Neutral-current background induced by atmospheric neutrinos at large liquid-scintillator detectors: II. Methodology for in situ measurements
NNeutral-current background induced by atmosphericneutrinos at large liquid-scintillator detectors:II. in situ measurement
Jie Cheng a ∗ , Yu-Feng Li a,b † , Hao-Qi Lu a ‡ , Liang-Jian Wen a § a Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China b School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Abstract
Future large liquid-scintillator (LS) detectors are competitive with and complementaryto the water-Cherenkov detectors on the searches for diffuse supernova neutrino backgroundand nucleon decay. In a companion paper, we have performed a systematic calculation ofthe neutral-current (NC) background induced by atmospheric neutrino interactions on Cnuclei in LS detectors, which are expected to be crucially important for the experimentalsearches for the diffuse supernova neutrino background and nucleon decay. In this paper, weperform a systematic study on the in situ measurement of the NC background and evaluatethe associated uncertainties. We first exploit the characteristics of the NC background, inparticular, the multiplicities of neutrons and pions, and the possible association with unstableresidual nuclei. It turns out that the neutron multiplicity distribution is very powerful todiscriminate among different models. Then, we develop a maximum-likelihood method tomeasure in situ the NC interactions with a triple-coincidence signature. Finally, a data-driven approach is proposed to evaluate the uncertainty of the NC background in the searchfor the diffuse supernova neutrino background. We conclude that future large LS experimentslike JUNO (Jiangmen Underground Neutrino Observatory) will be able to make a uniquecontribution to the worldwide data set to improve the prediction of atmospheric neutrinoNC interactions on C. ∗ Email: [email protected] † Email: [email protected] ‡ Email: [email protected] § Email: [email protected] a r X i v : . [ h e p - e x ] S e p Introduction
Atmospheric neutrino observations have played an important role in the field of neutrino physics [1],starting from the discovery of neutrino oscillations [2,3] to the precision measurements of neutrinomasses and mixing parameters [4–6]. In the future, atmospheric neutrinos offer the chance to mea-sure the unknown parameters of neutrino mass ordering [7, 8] and leptonic CP violation [9, 10].Meanwhile, atmospheric neutrinos will also contribute to the irreducible backgrounds for rare eventsearches in large neutrino detectors, e.g., the diffuse supernova neutrino background (DSNB), andnucleon decay.The DSNB is the integrated supernova (SN) neutrino flux from all past core-collapse events inthe visible Universe, holding precise information on the cosmic star-formation rate, the average SNneutrino energy spectrum, and the rate of failed SNe [11–13]. The existing and future large water-Cherenkov (wCh) and liquid-scintillator (LS) detectors, such as Super-K [14, 15], Hyper-K [18],JUNO [19] and Theia [20], have good potential to observe the DSNB via the inverse-beta-decay(IBD) reaction, ν e + p → e + + n , which consists of a prompt signal of positron and a delayedsignal of neutron capture. The LS detectors have intrinsically high efficiency of IBD detection dueto excellent neutron tagging. However, both wCh and LS detectors suffer from the most criticalbackground created by neutral-current (NC) interactions of atmospheric neutrinos with O and C, respectively.Nucleon decay, in particular for the proton or bound neutron decay with baryon numberviolation, is the smoking-gun signature for the Grand Unified Theories (GUTs), constituting onemajor physical goal of the existing and future large wCh and LS detectors. The golden decaychannels are p → e + + π , p → K + + ν and n → e + + π − , n → K + + e − [1]. Thereforethe typical detection signatures of π ± , K ± are important to recognize the signal events of nucleondecay. Again, the NC interactions of atmospheric neutrinos with O and C constitute importantbackgrounds in the wCh and LS detectors.The prediction of NC interactions induced by atmospheric neutrinos ( ν atm ) in either LS orwater has large systematic uncertainties, due to large variations of model predictions and limitedconstraints from experimental data. The uncertainties come from the atmospheric neutrino flux,the NC interaction cross-section and the nucleus deexcitation processes. In the search for extrater-restrial ¯ ν e ’s at KamLAND [21], the calculated NC background with the prompt energy between 7.5MeV and 30 MeV has an uncertainty of 29%. In the recent measurement of the neutrino-oxygenNC quasi-elastic (NCQE) cross section using atmospheric neutrinos at Super-K [22], the uncer-tainties on flux, ν/ ¯ ν ratio and cross sections for the NC processes other than NCQE are estimatedto be 18%, 5% and 18%, respectively. In a companion paper, referred to hereafter as “the pre-ceding paper” [23], we have performed a systematic study of ν atm - C NC interactions in LS. Therates and spectra of the NC backgrounds in LS are obtained by a two-fold calculation approach:the sophisticated generators
GENIE and
NuWro are implemented to calculate the neutrino-carboninteractions, then the
TALYS package is employed to deal with the deexcitation processes of theresidual nuclei. From these simulations we conclude there is a large uncertainty on the predictionof ν atm - C NC background for the DSNB search, i.e., 20%, that originates from the variations ofdifferent nuclear models. Similar uncertainty is found in the background prediction for nucleon2ecay searches via the p → K + + ν channel.Reducing the uncertainty of the ν atm - C NC background prediction is of prominent importancefor the searches for the DSNB and nucleon decay. Motivated by this, we perform a systematicanalysis of the calculated NC background from Ref. [23] for the DSNB search. First we exploitthe characteristics of the NC interactions, in particular, the correlations among the neutron mul-tiplicity, the daughter residual nuclei and the prompt energy deposit of the particles (e.g., p , α ,neutrons and γ -rays) in the exclusive channels of the neutrino- C NC interactions. Such correla-tions are utilized to measure in situ the NC background. Second, in a realistic detector, possiblebackground sources that can mimic the signatures of NC interactions should be evaluated, becausethey may degrade the precision of the in situ measurement of the NC background. To be concrete,we choose the JUNO detector for a demonstration, and toy Monte Carlo datasets are built and theevent selection criteria are developed. Using the toy datasets, we employ a maximum likelihoodmethod to extract the NC background with the triple-coincidence signature. The uncertaintyof the measured NC background is propagated to the DSNB signal region. Such a data-drivenapproach is promising to significantly reduce the uncertainty of the NC background prediction forthe DSNB search in LS detectors, from around 20% to 10% level.The remaining part of the paper is organized as follows. In Sec. 2, we highlight the keycharacteristics from the simulations of the ν atm - C NC interactions. Sec. 3 introduces the approachto the in situ measurement of the NC interactions and demonstrates the method of reducing theuncertainty of NC background prediction for the DSNB search. Finally, we summarize our studiesand conclude in Sec. 4. ν atm - C NC interactions
In Ref. [23], we have calculated the NC background induced by atmospheric neutrino interactionswith the C nuclei in the LS detectors. The Monte Carlo setup and data sample used in thiswork are inherited from the preceding paper. In that calculation, the up-to-date fluxes of atmo-spheric neutrinos at the JUNO site provided by the Honda group [24] are used. Six representativenuclear models from the generators
GENIE (2.12.0) [25] and
NuWro (1.7.10) [26] are used tocalculate the neutrino-nucleus interactions: one model from
GENIE (i.e., Model-G) and five mod-els from
NuWro (i.e., Model-N i for i =1,2,3,4,5). The notations and detailed descriptions of thesix models are in the preceding paper [23], and a brief summary is presented in the following.The adopted models differ in the input values of the axial mass M A in the parametrization ofthe nuclear axial-vector form factor. GENIE uses M A = 0 .
99 GeV [27] as the default setting. In
NuWro , this parameter can be tuned, and thus three different values, M A = 0.99, 1.35 [28], and1.03 [29] GeV are taken, respectively. Regarding the models of nuclear structure, GENIE uses therelativistic Fermi gas (RFG) model, while
NuWro includes both RFG and the spectral function(SF) approach. Furthermore, to illustrate the two-body current effects in quasi-elastic scattering(QEL), the transverse enhancement model (TEM) [30] of the meson exchange current from
NuWro is considered. It should be emphasized that only the axial mass M A in the treatment of QEL in NuWro has been changed. For both generators, we have employed their default setting for all otherprocesses. 3n different energy ranges from 100 MeV to GeV or even higher, the dominant contributionsto the cross section comes roughly from QEL, coherent and diffractive production (COH), nuclearresonance production (RES), and deep inelastic scattering (DIS). The event rates of the QEL,RES, COH and DIS processes of the NC interactions of atmospheric neutrinos with C nucleiare shown in Fig. 1. The rates are displayed with respect to the neutrino energy and the energytransfer, respectively, in the left and right panel. The energy transfer ( E trans ≡ E ν − E ν (cid:48) ) isdefined as the energy difference between incoming and outgoing neutrinos. Since the predictionsfrom Model-N i for i = 1 , , , -
10 1 10 [GeV] n E -
10 110 ] - y r - [ k t n E · ) n n ( E Model-GModel-N1Model-N5
QEL RES COHDIS 1 10 [MeV] trans E - - - -
10 110 ] - y r - [ k t t r a n s E · ) t r a n s n ( E Model-GModel-N1Model-N5
QEL RES COH DIS
Figure 1: Event rates of the QEL, RES, COH and DIS processes of neutrino- C NC interactionswith respect to the incoming neutrino energy (left panel) and the energy transfer (right panel).The rates are obtained in the preceding paper [23], and multiplied by the neutrino energy ( E ν ) andthe energy transfer ( E trans ) in two panels, respectively. Note that the event rates for all processes inthe series of models (i.e., Model-N i for i =1,2,3,4) are quite similar, thus only Model-G, Model-N1and Model-N5 are shown.The deexcitation processes of the final-state nuclei produced in the NC interactions are handledby using TALYS (1.8) [31]. Finally, a
GEANT4 based Monte Carlo simulation is used to convertthe kinetic energies of final-state particles in the NC interactions to the visible energies of thefinal events in the LS detectors. For simplicity, neither optical simulation nor specific detectorgeometry is involved, and only the quenching effect in LS is considered using the Birks’ constantsdescribed in Ref. [19]. A summary of some observations from the preceding paper is helpful andrelevant to this work. • The QEL process of neutrino- C interactions is the predominant background for the DSNBsearch. The neutron multiplicity distribution in the final-state will be useful to scrutinizethe nuclear models, e.g., the
GENIE generator produces significantly higher event rates inthe channels with more than two neutrons. Moreover, the NC interactions with one neutronproduction may mimic the DSNB-like signal. The event rate for the exclusive processeswith one neutron production is calculated to be (16 . ± .
8) kt − yr − in the whole rangeof visible energies. The rate reduces to (3 . ± .
5) kt − yr − if restricting into the energywindow 11 MeV (cid:46) E vis (cid:46)
30 MeV of interest. The associated uncertainty is about 20%,4epresenting the model variations of neutrino interactions. If adding in quadrature the extrauncertainty of 15% from the calculations of atmospheric neutrino fluxes, we obtain the overalluncertainty will be 25%. • For the search for nucleon decay in LS, the relevant region of visible energy is around severalhundred MeV, for which the COH, RES and DIS processes are significant contributors. Themost relevant backgrounds from NC interactions are identified as the production of singlecharged pions π ± or kaons K ± but no neutrons, because they may mimic the three-foldcoincidence signature of p → K + + ν . Many NC interactions produce multiple neutronsand π ± , and their multiplicity distributions can be measured via the neutron-captures andMichel electrons, which will also be very useful to scrutinize the nuclear models. Notethat the multiplicity of Michel electrons can also be used to discriminate the neutrinos andantineutrinos, e.g., in the water of Super-K [4].The signatures of DSNB and nucleon decay are quite different. Thus, it requires a dedicatedanalysis of the NC background induced by atmospheric neutrinos, in particular, a data-drivenapproach to utilize future experimental data to evaluate the nuclear models. In the following, wefocus on the DSNB search, and perform a systematic analysis of the most relevant NC background,i.e., the QEL processes, and leave the study of other processes relevant for nucleon decay searchfor the future. In the QEL process of the neutrino- C NC interactions in the LS detectors, one or more nucleonsmay be knocked out from the carbon nucleus. In Ref. [23], the event rates for the NC interactions inthe exclusive channels have been obtained and categorized by the associated neutron multiplicities,defined as the numbers of produced neutrons from an NC interaction. Moreover, many residualnuclei from the NC interactions are unstable isotopes. If the half-life is in a proper time window,the correlation between the isotopic decay and the parent NC interaction can be identified in LS.For this purpose, the NC interactions from QEL process can be divided into two categories: • Category I: the interactions associated with a suitably long-lived residual nucleus, i.e., C( T / = 20 .
39 min, Q β + γ = 1 .
98 MeV), C ( T / = 19 . Q β + γ = 3 .
65 MeV) and Li( T / = 0 .
840 s, Q β − = 16 . • Category II: the other interactions. Their associated residual nuclei include stable isotopes,i.e., B, B, Be and Li; very short-lived isotopes, i.e., Be ( T / ∼ . × − s) and B( T / ∼ × − s); and very long-lived isotopes, i.e., Be ( T / = 1 . × yr, Q β − = 0 . Be ( T / = 53 . Q EC = 0 .
862 MeV).Fig. 2 shows the neutron multiplicity distributions for the above two categories. For all sixnuclear models, about (cid:38) − - - -
10 1 A r b it r a r y U n it s Model-GModel-N1Model-N2Model-N3Model-N4Model-N5 >0 k Model-G w/ E
Residual nuclei: Li C, C, Neutron multiplicity - - - -
10 1 A r b it r a r y U n it s Other residual nuclei
Figure 2: Neutron multiplicity distributions for the QEL process of the NC interactions of atmo-spheric neutrinos with C. The top panel is for the final-states associated with C, C and Li,which have suitably long-lived half-lives, and the bottom panel is for the final-states with otherresidual nuclei, respectively. The red dashed line represents the
GENIE model, for which neutronswith zero kinetic energies are removed.the neutron multiplicities increase. Among the interactions with at least one neutron, the
GENIE prediction for Category II has about 23% probability to produce more than two neutrons, muchhigher than any of the
NuWro models in which such probability is (5 − GENIE produces neutrons with zero kinetic energies in the final states of n + p + B and2 n + C, while the other
NuWro models do not. The issue of neutrons with zero kinetic energiesis a known problem [32], that typically results from some nucleon knockout events with highmultiplicities. But the validity of the neutron productions with zero kinetic energies still needs tobe determined. In our following simulation, we add a tiny kinetic energy for the correspondingneutron, in order to enable the capture simulation in LS. Note that the up-to-date GENIE versionsare expected to improve the modeling of the processes of low-energy nucleon knockout. Due tothe uncertainty of the neutron productions with zero kinetic energies, we include the red dashedline in Fig. 2, to show the effect of removing the neutrons at rest. We find that the probability ofinteractions in Category I without neutrons increases to about 2% if neutrons with zero kineticenergies are removed. GENIE (2.12.0) had an empirical intranuclear model (i.e., INTRANUKE ‘hA’) to simulate hadron absorption,followed by multi-nucleon knockout. The entire target nucleus may be blown apart and several very low energynucleons can be knocked out. However, sometimes there is not enough energy or some oddities with binding energysubtractions, and some nucleons are produced with zero kinetic energies. ν atm NC interactions. In Ref. [22], theNCQE events were selected by the nuclear deexcitation gamma and the neutron capture signalon hydrogen, however, the neutron tagging efficiency in water was only (4 − (SO ) [16], which is achieved on August 17,2020 [17]. For Hyper-K, with 0.1% by mass of gadolinium-loading, the neutron tagging efficiencymay reach 67% (90% for capture efficiency and 74% for event selection) [33]. For LS detectorslike JUNO, the neutron efficiency is intrinsically high. The rates of the two categories have certain correlations among the six nuclear models, as shown inFig. 3. The values produced by
NuWro models approximately have a linear dependency, whereasthe value from
GENIE is significantly off the trend line of the
NuWro points. If selecting theinteractions with only one captured neutron, the values from all models show a slightly betterlinear-dependency, and a linear fit gives a slope of 1.53 ± Li, this slope will slightly increase to 1.55. Furthermore, with a single tagged neutron, thesignatures of Category I and II are triple-coincidence and double-coincidence, respectively. Thelatter typically consists of a prompt signal by fast-neutron recoil and the energy deposition ofheavy charged particles ( p , d or α ) and a delayed signal by neutron capture on hydrogen, whilethe former has an additional signal from the unstable residual nucleus decaying at a later time.If selecting the interactions with two tagged neutrons, the linear dependency is 1.95 ± ± i for i =1,2,3,4)are quite similar, thus the average value and the standard deviation of the predictions from thesefive models are shown with error bars, and labeled by “Model-N(1-5)”. The exclusive channels arecategorized into triple-coincidences and double-coincidences, which are separated by the dashedline. The triple-coincidences are dominated by the channels associated with C and C, whilethe double-coincidences have several major contributors. For both
GENIE and
NuWro models, theratio of the total double-coincidences to the total triple-coincidences is about 3 /
2. By definition,both the triple-coincidence and the double-coincidence have only one tagged neutron. However, afew channels with double-neutron in the final states (i.e., 2 n + C, 2 n + 2 p + Be and 2 n + p + B)fall into these categories, and it can be explained by two effects. First, the energetic neutrons maydisappear due to their inelastic interactions with C. To qualitatively investigate this effect, we use
TALYS to calculate the cross sections of the exclusive n − C reactions at different incident neutronenergies. Then, taking the 2 n + C final-state as an example, the neutron energy distributionin Fig. 5 is used to calculate the integrated cross sections of the exclusive reaction channels. We7 -1 yr -1 Li [kt C and C, QEL w/ 024681012 ] - y r - Q EL w / o t h e r r e s i du a l nu c l e i [ k t =2 multi N =1 multi
N >0 multi N Model-G Model-N1 Model-N2Model-N3 Model-N4 Model-N5
Figure 3: Correlation between the rates of the NC interactions in the two categories. The differentmarkers represent different nuclear models. The black points correspond to no selection on neutronmultiplicity. The red and blue points represent the case of one tagged neutron ( N multi = 1) andtwo tagged neutrons ( N multi = 2), respectively. The solid and dashed lines are the linear fits to thepoints with N multi = 1 and N multi = 2, respectively, and the shaded bands are the 1 σ variations.find that about 7% neutrons of the 2 n + C final-state will vanish mainly via the C( n, α ) Be(4.8%), C( n, dα ) Li (0.6%), C( n, d ) B (0.5%), C( n, p ) B (0.5%) and other sub-dominantprocesses. This simplified calculation qualitatively explains the existence of the final states withdouble-neutron in Fig. 4. The rates in Fig. 4 are in fact obtained by a
GEANT4 simulation, whichtakes into account the neutron propagation.To select a triple-coincidence signature, there are three pairs of time intervals and distances:(∆ t pn , ∆ R pn ) for the prompt and neutron-capture pair, (∆ t nd , ∆ R nd ) for the neutron-capture andisotopic decay pair, and (∆ t pd , ∆ R pd ) for the prompt and isotopic decay pair. Most neutrons fromthe NC interactions are fast neutrons, and the neutrons associated with C have higher kineticenergies (see the left panel of Fig. 5), resulting in a wider probability-density-function (PDF) of∆ R pd for C than the PDFs for C and Li, as shown in the right panel of Fig. 5. Note that theremoval of the neutrons with zero kinetic energy leads to the PDF for C from Model-G beingclose to that from Model-N1. The PDF of ∆ R pd obtained from Monte Carlo simulations will beused for the fitting later. The ∆ t pd distribution follows (cid:80) B i · e − t/τ i /τ i , where B i and τ i are theproduction fractions and lifetimes of the residual isotopes.The triple-coincidence signature will be used to measure the NC interactions in the followingsection. Similar triple-coincidence signatures have been widely used to study the cosmogenic long-lived isotopes in LS detectors, such as Li/ He which is the most important background for reactorantineutrinos (e.g., see Refs. [34, 35]), and C which is a dominant background for solar neutrinos(e.g., see Refs. [36,37]). In these analyses, the prompt signal consists of the energetic muon signalsand the possible spallation neutron recoils. The spectral shapes of the isotopic decays and thetimes since the preceding muons were used to extract the production of cosmogenic isotopes.8 ) ( n , C ) ( , L i ) ( n , , B ) ( n , p , B e ) ( n , , L i ) , a ( n , p , B e ) ( n , p , d , B ) ( n , d , B ) ( , p , B e ) ( , , o t h e r s t o t a l -
10 110 ] - y r - E v e n t r a t e [ k t +X x nfi C + x n Final-state of
Model-GModel-N(1-5)
Figure 4: Rates of the ν atm - C NC interactions in the exclusive channels associated with onlyone captured neutron and the visible prompt energy being less than 100 MeV. The channels arecategorized by the final-states of the residual nuclei. The “others” refer to the summation of thechannels that each has a contribution less than 1% and “total” refers to the summation of allchannels. The blue bars represent the predictions from Model-G. The red circles with error barsstand for the mean value of the predictions from Model-N i (for i =1,2,3,4,5) and 1 σ deviation. Thedashed line separates the channels into two categories: triple-coincidences and double-coincidences. Neutron kinetic energy [MeV] - - - - A r b it r a r y U n it s C : Model-G C : Model-N1 C : Model-G >0) k C : Model-G (2E C : Model-N1 Li : Model-G Li : Model-N1 Distance [m] - - - A r b it r a r y U n it s pd R D Figure 5: Distributions of the kinetic energies of fast neutrons (left panel) and the distancesbetween the fast neutron recoils (deposited-energy weighted vertexes) and the isotope decays(right panel) in the NC triple-coincidences associated with C, C and Li, respectively. In situ measurement of QEL interactions
Based on the above characteristics, we develop a maximum-likelihood method to measure in situ the NC interactions with the triple-coincidence signature. To be concrete, we choose the JUNO9etector as an example, as the JUNO detector is a suitable representative for future LS detectors.The mock data samples are produced, including ν atm - C NC interactions with a single neutron,DSNB, reactor antineutrinos, cosmogenic products ( C/ C, fast neutrons and Li/ He), andaccidental coincidences. The details of the JUNO detector are not required, instead, the rates aretaken from the publicly available references. We concentrate on the demonstration of the methodand leave the complex detector effects for better works by the experimental collaboration. Table. 1summarizes the rates of individual MC samples used in this work, and some comments are helpful. • The initial rate and spectral shape of reactor antineutrinos are taken from Ref. [19]. • The long-lived cosmogenic isotopes like C, C, Li and He are correlated with theirpreceding muons. However, after muon veto selection, the residual events can be regardedto be randomly distributed in time and space. They can coincide with the physical double-coincidence to form an accidental triple-coincidence, similar to the natural radioactivity.Many muon-induced isotopes have strong correlations with spallation neutrons, e.g., seeRefs. [38, 39]. Taking the veto strategy developed in Ref. [38], the rates of C, Li and He can be suppressed by a factor of 310, 94 and 78, respectively, while maintaining a live-time efficiency of 84%. Due to the long half-life of C, that veto strategy only reduces C approximately by 10%. As also pointed out in Ref. [38], the simulations by
FLUKA and
GEANT4 predict different yields. In the recent solar neutrino study at JUNO [39], anextrapolation based on the measurements from KamLAND [37] and Borexino [36] is used.All these calculations predict that C has the largest yield. Thus, in this paper we onlyconsider the cosmogenic C and use the larger rate value 2300 kt − d − from Ref. [39],furthermore we quote the veto strategy and efficiency from Ref. [38]. • The rate of the cosmogenic Li/ He is taken from Ref. [19], and the veto strategy andcorresponding efficiency for Li/ He is quoted from Ref. [38]. The fast-neutron rate is scaledfrom Ref. [19] according to the higher muon rate in Ref. [39], and the fast-neutron energyspectrum is assumed to be flat. • The energy spectra and spatial distributions of natural radioactivity is taken from Ref. [39],where the α ’s are rejected by a pulse shape discriminator (PSD). • The NC backgrounds induced by atmospheric neutrinos are taken from Fig. 4. The averagevalues of the
NuWro models are used. Both the
GENIE and
NuWro values are tested forcomparison. • For the charged-current (CC) backgrounds induced by atmospheric neutrinos, it includesthe CC interactions on C and protons (i.e., the IBD by the atmospheric ν e ). The CCinteractions on C are calculated using
GENIE and
NuWro . It shows that the prompt energyis larger than 100 MeV if a neutron-capture signal is required, thus the contribution of ν atm - C CC backgrounds is neglected in the mock data set. As for the IBD events induced by theatmospheric ν e , the rate is calculated with the up-to-date fluxes of atmospheric neutrinosat JUNO site provided by the Honda group [24] and the IBD cross section in Ref. [40].10 The IBD rate from DSNB is calculated to be 0.30 kt − yr − for the energy range from7.5 MeV to 100 MeV, by using a DSNB model with the rate of core-collapse supernovae R CCSN = 10 − yr − Mpc − , the average energy of the core-collapse supernovae (CCSN) (cid:104) E (cid:105) =14 MeV and the fraction of the failed supernovae rate f BH =0.27. The parameters R CCSN , (cid:104) E (cid:105) and f BH may have broad variations [41].The mock data sets are produced based on Table. 1. First, the individual MC samples aregenerated randomly in time and the LS volume, and the correlations inside the double-coincidencesand triple-coincidences are automatically kept. Then, the independent data sets are combined andsorted by time to form the mock data samples. A set of mock data sets are produced assumingdifferent experimental exposures.Table 1: Rates of the individual toy MC data samples in this work. Rate a Reduction(kt · yr) − [ E, ∆ R, ∆ T ] [PSD, µ -veto] ν atm NC Triple coincidence C) 65.0% 95% · C) 62.5%0.08 ( Li) 10.0%3.68 ( C) 79.6% 95% · C) 80%0.05 ( Li) 9.4% ν atm NC Double coincidence (GENIE) 6.73 70.0% 95% · Other Double coincidence ν atm CC 0.21 84.4% 20% · · · ν e · Li/ He 1533 14.7% 20% · Accidental coincidence
Hz/kton (cid:15) ( E d ) N acc a11 C from µ a Accidental background number in a decay selected window.
Using the notations in Sec. 2.1.2, the following criteria are applied to the mock data set toselect triple-coincidences: E p ∈ (7 . , .
0) MeV, neutron multiplicity N multi = 1, E n ∈ (1 . , . t pn ∈ (1 . µ s , . R pn < . E d ∈ (1 . , .
5) MeV, ∆ t nd ∈ (1 . , . R pd < . E p , E n and E d are the energies of the prompt, neutron-like and decay-like signals. The prompt energy cut will remove all geo-neutrinos, a significant portion of thereactor antineutrinos, as well as all accidental coincidences with a natural radioactivity as theprompt. The E d cut covers the energy spectra of both C and C decays, and removes ∼ Li. To further reduce the accidental triple-coincidences, a PSD can be constructed utilizingthe scintillation time profile and applied to the prompt signal, and the detailed PSD study is inpreparation and will be published elsewhere. In this paper, we assume that a proper cut canmaintain 95% of the ν atm − C NC interactions, while only 20% of the e -like and γ -like promptsignals survive. The PSD optimization for specific detectors should take into account the detaileddetector parameters, and it is nontrivial and beyond the scope of this work. The efficienciesdue to the above selection criteria are shown in Table. 1. Both the natural radioactivity andthe cosmogenic C may mimic the decay-like signature of the NC triple-coincidence, and theirraw rates and accidental coincidence rates are also listed in Table. 1. To calculate the accidentalcoincidences caused by the intrinsic U, Th, K and
Pb radioactivity in LS, a ‘median’LS radio-purity level is considered (10 − g g − U/ Th, 10 − g g − K and 10 − g g − Pb),which is assumed to be 10 times worse than the ‘ideal’ radiopurity in Ref. [19]. Under thisassumption, the cosmogenic C will dominate the accidental triple-coincidences.
For the selected triple-coincidence candidates in each mock data set, the time interval (∆ t ) andthe cubic-distance (∆ r ) between the prompt and third events, and the energy of the third event( E d ) are fit to the PDF of Eq. (1), using an un-binned maximum likelihood (ML) method. F (∆ t, ∆ r , E d ) = (cid:88) i N i τ i · e − ∆ t/τ i · D i nc (∆ r ) · S i nc ( E d ) + 1 T · D acc (∆ r ) · (cid:88) j N j acc · S j acc ( E d ) (1)The first term in Eq. (1) represents the true triple-coincidences from NC interactions. The numberof triple-coincidences associated with each isotope ( C or C) is N i with τ i as the decay lifetime,while the contribution from Li is too small to be included in the fitting. The spatial distributionand the β energy spectrum of each isotope are denoted by D i nc (∆ r ) and S i nc ( E d ), respectively.The second term in Eq. (1) represents the accidental triple-coincidences with T as the coinci-dence window, in which the ∆ t has a flat distribution. D acc (∆ r ) accounts for approximately flatcontributions in space. The superscript j represents the two main contributors: the cosmogenic C and the natural radioactivity. N j acc and S j acc ( E d ) account for the event numbers and energyspectra, respectively. Note that S j acc ( E d ) for cosmogenic C should be identical to S i nc ( E d ) for C induced by the ν atm -C NC interactions. Fig. 6 shows an example of the ML fit, where the MCdata set uses GENIE prediction and has an exposure of 200 kt · yr. The upper, middle and lowerpanels are shown for the distributions of the time and spatial intervals between the prompt andthird events, and the energy of the third event, respectively. It demonstrates that the combinedfit distinguishes the NC interactions from the accidental contaminations by the cosmogenic Cand radioactivity.The total uncertainties ( σ tot ) and statistical uncertainties ( σ stat ) versus the experimental ex-posure are shown in Fig. 7. The σ tot is obtained from 1000 mock data sets at each fixed exposure.We observe that the three-dimensional fit with Eq. (1) utilizes more information and reduces theuncertainties compared to any of the two-dimensional combined fit or the one-dimensional fit.The σ tot from the fitting are significantly larger than σ stat , in particular for the C channel, dueto the parameters’ correlations. The shaded bands in Fig. 7 represent different scenarios on the12 r (cid:215) MC data: 200 ktC NC C NC C Cosmogenic Radioactivity t [s] D -
10 110 ] - E v e n t s [ s (a) - - -
10 1 10 ] [m r D ] - E v e n t s [ m (b) [MeV] d E ] - E v e n t s [ M e V (c) Figure 6: Example of the distributions of the selected triple-coincidence candidates (black points)using the
GENIE prediction with 200 kt · yr exposure: the time interval between the prompt andthird events (a), the cubic distance between the prompt and third events (b), and the energy ofthe third event (c). A combined fit to these distributions statistically distinguishes the two NCinteractions associated C and C from the cosmogenic C and radioactivity.LS radio-purity level and the rate of residual cosmogenic C. The upper edge accounts for theworst case that the internal radio-purity is worse by one order, while the lower edge accounts for apossibly better rejection of cosmogenic C. A dedicated muon simulation indicates that C pro-duction is accompanied by a high multiplicity of spallation neutrons. The accompanying neutrons,with a mean kinetic energy of a few tens of MeV, are captured mostly within one meter from the C production location. This allows us to develop a veto scheme by searching for the spallationneutrons close in space and time with respect to the third signal in a NC triple-coincidence candi-date. If one coincident spallation neutron is found, the third signal is rejected. A preliminary test13
50 100 150 200 250 300 yr] (cid:215)
Exposure [kt R e l a ti v e un ce r t a i n t y GENIE: NuWro: tot d variations tot d stat d tot d variations tot d stat d C channel yr] (cid:215) Exposure [kt R e l a ti v e un ce r t a i n t y GENIE: NuWro: tot d variations tot d stat d tot d variations tot d stat d C channel Figure 7: The projected uncertainties of the in situ measurement to the two NC channels. The solidline and dashed line represent the total uncertainty σ tot (solid line) and statistical uncertainty σ stat (dashed line), respectively. The shaded bands represent the variations due to different scenarioson the LS radiopurity and the rate of the residual C. The blue and red colors represent the
GENIE and
NuWro models, respectively.indicates that a rejection efficiency of 56% for cosmogenic C can be achieved by a veto windowof 0.35 m and 0.85 hrs, while maintaining a 97% efficiency for the NC background. With thisapproach, the uncertainty curve is roughly in the middle between the solid line and the lower edgeof the shaded bands. More sophisticated veto strategies can be developed for a specific detectorto suppress the cosmogenic C further. However, it is beyond the scope of this paper.
The above MC analysis validates the approach of measuring in situ the NC interactions associatedwith a suitably long-lived isotope (Category I as defined in Sec. 2). Although the analysis presentedhere is done for the NC interactions associated with single neutron capture only, the cases withtwo neutrons can as well be evaluated. Taking the correlation in Fig. 3, one can extrapolate thenumber of Category II interactions from the measured Category I interactions. Eventually the ν atm NC backgrounds can be well understood by using this data-driven approach. The outcomeis to reduce the systematic uncertainty of the predicted ν atm NC backgrounds in the searches forDSNB. A typical DSNB selection can be transformed from the criteria in Sec. 3, by releasing therequirement of a decay-like third signal, reducing the E p range to (11, 30) MeV, and reversing thePSD cut to remove the ν atm NC backgrounds. The residual background, N b , can be estimatedfrom the measured rates in Category I and the extrapolated rates in Category II: N b = (cid:88) i = C , C N i ε i · (cid:0) ε dsnb i + η · ε dsnbdc (cid:1) + N Li · ε dsnbLi (2) N i has the same definition as that in Eq. (1), and its uncertainty is taken from Fig. 7. ε i accountsfor the corresponding total efficiency in Table. 1. ε dsnbdc and ε dsnb i represent the efficiencies of thetotal NC double-coincidences and the triple-coincidence channel that satisfy the DSNB criteria,14espectively. η is the extrapolation factor obtained in Sec. 2.1.2. Since the triple-coincidenceassociated with Li is difficult to measure, its contribution to the background is estimated entirelyby simulation. N Li and ε dsnbLi are the simulated number of events and the efficiency with the DSNBcriteria, respectively. Note that the efficiencies ε dsnbdc , ε dsnb i and ε dsnbLi include two detector-dependentefficiencies for the DSNB search, i.e., the muon veto and the PSD cut, which are assumed to bethe same for the three isotopes. In a specific detector, the PSD cut efficiency might be slightlydifferent for different isotopes. However, such an effect is not considered in this work for simplicity.Here the efficiencies in Eq. (2) are obtained from MC, and their differences between the GENIE and
NuWro models are used to estimate the uncertainties of the efficiencies. According to Table. 1, ε i differs significantly between GENIE and
NuWro , predominately due to different spectra of neutronkinetic energy shown in Fig. 5. However, if the prompt visible energy is greater than 7.5 MeV, theenergy spectral shapes are quite similar in the C channel, resulting in an estimated uncertaintyof <
1% on the ratio of ε dsnb i /ε i . For the C channel, the shapes between
GENIE and
NuWro havea larger discrepancy, and this leads to a larger uncertainty of 5% on the ratio of ε dsnb i /ε i . Theuncertainties on the ratios of ε dsnbdc /ε i are estimated to be 4% and 6% for the C and C channels,respectively. The Li item in Eq. (2) contributes about <
1% to N b with a relative uncertaintyof ∼ N b isdominated by the uncertainty of the measured N C shown in Fig. 7. Even with an exposure of40 kt · yr, the uncertainty estimated by the data-driven approach can surpass that estimated fromthe model predictions ( ∼ ∼
10% level with an exposure of 200 kt · yr at a JUNO-like detector. In the present work, we have developed a data-driven approach to reduce the uncertainties ofthe predicted NC background induced by atmospheric neutrino interactions with the C nucleiin LS detectors, which is expected to be of great importance for the experimental searches forDSNB. Our analysis is based on the systematic calculations in the preceding paper [23]. In theenergy range of the DSNB, the QEL process of neutrino- C interactions is known to be the mostimportant. We have exploited the measurable characteristics of the QEL process in LS, such as theneutron multiplicity and the association with the suitably long-lived isotopes, which will allow usto scrutinize the nuclear models. Future large LS detectors like JUNO with enormous amounts of C nuclei, ultra-low radioactivity and excellent neutron tagging efficiency, are expected to make aunique contribution to the worldwide data set to improve the prediction of atmospheric neutrinoNC interactions on C.Taking the JUNO detector as an example, a maximum-likelihood method is developed tomeasure in situ the NC interactions with a triple-coincidence signature. Furthermore, we havedemonstrated that the uncertainties of NC backgrounds in the searches for DSNB can be con-strained via a data-driven approach. One caveat is that, in order to significantly improve theuncertainty, the experimental collaboration needs further suppress the cosmogenic C and im-prove the LS radiopurity. Our analysis has demonstrated that with an exposure of 40 kt · yr ata JUNO-like detector, the uncertainties obtained from the data-driven approach can surpass the15stimated variation between models. It bears the promise to achieve ∼
10% uncertainty with anexposure of 200 kt · yr.The NC background induced by atmospheric neutrinos is critical for future experimentalsearches for DSNB. Besides large LS detectors [19, 45], other large-scale detectors with advancedtechniques based on water [18], water-based LS [20] or liquid-Argon [46, 47] have good potentialto measure the DSNB signal. The analysis performed in the present work will be not only usefulfor LS detectors, but also instructive for the parallel studies of other types of detectors. Acknowledgements
The authors would like to thank Costas Andreopoulos, Wan-lei Guo, Bao-hua Sun and Yiyu Zhangfor helpful discussions, to Guo-fu Cao and Yao-guang Wang for checking the neutron captureprocesses, and to Michael Wurm, Ze-yuan Yu and Shun Zhou for carefully reading the manuscriptand valuable comments. This work was supported in part by National Key R&D Program ofChina under Grant No. 2018YFA0404101, by the National Natural Science Foundation of Chinaunder Grant Nos. 11835013 and 11675203, by the Strategic Priority Research Program of theChinese Academy of Sciences under Grant No. XDA10010100, by the China Postdoctoral ScienceFoundation funded project under Grant No. 2019M660793, and by the CAS Center for Excellencein Particle Physics (CCEPP).
References [1] M. Tanabashi et al. [Particle Data Group], “Review of Particle Physics,” Phys. Rev. D no.3, 030001 (2018).[2] Y. Fukuda et al. [Super-Kamiokande], “Evidence for oscillation of atmospheric neutrinos,”Phys. Rev. Lett. , 1562 (1998). [arXiv:hep-ex/9807003 [hep-ex]].[3] T. Kajita, “Nobel Lecture: Discovery of atmospheric neutrino oscillations,” Rev. Mod. Phys. no.3, 030501 (2016).[4] K. Abe et al. [Super-Kamiokande], “Atmospheric neutrino oscillation analysis with ex-ternal constraints in Super-Kamiokande I-IV,” Phys. Rev. D no.7, 072001 (2018).[arXiv:1710.09126 [hep-ex]].[5] P. Adamson et al. [MINOS], “Measurement of Neutrino and Antineutrino Oscillations Us-ing Beam and Atmospheric Data in MINOS,” Phys. Rev. Lett. no.25, 251801 (2013).[arXiv:1304.6335 [hep-ex]].[6] M. Aartsen et al. [IceCube], “Measurement of Atmospheric Neutrino Oscillations at 6–56GeV with IceCube DeepCore,” Phys. Rev. Lett. no.7, 071801 (2018). [arXiv:1707.07081[hep-ex]].[7] M. Aartsen et al. [IceCube], “PINGU: A Vision for Neutrino and Particle Physics at theSouth Pole,” J. Phys. G no.5, 054006 (2017). [arXiv:1607.02671 [hep-ex]].168] S. Adrian-Martinez et al. [KM3Net], “Letter of intent for KM3NeT 2.0,” J. Phys. G no.8,084001 (2016). [arXiv:1601.07459 [astro-ph.IM]].[9] S. Razzaque and A. Y. Smirnov, “Super-PINGU for measurement of the leptonic CP-phasewith atmospheric neutrinos,” JHEP , 139 (2015). [arXiv:1406.1407 [hep-ph]].[10] K. J. Kelly, P. A. Machado, I. Martinez Soler, S. J. Parke and Y. F. Perez Gonzalez, “Sub-GeV Atmospheric Neutrinos and CP-Violation in DUNE,” Phys. Rev. Lett. no.8, 081801(2019). [arXiv:1904.02751 [hep-ph]].[11] S. Ando and K. Sato, “Relic neutrino background from cosmological supernovae,” New J.Phys. , 170 (2004) [astro-ph/0410061].[12] J. F. Beacom, “The Diffuse Supernova Neutrino Background,” Ann. Rev. Nucl. Part. Sci. ,439 (2010) [arXiv:1004.3311 [astro-ph.HE]].[13] C. Lunardini, “Diffuse supernova neutrinos at underground laboratories,” Astropart. Phys. , 49 (2016) [arXiv:1007.3252 [astro-ph.CO]].[14] J. F. Beacom and M. R. Vagins, “GADZOOKS! Anti-neutrino spectroscopy with large waterCherenkov detectors,” Phys. Rev. Lett. , 171101 (2004) [hep-ph/0309300].[15] C. Simpson [Super-Kamiokande Collaboration], “Physics Potential of Super-K Gd,” PoSICHEP et al. [Hyper-Kamiokande Collaboration], “Hyper-Kamiokande Design Report,”arXiv:1805.04163 [physics.ins-det].[19] F. An et al. [JUNO Collaboration], “Neutrino Physics with JUNO,” J. Phys. G , no. 3,030401 (2016) [arXiv:1507.05613 [physics.ins-det]].[20] M. Askins et al. [Theia Collaboration], “Theia: An advanced optical neutrino detector,” Eur.Phys. J. C , no. 5, 416 (2020) [arXiv:1911.03501 [physics.ins-det]].[21] A. Gando et al. [KamLAND Collaboration], “A study of extraterrestrial antineutrino sourceswith the KamLAND detector,” Astrophys. J. , 193 (2012) [arXiv:1105.3516 [astro-ph.HE]].[22] L. Wan et al. [Super-Kamiokande Collaboration], “Measurement of the neutrino-oxygenneutral-current quasielastic cross section using atmospheric neutrinos at Super-Kamiokande,”Phys. Rev. D ∼ mhonda[25] C. Andreopoulos, A. Bell, D. Bhattacharya, F. Cavanna, J. Dobson et al. , “The GENIE Neu-trino Monte Carlo Generator,” Nucl. Instrum. Meth. A , 87-104 (2010). [arXiv:0905.2517[hep-ph]]. See also at the website ”http://genie-mc.org/”.[26] T. Golan, J. Sobczyk and J. Zmuda, “NuWro: the Wroclaw Monte Carlo Generator of Neu-trino Interactions,” Nucl. Phys. B Proc. Suppl. , 499-499 (2012). See also at thewebsite ”https://nuwro.github.io/user-guide/”.[27] T. Kitagaki et al. “Study of νd → µ − pp ( s ) and νd → µ − ∆ ++ (1232) n ( s ) using the BNL 7-footdeuterium filled bubble chamber,” Phys. Rev. D , 1331-1338 (1990).[28] A. Aguilar-Arevalo et al. [MiniBooNE], “First Measurement of the Muon Neutrino ChargedCurrent Quasielastic Double Differential Cross Section,” Phys. Rev. D , 092005 (2010)[arXiv:1002.2680 [hep-ex]].[29] V. Bernard, L. Elouadrhiri and U. G. Meissner, “Axial structure of the nucleon: TopicalReview,” J. Phys. G , R1-R35 (2002) [arXiv:hep-ph/0107088 [hep-ph]].[30] A. Bodek, H. Budd and M. Christy, “Neutrino Quasielastic Scattering on Nuclear Targets:Parametrizing Transverse Enhancement (Meson Exchange Currents),” Eur. Phys. J. C ,1726 (2011) [arXiv:1106.0340 [hep-ph]].[31] A.J. Koning, S. Hilaire and M.C. Duijvestijn, ”TALYS-1.0”, Proceedings of the InternationalConference on Nuclear Data for Science and Technology, April 22-27, 2007, Nice, France,editors O.Bersillon, F.Gunsing, E.Bauge, R.Jacqmin, and S.Leray, EDP Sciences, 2008, p.211-214.[32] Private communications with Costas Andreopoulos from GENIE collaboration.[33] K. Abe et al. , “Letter of Intent: The Hyper-Kamiokande Experiment — Detector Design andPhysics Potential —,” arXiv:1109.3262 [hep-ex].[34] F. P. An et al. [Daya Bay Collaboration], “Observation of electron-antineutrino disappearanceat Daya Bay,” Phys. Rev. Lett. , 171803 (2012) [arXiv:1203.1669 [hep-ex]].[35] D. Adey et al. [Daya Bay Collaboration], “Measurement of the Electron Antineutrino Os-cillation with 1958 Days of Operation at Daya Bay,” Phys. Rev. Lett. , no. 24, 241805(2018) [arXiv:1809.02261 [hep-ex]].[36] G. Bellini et al. [Borexino Collaboration], “Cosmogenic Backgrounds in Borexino at 3800 mwater-equivalent depth,” JCAP , 049 (2013) [arXiv:1304.7381 [physics.ins-det]].1837] S. Abe et al. [KamLAND Collaboration], “Production of Radioactive Isotopes through CosmicMuon Spallation in KamLAND,” Phys. Rev. C , 025807 (2010) [arXiv:0907.0066 [hep-ex]].[38] J. Zhao, L. J. Wen, Y. F. Wang and J. Cao, “Physics potential of searching for 0 νββ decaysin JUNO,” Chin. Phys. C , no. 5, 053001 (2017) [arXiv:1610.07143 [hep-ex]].[39] A. Abusleme et al. [JUNO], “Feasibility and physics potential of detecting B solar neutrinosat JUNO,” [arXiv:2006.11760 [hep-ex]].[40] A. Strumia and F. Vissani, “Precise quasielastic neutrino/nucleon cross-section,” Phys. Lett.B , 42-54 (2003) [arXiv:astro-ph/0302055 [astro-ph]].[41] A. Priya and C. Lunardini, “Diffuse neutrinos from luminous and dark supernovae: prospectsfor upcoming detectors at the O (10) kt scale,” JCAP , 031 (2017) [arXiv:1705.02122 [astro-ph.HE]].[42] M. Honda, T. Kajita, K. Kasahara, S. Midorikawa and T. Sanuki, “Calculation of atmosphericneutrino flux using the interaction model calibrated with atmospheric muon data,” Phys. Rev.D , 043006 (2007) [astro-ph/0611418].[43] M. Honda, “Improving the prediction of the Atmospheric neutrino flux using the atmosphericmuon flux,” EPJ Web Conf. , 07001 (2019).[44] F. P. An et al. [Daya Bay Collaboration], “Cosmogenic neutron production at Daya Bay,”Phys. Rev. D , no. 5, 052009 (2018) [arXiv:1711.00588 [hep-ex]].[45] M. Wurm et al. [LENA Collaboration], “The next-generation liquid-scintillator neutrino ob-servatory LENA,” Astropart. Phys. , 685 (2012). [arXiv:1104.5620 [astro-ph.IM]].[46] A. Bueno et al. , “Nucleon decay searches with large liquid argon TPC detectors at shallowdepths: Atmospheric neutrinos and cosmogenic backgrounds,” JHEP , 041 (2007). [hep-ph/0701101].[47] R. Acciarri et al.et al.