for invisible neutrino decay. 4

Expected solar neutrino event rate
Figure 3 shows the prospects for solar neutrino detection at the next-generation observatories Hyper-Kamiokande, DUNE, and DARWIN.As its predecessor, Super-Kamiokande, Hyper-Kamiokande will be sensitive to 8 B and hep neutrinos from the Sun via ES on electrons [93].Our analysis considers the flux from both chains and the corresponding electron-neutrino survival and non-electron neutrino appearance probabilities.We perform the analysis in terms of the ratio between the expected event rate and the event rate in the absence of flavour conversions and decays. 5We account for energy-uncorrelated systematic uncertainties of the same order of magnitude as in Super-Kamiokande IV [95], which encode the impact of backgrounds and other uncertainties in the analysis, and consider an energy threshold of 4.5 MeV [71].In the left panel of Fig. 3, we display the expected number of events with and without neutrino decay for Hyper-Kamiokande as a function of the electron recoil energy, assuming perfect detection efficiency.
The low-energy physics program of DUNE features the investigation of solar neutrinos from 8 B and hep nuclear chains [66,67,71].Our expected number of events is displayed in the middle panel of Fig. 3.We account for backgrounds from 222 Rn and neutron capture with a free normalisation and 90% detection efficiency across all energies [67].Moreover, we set a low-energy threshold of 9 MeV for the reconstructed neutrino energy [71], since below those energies the backgrounds would completely overwhelm the signal.
DARWIN stands out for its sensitivity to low-energy neutrinos from pp thermonuclear reactions in the Sun via neutrino ES on electrons [76,96], see the right panel of Fig. 3.Note that, in addition, DARWIN would be sensitive to 7 Be neutrinos via ES and 8 B neutrinos via CEνNS; however, lower statistics is expected from these channels [76].We take into account the background from 124 Xe decays via double electron capture, assuming an abundance of 0.1% for this isotope [76].Relevant background contributions are also expected from 136 Xe, which undergoes double-beta decays [97].However, they could be removed by isotopic depletion and hence we neglect them [76,96].
In what follows, we do not consider the number of events expected from solar neutrinos in RES-NOVA.In fact, since the energies of solar neutrinos are relatively low, most of the nuclear recoil energies are lower than realistic energy thresholds for this experiment [98].Regarding JUNO, it will be sensitive to solar neutrinos, but its sensitivity to 8 B neutrinos will not be competitive with the one of Hyper-Kamiokande [99].JUNO is also expected to further reduce the uncertainties in the measurement of 7 Be and pep neutrinos [100].However, as shown in the next section, the bounds on neutrino decay are dominated by the measurement of the less energetic pp neutrinos.

Constraints on invisible neutrino decay from solar neutrinos
In our analysis, we assume an exposure of 300 t•year for DARWIN and 400 kt•year for DUNE.For Hyper-Kamiokande, we consider an exposure of 3740 kt•year.In all three cases, the exposures correspond to 10 years of data taking with the full detector configuration.We follow two approaches.In the first one, we allow for the absolute flux normalisation of each neutrino chain to vary freely.In the second one, we include priors on such flux normalisations, mainly σ pp = 0.5%, σ8 B = 4% and σ hep = 30%, based on the uncertainties of the SSM adopted [83].The sensitivity of each experiment and a combined fit is presented in Fig. 4, both with and without priors.For further details of the statistical analysis, we refer the reader to Appendix A.
Note that we do not explore the degeneracy between the oscillation and decay parameters [101].In fact, the medium-baseline reactor experiment JUNO will provide an accurate determination of the solar and reactor mixing angles, as well as the two mass splittings [64].With an average baseline of ∼ 52 km and given the current constraints in Eq. 1.2, the determination of the oscillation parameters by JUNO will be independent of neutrino decay.
A joint analysis of Hyper-Kamiokande and DUNE solar data will provide an accurate determination of the 8 B flux, since using two detection channels allows to break the degeneracy between the 8 B flux normalisation and the solar mixing angle [71,102].The reason is that the ES signal in Hyper-Kamiokande provides complementary information on the flavour composition of the flux and its absolute normalisation, while DUNE is only sensitive to electron neutrinos.Hence, one expects a joint fit to significantly improve the results with respect SOLAR NEUTRINOS to the individual experimental capabilities and break the degeneracy with the solar mixing angle [66].
Concerning the sensitivity of DARWIN, there exists a large degeneracy between the decay parameters and the absolute pp-neutrino flux normalisation.As shown in the left panel of Fig. 4, without prior information on the pp flux normalisation, DARWIN constraints on α 1 and α 2 are compatible with ν 2 almost decaying completely.Notice, however, that a combined fit with Hyper-Kamiokande and DUNE would exclude that region of the parameter space.Conversely, if one includes a prior on the pp flux normalisation, the bounds from DARWIN become significantly more stringent, as shown in the right panel of Fig. 4. In this case, a combined fit with 8 B neutrino data would not be of such relevance as DARWIN on its own dominates the constraints.
The expected exclusion regions from the combined analysis at 90% C.L. for one non-zero decay width at a time are α 1 < 6.4 × 10 −15 eV 2 and α 2 < 1.9 × 10 −14 eV 2 , ( or analogously, These limits are more than one order of magnitude more stringent than the current ones.This highlights the potential of DARWIN.Note that existing sensitivity studies on neutrino decay in xenon-based experiments consider a smaller energy range for the study of the signal and lower exposures [103], leading to weaker constraints than the ones presented in this work.

Supernova neutrinos in the presence of invisible neutrino decay
In this section, we introduce the signal expected from CCSN neutrinos and explore how it is modified by invisible neutrino decay.We then present the bounds from CCSN neutrinos on invisible neutrino decay, investigating the impact of the uncertainties on the neutrino flavour conversion physics in the stellar envelope, as well as the uncertainties on the CCSN properties and its distance.We explore the sensitivity of Hyper-Kamiokande, DUNE, RES-NOVA and DARWIN, as well as the impact of a combined analysis.We also present bounds on invisible neutrino decay obtained relying on the SN 1987A neutrino observations.

Supernova neutrino flux
Despite the significant progress made in recent years on the theory underlying the collapse of massive stars, our understanding remains incomplete, especially for what concerns the expected neutrino signal [104][105][106][107][108][109].In order to derive relevant bounds on invisible neutrino decay, we choose to focus on the neutronisation burst, which is with good approximation insensitive to astrophysical uncertainties [110,111].
In order to take into account variations in the neutrino emission properties due to the supernova mass, we rely on one-dimensional spherically symmetric hydrodynamical simulations [104,112] and consider CCSN models with mass of 11.2M ⊙ and 27M ⊙ .In addition, we use a black-hole forming collapse model with mass of 40M ⊙ (model s40s7b2) [104].All models employ Lattimer and Swesty equation of state with a nuclear incompressibility modulus of K = 220 MeV [113].
The flavour composition of the observed neutrino signal depends on neutrino interactions with the medium and among themselves [104].During the neutronisation burst, it is expected that the neutrino signal should be mostly affected by MSW conversion [114].Hence, we have: where Φ να and Φ να denote the final number of neutrinos and antineutrinos of a given flavour α, i.e. for electron and non-electron flavours (the latter being denoted with x) and the superscript 0 denotes the neutrino flux before flavour conversion.The probabilities p and p are defined according to the neutrino mass ordering as [114] p = |U e3 | 2 , (normal ordering, NO) and we calculated them using the best-fit values of the oscillation parameters from Ref. [87].
In the light of uncertainties on the physics linked to neutrino-neutrino interactions, we also consider other two mixing scenarios, one with maximum flavour conversion within the con-straints of conservation of the neutrino lepton number per flavour [115]: and the case with no flavour conversion for comparison.
Similarly to the case of solar neutrinos, one can estimate the order of magnitude of the decay parameters testable from a core-collapse supernova explosion from the fact that .9)

Expected supernova neutrino event rate
Figure 5 shows the expected sensitivity to invisible decay of active neutrinos with Hyper-Kamiokande, DUNE, DARWIN, and RES-NOVA for a CCSN with mass of 11.2M ⊙ and flavour composition resulting from the MSW effect for inverted ordering.Notice that, since the neutronisation burst lasts for about 50 ms, we assume our analyses to be background free.The main detection channel in Hyper-Kamiokande is IBD, whose number of events for a threshold of 3 MeV in the positron energy [58] is displayed in the top left panel of Fig. 5. Hyper-Kamiokande is also sensitive to neutrinos and antineutrinos of all flavours via ES on electrons, as displayed in the top right panel of Fig. 5. Its importance relies on the fact that it provides a measurement of the total flux.For DUNE (bottom left panel of Fig. 5), we consider a threshold of 5 MeV in the reconstructed neutrino energy [68].Being sensitive to electron neutrinos, DUNE is ideal to probe the neutronisation burst.The number of events expected in DARWIN and RES-NOVA is displayed in the bottom right panel of Fig. 5.The employment of DARWIN and RES-NOVA is particularly relevant since these detectors are insensitive to the neutrino flavour and, therefore, allow to further constrain the hypothesis of invisible neutrino decay.We do not include JUNO in our forecast analysis since its main detection channel is IBD, like in Hyper-Kamiokande, but with lower statistics due to the difference in their respective fiducial volume.Hence, our joint analysis would be dominated by the Hyper-Kamiokande constraints.However, JUNO would be crucial if the next galactic CCSN occurred before Hyper-Kamiokande was operational, as well as for real-time monitoring and to better discriminate the CCSN properties [116].
Note that Ref. [117] provided stronger projected sensitivity to α 1 and α 2 from Hyper-Kamiokande than the ones presented here.Such constraints rely on simplistic assumptions such as the accurate knowledge of the neutrino energy distribution and evolution of the neutrino signal (including the accretion and cooling phases) as well as the flavour composition of the emitted flux.In this work, we instead account for uncertainties on the expected neutrino signal and flavour composition focusing on the best understood phase of a CCSN: the neutronisation burst.

Constraints on invisible neutrino decay from supernova neutrinos
A network of neutrino observatories sensitive to CCSN neutrinos using different detection channels is necessary to derive meaningful constraints which account for the uncertainties .Expected number of events in time bins of 10 ms for a 11.2M ⊙ stellar collapse occurring at 10 kpc from Earth.The top left and right panels correspond to the expected number of events for IBD and ES, respectively, in Hyper-Kamiokande.The bottom left panel displays the predicted number of events at DUNE and the bottom right shows the number of CEνNS events to be observed by RES-NOVA and DARWIN (solid and dashed lines, respectively).In all cases, inverted mass ordering is considered for illustrative purposes.intrinsic to the signal [118].Focusing on the limits on α 2 as an example, Fig. 6 illustrates the potential of a combined analysis of the data collected at different experiments for a CCSN with a mass of 11.2 M ⊙ occurring at 10 kpc, and neutrino mixing resulting from the MSW effect for inverted ordering (cf.Appendix A for details on the statistical analysis).
The top left panel of Fig. 6 shows the sensitivity of each experiment to the decay parameter α 2 , if the emitted flux and flavour composition were perfectly known.The top right panel displays the expected sensitivity, if one knew the neutrino emission, marginalising over the different mixing schemes introduced previously.Conversely, in the bottom left panel, we assume that the flavour composition is known and marginalise over our three CCSN models.Finally, the bottom right panel shows how the sensitivity of each experiment worsens once one marginalises over the mixing schemes and CCSN models.
Figure 6 highlights how the existing uncertainties on the CCSN neutrino signal affect SUPERNOVA NEUTRINOS Figure 7. Sensitivity to the decay parameters α 1 , α 2 and α 3 for the MSW scenario in normal and inverted ordering for a CCSN at 10 kpc.We rely on a combined analysis of the detection channels and neutrino observatories and marginalise with respect to the CCSN distance and model.
the constraints inferred from different neutrino observatories.However, one can see that, in a combined analysis, strong bounds are recovered since the complementary information provided by the different detection channels breaks the existing degeneracies.Among the low-energy astrophysical signals considered in this work, the neutrino signal from a galactic CCSN is the only one that in principle allows to set constraints on the decay of the three neutrino mass eigenstates individually.Figure 7 shows the expected sensitivity for the three decay parameters for a CCSN at 10 kpc, for the MSW scenario in both mass orderings.These limits take into account the uncertainties in the neutrino emission and flavour composition, following the marginalisation procedure previously outlined: Notice that, for the neutrino observatories considered in this work, the detection of IBD events in Hyper-Kamiokande drives the sensitivity to CCSN neutrinos.Then, the expected limits for α 1 are stronger than for α 2 and α 3 because νe has a larger fraction of ν1 than ν2 and ν3 .
It is interesting to asses how the prospects of constraining invisible neutrino decay through CCSN neutrinos would depend on the distance of the stellar collapse from Earth.The results assume a combined analysis of data collected at Hyper-Kamiokande, DUNE, RES-NOVA, and DARWIN after marginalising over the three SN models and the different mixing schemes.Note that the limits for α 2 and α 3 degrade significantly with the distance, while this is not the case for α 1 .
To this end, Fig. 8 shows the sensitivity to each of the three decay parameters from a combined analysis of Hyper-Kamiokande, DUNE, RES-NOVA, and DARWIN, assuming that the CCSN occurs at different distances ranging from 5 to 50 kpc.One can see that the limits for α 2 and α 3 degrade significantly with the distance.For α 2 , this is due to the challenges in breaking the degeneracy between the mixing schemes with low statistics.For α 3 , the reason is that the limits are driven by RES-NOVA and DARWIN, which in general would collect fewer statistics than the IBD detectors.Figure 9 summarises the constraints on invisible neutrino decay in the planes (α 1 , α 2 ) and (α 2 , α 3 ).These limits assume a CCSN at 10 kpc from Earth.

Constraints on invisible neutrino decay from SN 1987A
The detection of electron antineutrinos from SN 1987A has been employed to constrain the neutrino lifetime [55].In order to infer the lifetime for invisible neutrino decays, the observed time-integrated flux of electron antineutrinos from SN 1987A is approximately given by where Φ 0 νe and Φ 0 νx indicate the time-integrated fluxes of electron and non-electron antineutrinos emitted by SN 1987A (note that in this case we consider the whole time interval over which neutrinos have been observed, i.e. 6 s, and do not focus on the neutronisation burst SUPERNOVA NEUTRINOS only).The distance of SN 1987A from Earth is estimated to be D = 51.4kpc [? ] and ⟨E⟩ = 12.5 MeV is the average energy of the emitted antineutrinos from the events recorded up to 6 s after bounce [119]. 6igure 10 shows our bounds on the invisible decay of ν1 and ν2 .Such constraints have been obtained assuming that the total energy emitted in νe 's from SN 1987A corresponds to the largest one obtained in the suite of simulations of Ref. [119], i.e. it is the total energy of νe 's (E νe ∼ 7.5 × 10 52 erg) emitted from the CCSN model with a 20M ⊙ progenitor, a protoneutron star mass of 1.93M ⊙ and the SFHx version of Steiner, Fischer, and Hempel equation of state [120].We contrast the total energy emitted in νe 's predicted from theory with the lowest value of the νe energy allowed by the data in the analysis presented in Ref. [119], E νe ∼ 2 × 10 52 erg.Requiring that neutrino decay is responsible for the difference between the largest predicted νe energy and the lowest bound on the observed one, we derive limits on the decay parameters following Eq.4.16.
These limits on invisible neutrino decay depend on how large the emitted flux of nonelectron antineutrinos is with respect to the one of electron antineutrinos.The impact of the assumptions of such ratio is shown in Fig. 10.We assume that the best-fit mean energy for νe 's is the same as for the non-electron flavours, for simplicity.As expected, for a larger total neutrino emission (dashed line), the bounds become stronger.The asymmetry in the exclusion region in the plane α 1 -α 2 displayed in Fig. 10 results from the different fraction of ν1 and ν2 in νe .
In Fig. 1, we display the SN 1987A bound corresponding to equal luminosity for the three antineutrino flavours as representative case.Such exclusion regions are based on coarse assumptions and should be interpreted as indicative yet not strict limits.
Finally, since only electron antineutrinos were detected from SN 1987A, and those are They have been obtained considering the overall duration of the neutrino signal, instead of focusing on the neutronisation burst only and rely on the recent analysis of the SN 1987A data presented in Ref. [119] (see main text for details).
mainly composed by ν1 and ν2 , even if all ν3 decayed invisibly, the impact on the observed luminosity would be negligible.In the future, such limitation could be overcome through the inclusion of data from detection channels sensitive to non-electron flavours, i.e.ES on electrons and CEνNS.
5 Diffuse supernova neutrino background in the presence of invisible neutrino decay In this section, after modeling the DSNB signal expected at Hyper-Kamiokande, DUNE, and JUNO, we investigate the sensitivity of the DSNB to invisible neutrino decay and its constraining power.

Diffuse supernova neutrino background
The DSNB is the cumulative flux of neutrinos emitted from all CCSN explosions that occur and have occurred in the Universe [104,[121][122][123].In order to model the DSNB, we rely on the CCSN models introduced in Sec. 4 and assume that flavour transformation is solely due to the MSW effect and loss of coherence when travelling to Earth.The DSNB depends on the CCSN rate, R SN , which depends on the redshift (z): Here, we have introduced the initial mass function, η(M ), and the star formation rate, ρ * .
For the former, we assume it follows the Salpeter law [124], i.e.
whereas the star-formation rate is defined as [125] ρ * ∝ (1 + z) −34 + 1 + z 5000 In addition, we chose a normalisation of the supernova rate such that The DSNB for each neutrino mass eigenstate is where H 0 = 70 kms −1 Mpc −1 [127], c is the speed of light, and we adopt z max = 5.The dark matter and cosmological constant energy density are Ω M = 0.3 and Ω Λ = 0.7 [128].In addition, the redshifted neutrino energy at Earth is E ′ = E(1 + z).The DSNB depends on the time-integrated neutrino flux Φ ν i (E ′ , M ) for a given neutrino mass eigenstate.
In what follows, we adopt the following baseline DSNB model.We assume that CCSNe with mass in the range [8M ⊙ , 15M ⊙ ] are well represented by our 11M ⊙ model; for CCSNe whose mass is in the range [15M ⊙ , 22M ⊙ ] and [25M ⊙ , 27M ⊙ ], we take as a benchmark CCSN the model with a mass of 27M ⊙ .Finally, we assume that for CCSNe with mass in the ranges [22M ⊙ , 25M ⊙ ] and [27M ⊙ , 125M ⊙ ], the reference emission model is the black hole forming collapse one with a mass of 40M ⊙ .This parametrisation corresponds to 21% of all stellar collapses leading to black hole formation, which is within theoretical and observational constraints [129][130][131][132].
The DSNB electron neutrino and antineutrino signals (and their related uncertainty) in the absence of invisible neutrino decay are represented through the blue line (band) in Fig. 11.
Neutrino decay alters the expected DSNB spectrum [133].In particular, for invisible decays, one expects a lower-than-nominal spectrally distorted flux.For each mass eigenstate, the expected flux is given by where the effective redshift-dependent parameter is [134]: (5.6) Figure 11 shows the expected DSNB spectra of ν e 's and νe 's at Earth for a few representative values of the decay parameters.Due to neutrino decay, the DSNB peak tends to decrease The ν e component of the DSNB flux is more sensitive to α 1 than to α 2 .In addition, even for large α 2 , the DSNB flux falls within the uncertainty band of our baseline prediction; this implies that we cannot expect stringent constraints on α 2 from the DSNB.
for increasing α i .One can see that, since the fraction of ν 1 in ν e is larger than the one of ν 2 , the electron-neutrino component of the DSNB flux is more sensitive to α 1 than α 2 .Moreover, despite the spectral difference, even for large values of α 2 , the DSNB flux falls within the uncertainty band of our baseline prediction.Hence, we should not expect stringent constraints to be placed on α 2 through the DSNB, except for a disfavoured region of the parameter space.Similar to what discussed earlier, the decay of ν 3 can not be constrained only from the DSNB measurement of ν e and νe .In fact, in this case, one can not disentangle the predicted signatures from the existing astrophysical and experimental uncertainties.

Expected diffuse supernova neutrino background event rate
Hyper-Kamiokande is expected to be sensitive to electron antineutrinos from the DSNB via IBD.However, in contrast to a nearby CCSN explosion, the backgrounds strongly limit the sensitivity to the DSNB.Atmospheric electron and muon neutrinos and antineutrinos are the main backgrounds for the DSNB detection [58].Additionally, 9 Li produced via spallation is another relevant background [58].One should also take into account neutral current atmospheric events, which are the dominant background for reconstructed positron energies in the range of 12-20 MeV [135,136].It has been argued that neutral current atmospheric backgrounds could be almost completely removed with neutron tagging techniques [137].In the following, we report our findings with and without these backgrounds to illustrate their relevance for what concerns the bounds of invisible neutrino decay.
At energies lower than 12 MeV, the flux of reactor antineutrinos is much larger than the one expected for the DSNB.Therefore, we limit our analysis to the energy window between Expected number of background and DSNB events in the energy region of interest at Hyper-Kamiokande, DUNE and JUNO (left, middle and right panels, respectively).The blue shaded band indicates the uncertainty in the number of signal events from the normalisation of the supernova rate.The fraction of background events is shaded in grey and marked with a grey dashed line, whereas the total number of events for different decay hypotheses is shown through the solid colour lines.For comparison, we display the expected events for several values of the decay parameters α 1 and α 2 .
12 and 30 MeV for the reconstructed positron energy.Note that, for Hyper-Kamiokande, atmospheric neutrinos can challenge the DSNB detection, hence dedicated investigations are required [138].DUNE could observe the ν e component of the DSNB.This measurement is of particular relevance to test the predicted flavour composition of the DSNB.In the case of DUNE, solar neutrinos dominate the signal up to energies close to 19 MeV.The other main background that needs to be accounted for is due to atmospheric ν e 's [139].These two backgrounds limit the region of interest in reconstructed neutrino energy to the range between 19 MeV and 31 MeV [67].
JUNO will be sensitive to the DSNB, despite being significantly smaller than Hyper-Kamiokande.The charged current and neutral current atmospheric backgrounds are not very prominent at lower energies after applying pulse-shape discrimination techniques [64,140,141].This is relevant to investigate neutrino decays, for which the lower the energy, the more prominent the signature of a decay is.The region of interest for the reconstructed positron energy is the same as for Hyper-Kamiokande.We conservatively assume a 50% detection efficiency, although recent work suggests the possibility of reaching an efficiency up to 80% [141].
Figure 12 displays the total number of events (both signal and background) for the three detectors considered in this section.The blue shaded band indicates the uncertainty in the number of signal events from the normalisation of the supernova rate.In the left panel, which depicts the number of events expected in Hyper-Kamiokande, the darkest shading indicates the fraction of events corresponding to the neutral current atmospheric backgrounds, which might be reduced or even removed.In the same panel, the lightest shaded region indicates the fraction of events corresponding to unavoidable backgrounds.Similarly, the central and right panels show the expected number of events at DUNE and JUNO, respectively.
Other detection channels have been considered for the potential detection of the DSNB in all flavours, mainly CEνNS [77,[142][143][144] and via neutrino interactions with deuterium [145], carbon [146], oxygen [147] or even ES on electrons [147], but the prospects for constraining invisible neutrino decay are not encouraging.The reason is that the main signature of invisible neutrino decay is an energy-dependent missing flux, yet only upper limits on the standard non-electron DSNB component could be extracted.

Constraints on invisible neutrino decay from the diffuse supernova neutrino background
In order to explore the constraints on invisible neutrino decay, we consider 20 years of exposure of Hyper-Kamiokande, JUNO, and DUNE.We adopt the inputs provided in Sec. 2, except for JUNO, for which we consider a 50% efficiency resulting from the cuts and background mitigation strategies optimised for the observation of the DSNB [64].We account for the uncertainty in the DSNB flux prediction from the normalisation in the CCSN rate and a 20% uncertainty in the normalisation of each of the backgrounds.Appendix A describes the statistical approach in more detail.
Figure 13 shows the sensitivity of the expected DSNB signal in Hyper-Kamiokande, JUNO and DUNE to α 1 and α 2 .For Hyper-Kamiokande, the solid line corresponds to the analysis with nominal backgrounds and the dashed one is the expected sensitivity, if full discrimination of the neutral current atmospheric backgrounds was achieved.We also show the sensitivity for a joint analysis of Hyper-Kamiokande, JUNO and DUNE.As one can see from Fig. 13, Hyper-Kamiokande is the most sensitive of the three detectors to the point that it would completely dominate the sensitivity to invisible neutrino decay, if neutral current atmospheric backgrounds were rejected.This highlights the importance of further exploring background mitigation techniques in Hyper-Kamiokande.
From Fig. 13, we also note that the DSNB would not be able to set meaningful constraints on α 2 even in the most optimistic scenarios.The reason is that the uncertainty in the CCSN rate is larger than the fraction of ν 2 (ν 2 ) in electron neutrinos (antineutrinos).Therefore, it would not be possible to differentiate if a lower flux of neutrinos would be due to the decay of ν 2 or if the reference DSNB flux prediction was computed using an optimistic CCSN rate.The projected limits from the DSNB at 90% C.L. are α 1 < 8.0 (8.5) × 10 −25 eV 2 or τ 1 /m 1 > 8.4 (7.9) × 10 8 s/eV , for normal (inverted) ordering, assuming the nominal neutral current backgrounds in Hyper-Kamiokande.Conversely, for the decay parameter α 2 , non-zero values would be disfavoured at ∼ 1.1σ at most, both for normal and inverted ordering.If full discrimination of the neutral-current atmospheric backgrounds was achieved, the projected limits would read and a non-zero value of α 2 could be discarded at 1.6 σ.
In order to explore the potential interplay between a finite lifetime of two neutrino mass eigenstates, the left panel of Fig. 14 shows the allowed regions of the parameter space for each neutrino observatory and for a joint analysis.The left panel shows how a joint analysis significantly boosts the sensitivity to non-zero neutrino decay parameters.The reason for the improvement in sensitivity is that a combination of the signals from different neutrino telescopes enhances the statistical significance with whom the decay hypothesis is rejected.Additionally, a combined analysis breaks existing degeneracies between the spectral shape of the signal and some of the backgrounds, which differ for the three detectors.The right panel of Fig. 14 shows how the results of such combined analysis would change, if the neutral current atmospheric backgrounds in Hyper-Kamiokande were fully discriminated from the DSNB events.

Conclusions
Astrophysical neutrinos traveling over cosmic distances are ideal probes of the stability of these elusive particles.In particular, neutrinos from the Sun, CCSNe, and the DSNB allow for an optimal combination between distance traveled and characteristic energy to test the possibility that neutrinos decay invisibly (i.e. the decay products evade detection).This work investigates the future prospects for learning about invisible neutrino decay while realistically addressing the astrophysical unknowns in the picture.Our main findings are based on a forecast of the signals from solar, CCSN neutrinos and the DSNB expected in  next-generation neutrino observatories (such as Hyper-Kamiokande, DUNE, JUNO, DAR-WIN, and RES-NOVA) and are summarised in Fig. 1.When solar neutrinos detected by DARWIN, DUNE and Hyper-Kamiokande are employed as probes of invisible neutrino decay, a priori knowledge on the magnitude of the solar flux from the SSM allows to constrain the lifetime-mass ratios to be larger than ∼ 0.1-0.01s/eV for the mass eigenstates ν 1 and ν 2 .
Intriguingly, we find that CCSN neutrinos can potentially provide constraints on the decay of all three mass eigenstates.The bounds on invisible neutrino decay derived relying on CCSN neutrinos could be significantly more restrictive than the ones obtained from solar neutrinos, if a CCSN explosion occurs at a maximum distance of 10-20 kpc.The upcoming detection of the DSNB could potentially set the strongest limits on α 1 , improving the ones from cosmology.Nonetheless, the current uncertainty on the CCSN rate limits the sensitivity to α 2 .
Our findings also suggest that the employment of different detection channels at nextgeneration neutrino observatories would boost the sensitivity to invisible neutrino decay, allowing to break the degeneracy between the model uncertainties and the new physics parameters.
In summary, after approximately 10 years of data taking, solar data should provide stringent bounds on α 1 and α 2 , namely α 1 < 7.8 × 10 −15 eV 2 and α 2 < 2.3 × 10 −14 eV 2 , (6.1) at 2σ.This would correspond to a factor of 20 improvement with respect to current bounds from solar data (cf.Eq. 1.2).After collecting approximately 20 years of data, the DSNB   [19,20,24,148], solar neutrinos (present limits [53,54] and forecast from this work), high energy neutrinos (existing limits and forecast [41]), and supernova neutrinos for a collapse occurring at 10 kpc (forecast from this work) and the DSNB (forecast from this work).The lifetime of the mass eigenstates that can be tested is indicated.Indirect constraints from Big Bang Nucleosynthesis (BBN) [29] and the cosmic microwave background (CMB) data [34] are also shown with thin lines for comparison.The bands indicate the difference between the existing limits and the future sensitivity reach, except for CCSN neutrinos for which the band is the difference between the sensitivity for α 1 and α 3 .Note that the limits from high-energy neutrinos and SN1987A assume that the two mass eigenstates indicated decay at a similar rate.measurements will improve the limits from solar neutrinos on α 1 by ten orders of magnitude.If neutrinos from a nearby CCSN should be detected, the limits on α 1 and α 2 would improve by about 6 orders of magnitude with respect to the ones expected from future observation of solar neutrinos.Similar limits could also be set on α 3 , which would not be possible from solar data only.Actually, the limits on α 3 would be more than 14 orders of magnitude more stringent than those from accelerator and atmospheric data, which are α 3 ≳ 10 −6 eV 2 [20].Hence, although large exposures are needed, this work shows that a network of next-generation neutrino observatories has the potential to probe finite neutrino lifetimes using keV-MeV astrophysical neutrinos while consistently accounting for the uncertainties in the source modelling and in the neutrino emission properties.This potential is highlighted in Fig. 15, where the existing limits and the projected sensitivities derived in this work are contrasted.
In this work, we have focused on invisible neutrino decay, which leads to a suppression of the expected neutrino flux with respect to the standard theoretical prediction.Other decay channels may also be realised in Nature.Neutrino decays involving the emission of photons are strongly constrained for instance from the non-observation of a gamma-ray burst in connection with SN 1987A [149,150].For neutrino decays to lighter neutrinos and other daughter products, the main signature is not a reduction of the initial flux, but a spectral distortion and modification of the detected flavour composition.Such visible neutrino decays have also been studied for instance using solar neutrinos [92,151,152], SN 1987A [15,92,153], and could also be constrained with data from a future nearby CCSN explosion [154,155] as well as the DSNB detection [156,157], and the diffuse flux of high-energy astrophysical neutrinos detected by the IceCube Neutrino Observatory [158][159][160][161]. Yet, the ideal ratio between the large distances travelled and the energy range for solar and CCSN neutrinos sets favourable conditions to investigate other forms of neutrino decay, extending the strategies presented here.
to the minimum value of the total χ 2 function after marginalising over CCSN models and mixing scenarios.
Similar to CCSN neutrinos, for our sensitivity study of neutrino decay from the DSNB, we take the following χ 2 function for each experiment k: As in the previous cases, S i,k and B i,k are the mock number of signal and background events in the i-th energy bin of the k-th experiment, and N i,k is the number of events expected in the presence of invisible decay.The pull parameter ξ accounts for the uncertainty from the normalisation of the CCSN rate, σ R SN = 0.2, and η n parameterises the uncertainties in the background (σ n = 0.2).Note that the index n denotes the different sources of backgrounds in each experiment.

α 2 = 10 −12 eV 2 α 2 = 10 −13 eV 2 SOLAR NEUTRINOS Figure 2 .
Figure 2. Top panel: Solar neutrino flux expected at Earth for the different neutrino production channels (pp, 7 Be, pep, CNO, 8 B, and hep), according to SSM GS98-16.The neutrino energy ranges explored by DARWIN (ES), Hyper-Kamiokande (ES) and DUNE are highlighted through grey bands for orientation.Bottom panels: Electron neutrino survival probability as a function of the neutrino energy for different choices of the decay parameters α 1 (bottom left panel) and α 2 (bottom right panel).For comparison, the survival probability in the absence of invisible neutrino decay is displayed (blue dashed line).In all cases, the probability is computed for the SSM GS98-16 and weighted according to the contribution of each chain to the total solar neutrino flux for each neutrino energy.One can see that invisible neutrino decay induces an overall reduction of the survival probability; this effect is inversely proportional to the neutrino energy.

Figure 4 .
Figure 4. Projected sensitivity to the neutrino decay parameters α 1 and α 2 at 90% C.L. The left and right panel correspond to the results without and with priors on the normalisation of the solar neutrino flux, respectively.Solid and dashed black lines correspond to the results for Hyper-Kamiokande (HK) and DUNE.Their joint constraints are represented by the blue-shaded exclusion region.The orangeshaded region would be excluded by DARWIN, whereas the green region corresponds to the exclusion prospects from a combined analysis of all three neutrino observatories.

α 1 = 10 −20 eV 2 α 2 = 10 −20 eV 2 α 3 = 10 −Figure 5
Figure 5. Expected number of events in time bins of 10 ms for a 11.2M ⊙ stellar collapse occurring at 10 kpc from Earth.The top left and right panels correspond to the expected number of events for IBD and ES, respectively, in Hyper-Kamiokande.The bottom left panel displays the predicted number of events at DUNE and the bottom right shows the number of CEνNS events to be observed by RES-NOVA and DARWIN (solid and dashed lines, respectively).In all cases, inverted mass ordering is considered for illustrative purposes.

τ 2 Figure 6 .
Figure 6.Sensitivity to α 2 for a stellar collapse occurring at 10 kpc from Earth.We consider the following observatories: Hyper-Kamiokande, DUNE, RES-NOVA and DARWIN corresponding to the blue, orange, green, red, and yellow curves, respectively.The outcome from the combined analysis is plotted with a black dashed line.The top left panel assumes that both the CCSN model and the flavour composition are known.The top right panel shows the result after marginalising over the mixing schemes, whereas the bottom left panel corresponds to the results obtained after marginalising over the CCSN models.The bottom right panel displays the sensitivity after marginalising over the CCSN models and mixing schemes.The uncertainties on the expected neutrino signal affect the constraints from different neutrino observatories.To this purpose it is crucial to exploit the complementary information provided by the different detection channels to break the model degeneracies and recover strong bounds on invisible neutrino decay.

10 − 23 2 10Figure 8 .
Figure 8. Dependence of the sensitivity on the three decay parameters α 1 (left panel), α 2 (middle panel), and α 3 (right panel) on the CCSN distance (d = 5, 10, 15, 20, and 50 kpc).The results assume a combined analysis of data collected at Hyper-Kamiokande, DUNE, RES-NOVA, and DARWIN after marginalising over the three SN models and the different mixing schemes.Note that the limits for α 2 and α 3 degrade significantly with the distance, while this is not the case for α 1 .

Figure 9 .
Figure 9. Forecasted exclusion region at 90% C.L. from CCSN neutrinos in the plane spanned by α 1 and α 2 (left panel) as well as α 2 and α 3 (right panel).Such predicted exclusion regions have been obtained after marginalising over the CCSN mass and mixing schemes.

Figure 10 .
Figure 10.Exclusion region in the α 1 -α 2 plane from the observation of SN 1987A electron antineutrinos.These bounds are shown for different choices of the ratio between the flux of electron and non-electron flavour antineutrinos emitted by the SN 1987A (cf.solid, dashed and dotted contours).They have been obtained considering the overall duration of the neutrino signal, instead of focusing on the neutronisation burst only and rely on the recent analysis of the SN 1987A data presented in Ref.[119] (see main text for details).

α 1 = 10 −24 eV 2 α 2 = 10 −24 eV 2 α 1 = 10 −25 eV 2 α 2 = 10 −25 eV 2 Figure 12 .
Figure 12.Expected number of background and DSNB events in the energy region of interest at Hyper-Kamiokande, DUNE and JUNO (left, middle and right panels, respectively).The blue shaded band indicates the uncertainty in the number of signal events from the normalisation of the supernova rate.The fraction of background events is shaded in grey and marked with a grey dashed line, whereas the total number of events for different decay hypotheses is shown through the solid colour lines.For comparison, we display the expected events for several values of the decay parameters α 1 and α 2 .

τ 2 Figure 13 .
Figure 13.Expected sensitivity of the DSNB to invisible neutrino decay parameters to α 1 (left panel) and α 2 (right panel), obtained relying on Hyper-Kamiokande (orange), DUNE (blue), JUNO (green) and all three detectors together (red).The solid lines correspond to the case in which nominal backgrounds are considered for Hyper-Kamiokande.Dashed lines show the expected sensitivity assuming full discrimination of neutral-current atmospheric events was achieved in Hyper-Kamiokande.Hyper-Kamiokande is the most sensitive neutrino detector, and it would dominate the sensitivity to invisible neutrino decay, if neutral current atmospheric backgrounds were rejected.The DSNB cannot robustly constrain α 2 because the uncertainty in the supernova rate is larger than the fraction of ν 2 /ν 2 in electron neutrinos/antineutrinos.
DS NB (ν1 , thi s wo rk) Su pe rn ov a ne ut rin os (ν1 , ν2, ν3, thi s wo rk) Hi gh en erg y ne ut rin os (ν2 & ν3) So lar ne ut rin os (ν1 , ν2, thi s wo rk) At mo sp he ric , Ac ce ler at or & Re ac to r ne ut rin os (ν3 ) C M B BBN SN 19 87 A (ν1 & ν2, thi s wo rk)

Figure 15 .
Figure15.Sensitivity reach to finite neutrino lifetime from invisible neutrino decay as a function of the neutrino mass.Experimentally accessible regions are shown for atmospheric, accelerator and reactor neutrinos[19,20,24,148], solar neutrinos (present limits[53,54] and forecast from this work), high energy neutrinos (existing limits and forecast[41]), and supernova neutrinos for a collapse occurring at 10 kpc (forecast from this work) and the DSNB (forecast from this work).The lifetime of the mass eigenstates that can be tested is indicated.Indirect constraints from Big Bang Nucleosynthesis (BBN)[29] and the cosmic microwave background (CMB) data[34] are also shown with thin lines for comparison.The bands indicate the difference between the existing limits and the future sensitivity reach, except for CCSN neutrinos for which the band is the difference between the sensitivity for α 1 and α 3 .Note that the limits from high-energy neutrinos and SN1987A assume that the two mass eigenstates indicated decay at a similar rate.
8.1) × 10 −22 eV 2 , Forecasted exclusion at 90% C.L. from the DSNB in the plane spanned by α and α 2 .The left panel shows the regions of the parameter space excluded by JUNO (red), DUNE (orange), Hyper-Kamiokande (green; obtained assuming baseline backgrounds), and a combined analysis of the three experiments (blue).The right panel displays the exclusion region for a joint analysis of Hyper-Kamiokande, DUNE and JUNO with (without) neutral-current atmospheric backgrounds in dark (light) blue.Hyper-Kamiokande has the strongest potential to constrain invisible neutrino decay, especially if the neutral-current atmospheric background is fully tagged.