Prospects for the detection of the Diffuse Supernova Neutrino Background with the experiments SK-Gd and JUNO

The advent of gadolinium-loaded Super-Kamiokande (SK-Gd) and of the soon-to-start JUNO liquid scintillator detector marks a substantial improvement in the global sensitivity for the Diffuse Supernova Neutrino Background (DSNB). The present article reviews the detector properties most relevant for the DSNB searches in both experiments and estimates the expected signal and background levels. Based on these inputs, we evaluate the sensitivity of both experiments individually and combined. Using a simplified statistical approach, we find that both SK-Gd and JUNO have the potential to reach $>$3$\sigma$ evidence of the DSNB signal within 10 years of measurement. The combined results are likely to enable a $5\sigma$ discovery of the DSNB signal within the next decade.


I. INTRODUCTION
Core-collapse Supernovae (SNe) count among the brightest sources of low energy neutrinos (E ν 50 MeV). A supernova occurring within the Milky Way will cause an intense burst of events in currently running neutrino detectors. The signal will encode details of the astrophysics of the explosion superimposed with the effects of neutrino properties and oscillations (for a comprehensive review, see e.g., Ref. [1]). However, even compared to the decades of operation of large-volume neutrino observatories, galactic SNe are rare. This makes the Diffuse Supernova Neutrino Background (DSNB), i.e., the faint but constant flux of neutrinos emitted by core-collapse SNe on cosmological distances, an attractive research objective [2][3][4][5][6][7][8][9][10][11]. A first measurement of the DSNB has the potential to provide valuable information on the redshift-dependent SN rate as well as on the average and variability of the SN neutrino spectrum.  [12]. This result is already cutting into the parameter range predicted by current DSNB models (e.g., [11]).
During the next decade, a first detection of the long-sought DSNB signal is finally coming within reach. The two neutrino observatories most likely to achieve first evidence (3σ) of the DSNB signal are Super-Kamiokande and JUNO. In 2020, the Super-Kamiokande collaboration has performed an upgrade of the detector by dissolving gadolinium salt in the water target. This greatly enhances neutron detection capabilities [13][14][15], leading to a significant improvement in the efficiency and background rejection for the Inverse Beta Decay (IBD) detection channel and thus theν e component of the DSNB. Data taking in the new SK-Gd configuration commenced in August 2020. In parallel, the JUNO liquid scintillator (LS) experiment in southern China is entering its construction phase [16]. With first data expected in 2023, JUNO will acquire IBDs at a rate only slightly lower than SK-Gd, relying on the intrinsic neutron tag and pulse-shape discrimination (PSD) capabilities of liquid scintillator [16,17].
We would like to note that beyond the operational SK-Gd and the soon-to-be operational JUNO, there are a number of other experiments on the horizon with varying degrees of sensitivity to the DSNB. In particular, Hyper-Kamiokande, which is currently under construction, will directly continue the search of SK from ∼2027 using eight times SK's fiducial volume [18]. This is briefly discussed in Section III D. Large noble-liquid detectors, while challenged by expected low signal event rates and as-yet undetermined backgrounds, could in principle provide sensitivity for other neutrino flavors (DUNE/liquid argon for ν e , DARWIN/liquid xenon for ν µ,τ flavors), while conceptual hybrid Cherenkov-scintillation detectors such as Theia, if someday realized, could feature enhanced detection efficiencies for ν e 's [19][20][21][22].
The present article aims to review the DSNB detection potential of the two experiments.
Based on the relatively simple model of the DSNB flux and spectrum presented in Section II, we discuss the signal and background rates expected for SK-Gd and JUNO (Sections III and IV). Based on these numbers, Section V tracks the signal rates and sensitivities of both experiments as a function of their respective measuring times. Since both experiments can hope to gain first 3σ-evidence of the DSNB signal within the next decade, a 5σ-observation may be achieved by a combination of their results over a similar time scale.

II. SIGNAL OF THE DIFFUSE SUPERNOVA NEUTRINO BACKGROUND
The DSNB flux and spectrum results from a superposition of the neutrino bursts from core-collapse SNe happening on cosmic distance scales. Given the large numbers and distances to the parent SNe, the resulting DNSB flux is of the order of 10 2 per cm 2 s and nearly isotropic. The effective energy spectrum represents an average of the entire population of stellar core collapses from a wide range of progenitor stars, including failed explosions that lead to the formation of a Black Hole (BH). Spectral contributions from far-out SNe are substantially red-shifted. Hence, the signal range detectable in SK-Gd and JUNO (above ∼10 MeV, see below) is dominated by relatively close-by SNe up to red-shifts z ≈ 1 (see, e.g., Ref. [2]).
The expectation for the differential electron antineutrino flux of the DSNB is given by where E ν (E ν ) is the (redshifted) neutrino energy, c is the speed of light and H 0 , Ω Λ , Ω m are cosmological parameters (e.g. [8]). R CC (z) is the redshift-dependent rate of corecollapse SNe, whose z dependence is derived from the star formation rate [23] with the following relation: where a = 0.0170, b = 0.13, c = 3.3, d = 5.3 and h = 0.7 parametrize the z-dependence.
R CC (0) is the present rate of core-collapse SNe and taken as 1.0 × 10 −4 yr −1 Mpc −3 in the following DSNB reference model.
An important choice for the DSNB modeling is the average SN neutrino energy spectrum dN /dE ν . In accordance with Ref. [8], we take into account the contributions from both successful and failed SNe: with f BH indicating the fraction of black hole (BH) forming core-collapse SNe in the total event sample.
The average energy spectrum for both types of SNe can be parametrized as where E total is the total energy emitted, E ν is the average energy of the SN neutrino spectrum, and describes the spectral deviation from a thermal Fermi-Dirac spectrum (pinching) [24].
Inspired by the current state-of-the-art on DSNB modeling, we choose the following parameters to define our DSNB reference model : For successful SNe, we take E total = 5.0 × 10 52 erg, γ α = 3 and E ν = 15 MeV. For failed SNe, we assume E total = 8.6 × 10 52 erg, E ν = 18.72 MeV and E 2 ν = 470.76 as in Ref. [8]. For the relative fraction of BH forming SNe, we use f BH = 0.27 adopted from Refs. [7,8].
Given that many of the discussed input parameters are not known with great precision, the actual DSNB spectrum might deviate considerably from our DSNB reference model.
Consequently, we have introduced value ranges for the parameters that have the largest impact on the final DSNB event rate. In particular, we scan E ν from 12 to 18 MeV, f BH from 0 to 40%, and 0.5 The corresponding variability in the signal prediction is indicated by the shaded areas in Figure 1.
The parameters and ranges of the reference model are summarized in Table I. We note that the relatively wide ranges quoted implicitly envelope a wide span of astrophysical observations (e.g. the soft neutrino spectrum emitted by SN1987A or possible variations in the total explosion energy) and the effects of flavor oscillations on the detectedν e spectrum (with a potential for spectral hardening by the admixture of a higher-temperature ν x component).
To obtain the energy-dependent interaction rate dR/dE ν of electron antineutrino interactions shown in Figure 1, we evaluate the product where σ IBD (E ν ) is the IBD cross-section taken from [25] and N p is the number of free protons contained per unit detector mass. Figure  Detecting the gamma ray(s) from the delayed captures will be the key ingredient for a successful DSNB detection (see below).  Table I on the expected rates.

A. A Brief History of Super-Kamiokande
Since the start of data taking on 1st April 1996, the Super-Kamiokande experiment has spent the last quarter century conducting ground-breaking studies of neutrinos from the Earth's atmosphere [26], the Sun [27,28], and long-baseline accelerator-generated beams from KEK [29] and J-PARC [30], while also searching for nucleon decay [31][32][33][34], dark matter [35,36], and both galactic [37,38] and diffuse supernova neutrinos [12,[39][40][41]. The gamma. Not only was this energy below typical SK trigger thresholds, but it also fell in an energy range strongly contaminated with backgrounds from a variety of naturally occurring radioactive decays such as radon. While great efforts have been made to overcome these limitations, the most advanced hydrogen-based studies still only achieved neutron tagging efficiencies around 20% at the cost of 1 in 100 of the copious accidental backgrounds getting through [41].

B. A Blend with Benefits
To enable highly efficient neutron tagging while simultaneously providing powerful background rejection, Beacom and Vagins first proposed a concept they called "GADZOOKS!" (Gadolinium Antineutrino Detector Zealously Outperforming Old Kamiokande, Super!), dissolving a gadolinium (Gd) salt -such as gadolinium chloride, GdCl 3 , or the somewhat less soluble but also considerably less corrosive gadolinium sulfate, Gd 2 (SO 4 ) 3 -in Super-Kamiokande's pure water [42]. The primary goal of this proposal was to make observing the DSNB in Super-K possible; in fact, this paper is where the term "DSNB" was first introduced to help explicitly differentiate this subtle supernova neutrino signal from other "relic" fluxes.
Gadolinium has the highest cross section for the capture of thermal neutrons of any naturally occurring stable substance, more than 100,000 times that of hydrogen, and following neutron capture the excited Gd nucleus emits an easily detected gamma cascade of ∼8 MeV. This leads to a distinct IBD signature sometimes called the "gadolinium heartbeat": a prompt positron event followed a few 10s of microseconds later by a delayed neutron capture event. The Cherenkov light of both events appears to originate nearly from the same place in the detector, as they typically occur close enough to fall within the position resolution of SK's vertex fitter. Requiring such a double flash of light within such a short period of time, about 1/10 th the delay for captures on hydrogen in pure water, serves to reduce accidental backgrounds by a factor of roughly 10,000, or 100 times cleaner than relying on captures on hydrogen alone.

C. Putting the Gd in SK-Gd
After years of R&D to develop the necessary water filtration technology as well as establish that loading gadolinium into Super-K would be both safe and effective [43], on 14 July 2020, the first dissolved gadolinium salt was injected into the SK detector. This first stage of loading, which was completed on 17th August 2020, saw 13.2 tons of gadolinium sulfate octahydrate added to the SK water, resulting in a gadolinium concentration of 0.01% by mass [44]. As shown in Figure  As described above, there will be no remaining accidental backgrounds to speak of, and requiring the DSNB events to be above 12 MeV and below 30 MeV effectively suppresses the physics backgrounds arising from nuclear power reactor antineutrinos causing low energy IBD events and atmospheric neutrinos' charged current (CC) reactions, respectively.
Muon cuts in combination with the 12 MeV energy threshold will remove almost all background events caused by nuclear spallation, with the efficient neutron tagging now provided by gadolinium allowing even better spallation cut efficiencies than those employed by SK to date [40,45,46]. Most of the remaining physics background are therefore expected to come from neutral current (NC) interactions involving energetic atmospheric neutrinos interacting with oxygen nuclei, but a recent paper has shown that these can be significantly and efficiently suppressed through the use of a machine learning (specifically a convolutional neural network) approach, removing 98% of the NC background at the expense of just 4% of the signal yielding a signal-to-background rate of 4:1 [47]. In all, we rather conservatively assume a total residual background rate of 0.8 events per year in this energy range.

D. The Future of Gd-Loaded Water Cherenkov Detectors
Data collection in the Gd-enhanced Super-Kamiokande has been underway since the middle of 2020, and is expected to continue until at least 2028. In 2027, the new Hyper-Kamiokande (Hyper-K, HK) detector, some eight times the fiducial volume of SK and currently under construction, is scheduled to come online [18,48]. As was the case with Kamiokande ceding the field to Super-Kamiokande and turning off in 1997, it is expected that Super-K will also be permanently decommissioned once Hyper-K is complete and operating stably. While HK will not contain gadolinium on Day 1, it is assumed that gadolinium will very likely be added to the new detector eventually, such that all proposed HK detector components and materials must be certified to be compatible with extended immersion in Gd-loaded water. From simple scaling, a Gd-loaded Hyper-K can be expected to observe an SN1987A-like number of supernova neutrino events from the DSNB every year it is in operation, an exciting prospect indeed.

IV. THE JUNO EXPERIMENT
The JUNO experiment is located at Jiangmen in South China. Its primary goal is to determine the neutrino mass ordering and precision measurements of neutrino oscillation parameters using reactor neutrinos from the powerful Taishan and Yangjiang nuclear power plants [16,17]. Ref. [17].
veto system, the calibration system, the online LS monitoring system, and a satellite TAO reference reactor spectrum detector [50]. JUNO is expected to take data in 2023.
The primary detection channel for the DSNB is the IBD reaction on free protons, in which the prompt positron signal takes away most of the neutrino energy, and the delayed neutron with single neutron production may contaminate the IBD signals. To model the NC interaction between the atmospheric neutrinos and the carbon nuclei, one needs to employ both the neutrino interaction generator tools [51,52] and the package for deexcitations of the final-state nuclei [53]. A careful investigation of the atmospheric neutrino NC background has been accomplished in Refs [54,55], which are shown to be larger than the DSNB signal by one order of magnitude.
Pulse shape discrimination (PSD) is expected to be a very efficient technique to further improve the signal-to-background ratio. Regarding all the possible IBD-like backgrounds, the prompt signal of fast neutron and atmospheric neutrino NC events is predominantly created by heavy particles such as neutrons, protons and α's. In LS detectors, the distinct time profiles of different types of particles permit effectively distinguishing between the light γ-like particles (i.e., e + , e − , and γ) and heavy proton-like particles (i.e., proton, neutron, and α). By virtue of the high light yield and excellent time resolution at JUNO, it is estimated that the atmospheric NC background can be reduced by two orders of magnitude while the signal efficiency of the DSNB remains at least above 50% [17]. Recent studies indicate that JUNO's sensitivity could be substantially improved based on a refined scheme for the PSD-based particle identification [56].
To summarize, with all the possible background contributions and suppression techniques are taken into account, a total background level of 0.7 events per year is estimated anddepending on the DSNB event rate-an excellent signal-to-background ratio of 1:1 to 4:1 can be achieved. Therefore, we can anticipate a good discovery sensitivity of the DSNB in the coming decade.

V. PROJECTED DSNB SENSITIVITIES
Even in experiments the size of Super-Kamiokande and JUNO, accumulating the data for a DSNB detection is a waiting game. Table II  using the time and rate information as quoted in Table II. The solid lines correspond to the rates of the DSNB reference model, the shaded areas reflect the range implied by the variability of the signal (Section II). Please note that recent studies for JUNO indicate that a higher signal efficiency could be reached [56], thus the event rates per year for both experiments are rather compatible.
note that while the reactorν e background at the location of SK will be smaller, this advantage is at least partially compensated for by the better energy resolution of JUNO [17].
• For background rates, we use the numbers lined out in sections III and IV. The dominant contribution in JUNO is formed by NC interactions of atmospheric neutrinos.
In SK-Gd, invisible muons will play an important role.
• Finally, for SK-Gd, we cite two sets of numbers in dependence of the gadolinium concentration that is set to be increased in mid-2022 from 0.01% to 0.03% (Section III).
Please note that both experiments feature a rather similar ratio of signal (S) and background (B) rates of S : B ∼ 2.
The discovery potential for the DSNB lastly depends on the total number of signal and background events accumulated over a longer period of measuring time. Figure 5 displays This number refers to our DSNB reference model (Section II). Based on the uncertainties of the DSNB signal prediction, the actual event number and thus rate of signal collection might substantially deviate from the reference prediction. The corresponding ambiguity is reflected by the shaded areas. Naturally, a low signal rate would affect both experiments in the same way. Therefore, the shaded regions should not be mistaken to be classical uncertainty bands but are instead fully correlated.
Given the earlier start, larger fiducial mass and higher efficiency after the increase in Gd concentration, SK-Gd is expected to accumulate statistics somewhat faster than JUNO.
However, we note here that recent studies for JUNO indicate that a higher signal efficiency could be reached using a more advanced method of pulse shape discrimination, bringing both experiments roughly on par [56].
Based on these numbers, it becomes possible to estimate the experimental sensitivities of the individual and combined measurements. While the eventual DSNB analyses will apply more sophisticated techniques, here we restrict ourselves to a simple count rate analysis for signal and background in the energy window of interest (12−30 MeV). As a measure of sensitivity, we adopt the ratio S/ √ S + B, i.e., the significance of the signal strength over the expected statistical variation of the count rate. Clearly, this simplified approach Using the signal and background numbers listed in Table II,  The combined sensitivity curve of Figure 6 illustrates that the sum signal of both experiments could be used to achieve a level of 5σ observation of the DSNB reference model within the next 10 years. The corresponding signal and background rates as well as statistical sensitivities are summarized in Table III. As before, we have neglected systematic uncertainties Finally, it should be noted that-even if the data sets of both experiments were combined-only several tens of signal events are expected for the reference model, reaching close to 10 2 under the most optimistic assumptions. Consequently, the spectral information that can be obtained from this next generation of DSNB experiments will be rather limited, at best comparable to the accuracy gained from the neutrino burst of SN1987A. Therefore, while indeed a first positive detection of the DSNB is within reach within the next decade, a substantially larger detector such as HK-Gd (i.e., with enhanced neutron tagging) will be required to extract details on the DSNB spectrum, thus offering a window to the underlying physics of SN core collapse, black-hole formation and redshift-dependent collapsar rate.

VI. CONCLUSIONS
The start of SK-Gd data taking in late 2020 and the expected start of JUNO data taking in 2023 indicate a substantial improvement of the worldwide sensitivity for diffuse Supernova neutrinos (or, more precisely, itsν e component). Given the large unknowns of the signal flux and spectrum and the potential systematics associated with background rates and subtraction, it is difficult to forecast the exact level of sensitivity to be achieved by the two experiments. However, using our DSNB reference model (Section II) and making simplified assumptions on the signal significance (Section V), we can conclude that both experiments on their own are likely to obtain statistical evidence of the signal (3σ level) within about 10 years of running time. The combination of their results may even allow a 5σ discovery of the DSNB in the same time frame. After more than 20 years of experimental searches, a first observation of the DSNB signal seems thus well in reach within the next decade.