Large Energy Singles at JUNO from Atmospheric Neutrinos and Dark Matter

Large liquid scintillator detectors, such as JUNO, present a new opportunity to study neutral current events from the low-energy end of the atmospheric neutrinos, and possible new physics signals due to light dark matter. We carefully study the possibility of detecting ``Large Energy Singles'' (LES), i.e., events with visible scintillation energy $>15$\,MeV, but no other associated tags. For an effective exposure of 20 kton-yr and considering only Standard Model physics, we expect the LES sample to contain $\sim40$ events from scattering on free protons and $\sim 108$ events from interaction with carbon, from neutral-current interactions of atmospheric neutrinos. Backgrounds, largely due to $\beta$-decays of cosmogenic isotopes, are shown to be significant only below 15 MeV visible energy. The LES sample at JUNO can competitively probe a variety of new physics scenarios, such as boosted dark matter and annihilation of galactic dark matter to sterile neutrinos.


I. INTRODUCTION
Atmospheric neutrinos are produced in the interactions of cosmic rays with Earth's atmosphere. Measurements of these atmospheric neutrinos at detectors such as Super-Kamiokande have been crucial for the discovery of neutrino oscillations [1]. Despite extraordinary achievements over several decades, the detection of low-energy non-electron neutrino flavours, i.e., ν µ ,ν µ , ν τ , andν τ , has remained elusive essentially because at Cherenkov detector like Super-Kamiokande, such a detection depends on having a charged particle above the Cherenkov threshold [2].
Scintillator detectors do not require charged particles to cross the Cherenkov threshold for them to be detected. In particular, neutral-current interactions such as ν + p → ν + p lead to a prompt visible scintillation, which can be detected even for neutrinos with energies of tens of MeV [3]. The difficulty is that the signal has a single component, as opposed to inverse beta decays where a neutron tag is possible in addition to the initial prompt scintillation from the charged lepton. The "singles" from neutrino sources can be mimicked by other processes, and therefore the backgrounds are usually quite large. Indeed, for small detectors, the singles from atmospheric neutrinos are often considered as a background [4,5]. However, upcoming large volume liquid scintillator detectors, such as JUNO (Jiangmen Underground Neutrino Observatory) [6], will accumulate a significant number of such singles, which may allow a first measurement of the low-energy end of the ν µ ,ν µ , ν τ , andν τ atmospheric neutrino spectra.
One may ask what sources and interaction channels could lead to such singles. In a scintillator detector, the events below a few MeV visible energy will be dominated by intrinsic radioactivity.  MeV, the events are dominated by decays of cosmogenic isotopes. At "large" visible energies, i.e., above 15 MeV, the events are dominated by neutral-current interactions of atmo-spheric neutrinos. We propose that JUNO maintain a Large Energy Singles (LES) database comprising of singles with visible energy E vis ∈ (15, 100) MeV, which will contain evidence of neutral-current interactions of atmospheric neutrinos, and possibly even of interesting physics beyond the standard model.
In this paper, we predict the LES spectrum at JUNO. We identify the main contributions to the signal in § II, study the dominant backgrounds at low energy and estimate the threshold from a veto analysis in § III, and present our main result in § IV. Further in § V, we explore well-motivated new physics scenarios that can have a visible imprint in the JUNO LES data. For example, we discuss the sensitivity to boosted dark matter and annihilation of galactic dark matter to sterile neutrinos. We end the paper with a brief summary and outlook in § VI.

II. SINGLES AT JUNO
The LES events from atmospheric neutrinos arise mostly from elastic scattering with protons (νp ES), and quasi-elastic-like scattering with carbon (νC QEL) which results in single or multiple proton knockouts. The scintillation signal from elastic scattering and "proton-only" knockouts cannot be distinguished, and the detector only measures the sum of these two channels.
The neutral-current interactions of neutrinos are sensitive to all flavors; however, they do not distinguish between flavors. Therefore, the only measurable quantity is the spectrum of the sum of events from all flavors. In general, the differential event rate with respect to the recoil energy of the proton (T p ) is given by where f ∈ {ν e ,ν e ν µ ,ν µ , ν τ ,ν τ }, N t is the number of targets, and T is the data-taking time period which we have arXiv:2111.14586v1 [hep-ph] 29 Nov 2021 considered to be 1 yr, unless specified. For a 20 kton fiducial volume detector, the number of target protons from hydrogen (i.e., free protons) is N p = 1.5 × 10 33 and the number of target carbon nuclei is N C = 8.8 × 10 32 [6].

A. Atmospheric neutrino fluxes
The flux of atmospheric neutrinos for E ν > 100 MeV at the site of JUNO is calculated in Ref. [7] based on the predictions of Honda et al. [8]. As it is located at a lower latitude than Super-Kamiokande, it is estimated that the atmospheric neutrino flux at JUNO is ∼ 10% smaller [7].
The atmospheric neutrino flux for E ν < 100 MeV has been determined by the FLUKA group for Super-Kamiokande and Borexino [9]. There are large uncertainties (∼ 25%) in the flux prediction originating from the dependence on the geomagnetic field. The predicted flux for E ν < 100 MeV at JUNO can be approximately obtained by scaling the Super-Kamiokande prediction by a factor of 0.9.
For our analysis, we use the scaled Honda et al. fluxes above 100 MeV and scaled FLUKA fluxes below 100 MeV with appropriate matching. Our simplified estimates agree with the predictions in Ref. [7].

νp ES cross section
The νp ES cross section is a robust prediction of the Standard Model and has been measured experimentally [10]. The differential cross section for this process in terms of the neutrino energy (E ν ) and recoiling proton kinetic energy (T p ) is given as where M p is the mass of proton, s−u = 4M p E ν −2M p T p , while the functions A, B, and C depend on E ν , the momentum transfer (Q 2 = 2M p T p ), and form factors of proton. The expressions can be found in Ref. [10]. A more familiar expression for low-energy interactions, in the small-Q 2 limit, is given in Ref. [3]. We retain the Q 2dependence in our analysis, but note that the impact on the event rates is small. Due to the large energy loss rate of proton, the scintillation from a recoiled proton is nearly isotropic and the direction of proton (and hence, that of the incident neutrino) is not reconstructed. As a result, the angular distribution of these events is not measurable and we, therefore, only focus on the angle-averaged cross section and flux.
The main uncertainty in the differential cross section originates from the uncertainties associated with the axial-mass parameter M A in the axial form-factor.
There are contributions from strange sea-quark to all of the form factors, however these have not been taken into account for our estimations. For this analysis, we fix M A = 1.03 GeV [11], and conservatively assume that the cross section uncertainties are O(10%).
For neutrinos and anti-neutrinos with E ν ≥ 550 MeV, the momentum transfer to proton is large enough for the single-pion production through the delta resonance. However, we expect such processes to have much smaller cross sections than νp ES, and the corresponding event rates can be ignored. The νe ES cross section is relatively smaller, and we can safely ignore these interactions in our analysis.

Quenched proton scintillation
Due to photosaturation losses, i.e., quenching, the visible energy (E vis ) is different from the kinetic energy of the recoiling proton. The differential event spectrum in terms of visible energy is given by The visible energy is related to T p through where k B = 6.5 × 10 −3 g/cm 2 /MeV and k C = 1.5 × 10 −6 (g/cm 2 /MeV) 2 are Birks' constants [12]. The average energy loss during propagation, dE/dx , is determined by the baseline parameters 1,2 of JUNO simulations [6]. Note that, the non-linear but one-to-one mapping between E vis and T p , and good energy resolution of the detector imply that the effects of quenching can be inverted and one can, in principle, obtain dN/dT p from dN/dE vis . This is useful in reconstructing the incident neutrino spectrum and has been studied in the context of supernova neutrinos [13,14].

Predicted νp ES spectrum
The atmospheric neutrinos with E ν ∈ (100, 200) MeV are special, because only the electron-flavor component has been measured through charged current interactions. We ask if the muon and tau flavor components have a detectable imprint on νp ES events spectrum. For this purpose, we take a closer look at the distribution of events The binned event spectrum (∆E bin = 5 MeV) from three energy ranges of the atmospheric neutrino spectrum, and the total spectrum. The shaded regions represent the uncertainties arising from the cross section and flux estimates. Note that the uncertainties are larger in the lower energy bins, mostly because of the uncertain neutrino flux for Eν < 100 MeV.
from various parts of the atmospheric neutrino spectrum, and divide the flux into three energy ranges: 1. E ν < 100 MeV, which has large uncertainties, 2. E ν ∈ (100, 200) MeV which is partly measured, and 3. E ν > 200 MeV, which is well determined.
The event spectrum from these three energy ranges and the total event spectrum, is shown in Fig. 1. We also show the uncertainty in the event spectrum from cross section as well as flux estimates.
The events from an incident neutrino with energy E ν are distributed over the range 0 ≤ T p ≤ 2M p E ν /(M p + E ν ) 2 . As a result, there is a significant contribution to low-energy bins from the high energy part of the atmospheric neutrino spectrum. It seems, a priori, that reconstruction of the incident spectrum from νp ES events will be challenging.
From Fig. 1, one notes that in the visible energy range E vis ∈ (15, 40) MeV, the contribution from neutrinos with E ν ≥ 200 MeV is similar for all the energy bins, whereas the contribution from E ν ∈ (100, 200) MeV decreases with energy. With much larger exposure, this excess of events at low energies can become statistically significant, and if detected, would represent a measurement of the flux of ν µ +ν µ +ν τ +ν τ for E ν ≤ 200 MeV, after statistically subtracting the contribution from ν e +ν e . One can also note that the contribution from the flux with E ν < 100 MeV, which has large uncertainties, is mostly in the low energy bins, and will not be relevant if we have an energy threshold of E vis ∼ 15 MeV.

C. Singles from νC QEL
The neutral-current interactions of atmospheric neutrinos in JUNO have been studied in Ref. [15]. These interactions are dominated by quasi-elastic-like (QEL) processes where one or more nucleons can be knocked out of 12 C. A detailed study of this process has been carried out in Ref. [15], which reports the event rates for various channels (1p, 1n, 1p1n, 2p, 2n, ...), as well as the recoil proton spectrum from the sum of these channels. The total event rate with at least one proton in the final state 3 is found to be ∼ 30 kton −1 yr −1 . For 20 kton-yr exposure of JUNO, this implies an aggregate of ∼600 events, distributed over T p ∈(0.1, 300) MeV.
We need to estimate the singles event rate from νC QEL process, which arises from the single proton knockout 1p : ν and from multiple proton knockouts such as 2p : ν 3p : These protons are a part of the total proton spectrum given in Ref. [15]. To isolate the singles events, we calculate the fraction of "proton-only" knockout events that do not have a neutron in the final state. Using the results in Ref. [15], we find that which implies that roughly half of the protons do not have a neutron tag. Therefore, the singles spectrum from νC QEL interaction can be approximated by scaling the proton spectrum given in [15] by 0.52. The E vis distribution is obtained by applying the effects of quenching using Eq.(3). The daughter nuclei in a QEL process can de-excite through protons and/or alpha particle emission. However, these particles are estimated to be lower in number, and most of them have kinetic energies below 20 MeV [15]. Considering the effects of quenching, these particles will be below threshold, and hence can be ignored. Moreover, after de-excitation, some of the channels result in unstable nuclei with short lifetimes that undergo β decay. These β decays can be used to tag the proton scintillation events, as has been demonstrated in Ref. [16]. While this will allow us to identify a fraction of the LES sample as coming from νC QEL, we do not use this information in our analysis. It is also possible that the elastic scatterings between a knockout neutron and free proton in detector results in visible scintillation. However, these events will be vetoed by the accompanying neutron capture.
The event rate predictions in Ref. [15] depend on the choice of Monte Carlo generator for neutrino interactions. In Fig. 2, we show the expected rate of νC QEL singles at JUNO, as predicted by the neutrino event generators GENIE [17] and NuWro [18]. It appears that νC QEL predictions are sensitive to details of the nuclear structure, unlike the robust predictions for νp ES. For our analysis in the rest of the paper, we use the results obtained by GENIE [17], with 10% uncertainty.

A. Cosmic muon spallation
The passage of cosmic muons through the detector produces isotopes through spallation. These unstable isotopes decay in the detector, and their daughter particles can lead to visible signals. The singles background (i.e., without an associated neutron capture) originates from β ± , β ± γ, β ± p, and β ± α decays of these cosmogenic isotopes. The βn decays do not contribute to singles as the neutron can be tagged.
The cosmic muon spallation and isotope yields have been extensively studied for Super-Kamiokande in Refs. [19][20][21]. The liquid scintillator detector KamLAND has measured the yields of some cosmogenic isotopes [22]. Since the average muon energy at the JUNO site is lower than that at KamLAND 4 , the isotope yields at JUNO 4 Eµ ∼ 215 GeV for JUNO [6], and Eµ ∼ 260 GeV for Kam-LAND [22].
would be nearly 90% of that at KamLAND [6]. In this paper, we scale the measured KamLAND yields to JUNO where available, and for other cosmogenic isotopes, we use simulation yields from Table 13-9 in Ref. [6]. The isotope yields and other details are given in Table I.

Decay of cosmogenic isotopes
To predict the visible-energy distribution of singles from cosmogenic isotopes, we estimate their production rate in the detector. Looking at their half-lives (cf., Table I), it is reasonable to assume that all the cosmogenic isotopes would decay within a day. The production count per day (CPD) of the radio-isotope i is given as where Y i is the isotope yield, R µ = 3 Hz is the rate of cosmic ray muons traversing through in JUNO, T = 86400 s is the time interval, and L µ ≈ 23 m is the average muon track length in JUNO [6]. These values give a more useful and simplified expression which we use in the evaluation of the event rate R i = B i × CPD i , as well as the event spectrum Here B i is the branching ratio of the isotope to the singles channels, and f i is the normalized distribution of E vis for the i th isotope 5 . As the individual isotopes cannot be identified, only the cumulative event spectrum from these isotopes can be measured.

Veto criterion
The cosmogenic isotopes that decay within a few seconds of the muon passage can be tagged, and the events can be removed by imposing appropriate spatial and temporal cuts. This was demonstrated for Super-Kamiokande in Ref. [20]. By accounting for the muon energy deposition along the track, it was proposed to veto a small cylindrical volume centered around the muon track. A similarly detailed analysis for JUNO is required, but is beyond the scope of this paper. To get rid of cosmogenic isotope decays, we propose a much more conservative veto -a cylindrical volume around the entire track of the cosmic muon with radius R veto for a time ∆t veto . This results in a dead volume fraction of where R CD = 17.7 m is radius of the central detector and L µ ≈ 23 m is the average muon track length in JUNO [6]. For R veto = 3 m and ∆t veto = 1.2 s (similar to Ref. [6]), the dead volume fraction is ∼10%, whereas for ∆t veto = 2 s, the dead volume fraction increases to ∼17%. We envision that this dead volume fraction of detector will be compensated by longer duration of data taking, to get the appropriate effective exposure.
Note that, these estimates do not account for the muon tagging and track reconstruction efficiencies. A detailed Monte Carlo simulation, which also accounts for detector systematics, is required to optimize the veto criterion. In Ref. [6], similar cuts were proposed to identify the inverse beta-decay events in JUNO, with additional cuts to tag the neutron capture.

Irreducible background and threshold
The fraction of cosmogenic isotopes that decay outside the ∆t veto window cannot be tagged, and constitute the irreducible background. The effective rate of background events from a cosmogenic isotope is given bỹ ) and the half-life T 1/2 were obtained from www-nds.iaea.org. The experimentally measured yields by KamLAND [22] have been scaled to obtain the yields in JUNO. Wherever KamLAND measurements are not available, results of JUNO simulations [6] have been used. The isotope production count per day (CPD) from Eq. (9) captures the number of isotopes that are produced in the detector per day. The fraction of these isotopes that decay outside the ∆tveto = 2 s constitute the irreducible background, whose rateR (using Eq. (13)) is tabulated. which is provided in Table I. The effective event spectrum is estimated by

Radio
In Fig. 3, we have shown the cumulative event spectrum from cosmogenic isotope decay for ∆t veto = 0 s (equivalent to without veto), 1.2 s, and 2.0 s. Without any veto, the cosmogenic isotope decays constitute a wall -like background at E vis ∼16.5 MeV. Our veto criterion, with ∆t veto = 2 s, allows lowering the threshold up to 14 MeV. We present our results with a conservative threshold of 15 MeV. Note that, by considering the energy deposition along the track, the length of the cylindrical volume veto can be reduced and ∆t veto can be increased with little change to dead volume fraction. This significantly reduces the cosmogenic backgrounds [20].

B. Other backgrounds
The other known singles backgrounds include intrinsic radioactivity and reactor neutrinos. However, these neutrinos contribute for E vis ≤10 MeV. As cosmogenic backgrounds already overwhelm the signal at these energies, we do not discuss them in detail.
Incomplete reconstruction of events, e.g., missing one or more final state particles, can lead to LES events. For example, a low-energyν e interacting via charged current produces a positron and a neutron; if the neutron is not tagged this can contribute to an LES event. However, for the E vis ∈ (15 − 100) MeV window considered for LES events, the relevant low-energyν e have a small event rate. Therefore we expect such backgrounds to be small. However, a detailed study of the detector efficiencies and reconstruction is warranted.

IV. FORECAST FOR JUNO-LES
It is clear that the low-energy singles spectrum at JUNO will be dominated by irreducible cosmogenic isotope decay, intrinsic radioactivity, solar and reactor neutrinos. Above 15 MeV visible energy, the events dominantly arise from νp ES and νC QEL interactions. This JUNO-LES sample will provide evidence of neutralcurrent interactions of atmospheric neutrinos. In Fig. 4, we have shown our estimate for the binned event spectrum for E vis ∈ (15, 100) MeV from νp ES, νC QEL, and the "Total" sum of the two. There are a few events expected above 100 MeV, but we do not include them in our counting. For 20 kton-yr exposure, we expect ∼40 events from νp ES, and ∼108 events from νC QEL. Therefore, we expect a total of ∼148 events with E vis ∈ (15, 100) MeV in the JUNO-LES sample.
The first goal of JUNO would be to establish the existence of LES events, and therefore, the neutral current interactions of atmospheric neutrinos. In this analysis, the backgrounds for E vis ≥ 15 MeV have been assumed to be negligible. Therefore, the first LES events may be observed with a few tenths of kton-yr exposure, according to our estimations. If we further want to claim a discovery of νp ES events above the "background" of νC QEL events, we need a larger exposure. Assuming only statistical errors 6 and no other background, we estimate that JUNO can discover νp ES at 3 σ (5 σ) with 12 (34) kton-yr exposure. Note that, these estimates are only based on the counting of events, and more detailed analysis can be performed which also accounts for the energy distributions of the νp ES and νC QEL events.

V. SENSITIVITY TO NEW PHYSICS
Measurement of the LES sample at JUNO will open the window to testing many new physics scenarios. In this section, we first show that interesting limits can be obtained using model-independent analysis. Later, through two examples, we will also show how one can obtain model-dependent limits on possible fluxes of energetic new particles. 7

A. Model independent limits
A flux of "Beyond Standard Model" particles ψ can arise from the annihilation/decay of galactic or solar dark matter [25][26][27][28]. They can also be emitted during evaporation of the primordial black holes [29,30]. These particles can also be produced in astrophysical processes or through cosmic ray interactions [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. We choose to remain independent of the production mechanism and assume a flux of boosted (E > m) particles with monochromatic energy spectrum. The flux at a detector can be written as where φ 0 is the normalization in units of cm −2 sec −1 and E ψ is the energy of the boosted particle. If this flux arises from dark matter annihilation (DM + DM → ψ + ψ) or decay (DM → ψψ), then E ψ = M DM or E ψ = M DM /2, respectively. The boosted particle would be detected through elastic scattering with protons in the detector (ψ + p → ψ + 6 We use the figure of merit S/ √ B as a measure of discovery sensitivity, and S/ √ S + B to obtain exclusion limits [24]. 7 Novel interactions can also modify the νp ES cross section itself, which we do not study here. p). The cross section for this process depends on the details of the particle physics model. We consider two benchmark scenarios for the mediator -heavy and light, and two models for the interaction -vector and axial vector.
For the heavy mediator case, one is only sensitive to a ratio of coupling strength (g H ) and the mediator mass (M Z ). On the other hand, for the light mediator case, one is only sensitive to the coupling strength. In order to compare quantities with the same dimensions, for the light mediator scenario we take the heavy scale (corresponding to M Z above) to be the mass of proton. As a result, the strength of interaction in these two scenarios is captured by an effective parameter where c V (A) = 0.04 (0.64) arises from the form-factors of proton. The differential cross section for ψp ES is where -(+) are for vector (axial-vector) current.
We can now compute the quenched proton spectrum from ψp ES. The event rate depends on E ψ and the prod-uct φ 0 × G 2 eff . To obtain the 90% C.L. sensitivity of JUNO to the flux of these boosted particles, we consider the events from ψp ES as signal and the total Standard Model LES events as the background. As the spectrum from both interactions is predictable, a bin-by-bin comparison will lead to better sensitivity, but is not required for our simple analysis. The boosted particle parameter space that can be probed by JUNO is shown in Fig. 5. We find that the event rate is higher for light mediator scenario and axial-vector current interaction, as expected.
The volume of KamLAND is 0.697 kton. Using a fiducial exposure of 123 kton-day, KamLAND has reported one event with E vis ∈ (13.5, 20) MeV which is consistent with their estimate for background [5]. The nonobservation of excess events in this bin allows us to put 90% C.L. exclusion limits on the flux of boosted particles. These limits for the various cases are shown in Fig. 5. The projected sensitivity of JUNO is ∼ 100 times more than KamLAND due to larger exposure and a wider E vis range of the LES sample.

B. Dark matter annihilating to sterile neutrinos
One of the simplest extensions to the Standard Model is a neutral fermion called sterile neutrino (ν s ) which can also act as a portal to dark matter. In these models, the annihilation of dark matter is dominated by χχ → ν s ν s which determines the relic density [26][27][28]. If the mixing angle between sterile and active neutrino is large (∼ 0.1), the flux of sterile neutrinos will be accompanied by a flux of active neutrinos, albeit smaller, which can be detected. However, if the mixing angle is small (< 10 −3 ), the flux of active neutrinos will be too small to be detected and one must rely on the detection of ν s . One of the possibilities is to detect ν s p elastic scattering (ν s + p → ν s + p) in the LES sample at JUNO.
The flux of sterile neutrinos from s-channel annihilation of galactic dark matter is given by where J = 2.3 × 10 23 GeV 2 cm −5 is the all-sky J-factor [48], and σv is the thermal averaged cross section adapted from Ref. [49]. We have assumed the dark matter to be a Majorana fermion. In case it were a Dirac fermion, the flux would smaller by a factor of two. To obtain conservative estimates, we ignore the contribution to flux arising from the extra-galactic component. We also assume that ν s p ES is mediated by a light vector boson, and take the coupling g L = 0.1 for illustration. The parameter space excluded by KamLAND data, and the 90% C.L. discovery sensitivity of the LES sample at JUNO with 20 kton-yr exposure are shown in Fig. 6. We also show the thermal averaged cross section for obtaining the correct relic abundance, and find that JUNO can probe this model for dark matter mass in the range FIG. 6. The 90% C.L. exclusions limit from KamLAND [5], and discovery sensitivity of JUNO to the parameters of dark matter annihilation to sterile neutrino, assuming light mediator and g L = 0.1. The parameter space above the red curve would result in detectable events in the JUNO-LES sample with an exposure of 20 kton-yr. The gray curve shows the thermal rate required for obtaining the observed dark matter abundance. For comparison, we show the exclusion limit from Super-Kamiokande obtained from dark matter annihilation to neutrinos [48,50]. We also show the projected sensitivity from DUNE [48] and Hyper-Kamiokande [51] to the active neutrino channel. These are relevant for the case of large mixing angle between active and sterile neutrino.
100 MeV to a few GeV. We also show the exclusion limits from Super-Kamiokande and the projected sensitivity of DUNE and Hyper-Kamiokande for dark matter annihilation to active neutrinos, relevant when the mixing angle between active and sterile neutrino is large. Note that the above limits were calculated assuming a light mediator. For a given value of M χ , the limits for the heavy mediator case can be obtained using Eq. (16), which gives the substitution rule where the subscript L(H) denote the parameters in the light (heavy) mediator scenario.

C. Boosted Dark Matter
The elastic scattering between dark matter and proton (χ + p → χ + p) in scintillator detector like JUNO will lead to a singles event from the scintillation signal of the recoiled proton. In general, the momentum transfer to protons from the scattering with cold and nonrelativistic dark matter is small, quenched, and cannot be detected. However, the interaction of cosmic rays on galactic dark matter can boost these particles to higher velocities, which allows for larger momentum transfers in a detector [32,33]. In Ref. [52], constraints on the FIG. 7. The 90% C.L discovery sensitivity with the JUNO-LES 20 kton-yr sample to the parameters of boosted dark matter is shown in red. The gray dashed line is the corresponding estimate from Ref. [52]. The exclusion limits from XENON1T and other direct detection experiments are adapted from [32,33]. The limit from cosmology is taken from [53].
interaction cross section σ χp and the mass of dark matter M χ were obtained from neutrino experiments. The sensitivity of JUNO was projected by appropriate scaling of KamLand data. The LES spectrum computed in this paper will act as a background in the search for such boosted dark matter. We recalculate the projected sensitivity of JUNO to σ χp in the light of the LES background.
As the main objective of this paper is to highlight the importance of measurement of the LES sample, we do not compute the flux of boosted dark matter in detail. In Ref. [52], the differential flux is provided for a few benchmark values of dark matter mass. By fitting to a broken power law, we find that, for dark matter masses below a few hundred MeV, the flux can be approximated by a simplified expression The differential cross section for χp ES is taken to be dσ χp /dT p = σ χp /T max p [52]. We compute the total number of events with E vis ∈(15, 100) MeV, and obtain the 90% C.L. discovery sensitivity of JUNO by comparing with the total events in the LES sample, which we consider as background. The results are shown in Fig. 7 along with other relevant limits. Our projected sensitivity is consistent with [52] at higher DM masses, however it indicates a degradation in sensitivity for M χ < 100 MeV.

VI. SUMMARY AND OUTLOOK
The neutral-current interactions of atmospheric neutrinos in a large volume liquid scintillator detector, such as JUNO, is mainly through elastic scattering (ES) on protons and quasi-elastic-like (QEL) scattering on carbon nuclei. The recoiled protons are detected through their scintillation signal. Such prompt-only events are also called as "singles". In this paper, we predict the visible energy distribution of singles at JUNO, due to atmospheric neutrino interactions through the νp ES and νC QEL channels.
We determine the background due to cosmogenic isotope decay, which would dominate for E vis ≤ 16.5 MeV. Using veto on singles in the vicinity of a muon track, we show that the threshold may be reduced to E vis ∼ 15 MeV, above which the atmospheric neutrino signal dominates. Based on our estimates, we propose that JUNO can maintain a Large Energy Singles (LES) database (i.e., E vis ≥ 15 MeV and no delayed neutron capture signal) wherein the neutral-current interactions of atmospheric neutrinos can be detected. The main results of this paper are shown in Fig. 4.
The first goal with the LES events would be to establish their existence, and therefore ensure the detection of neutral-current interactions of low-energy atmospheric neutrinos. Assuming only statistical errors and no other background, we expect JUNO would discover these events with the exposure of a few tenths kton-yr. The next step would be a confirmed detection of νp ES events, which is a robust prediction of Standard Model with small uncertainties. We estimate that JUNO can find evidence of νp ES by rejecting the QEL-only hypothesis at 3 σ (5 σ) with 12 (34) kton-yr exposure.
The LES database can also probe new physics scenarios, which can give rise to singles in the detector. The LES sample is particularly advantageous if the new physics model does not admit charged-current-like interactions, for example, in the case of boosted dark sector particles. We have estimated the discovery sensitivity of the LES sample for such scenarios. We also estimate the discovery sensitivity for two well-motivated new physics scenarios -dark matter annihilation to sterile neutrinos, and boosted dark matter. In principle, the LES sample would also be sensitive to neutral-current non-standard interactions that modify the predictions of νp ES and νC QEL channels. However, we have not considered this possibility in this work.
The estimates obtained in the paper are promising. Future work with detailed studies of neutrino interactions in JUNO detector will shed more light on backgrounds, and aid in developing mitigation techniques. We look forward to a detailed study of the muon spallation at JUNO, and veto analysis including pulse shape discrimination. This will allow for a lower threshold, and therefore, enhance the prospects for the detection of low-energy atmospheric neutrinos and possible new physics signals. The event rate per day for the cosmogenic isotopes is shown against the end point of their beta decay spectrum without (Top) and with (Bottom) ∆tveto = 2 s. Right: The singles spectrum from decays of cosmogenic isotopes without (Top) and with (Bottom) ∆tveto = 2 s. The color convention is such that the isotopes with lower (higher) E max β are shown with blue (red) shades. The black curve represents the total cosmogenic background. We have also shown the LES spectrum with dashed light-purple curve for comparison.