di use supernova neutrino background search at super
TRANSCRIPT
Diffuse Supernova Neutrino Background Search at Super-Kamiokande
K. Abe,1, 43 C. Bronner,1 Y. Hayato,1, 43 K. Hiraide,1 M. Ikeda,1 S. Imaizumi,1 J. Kameda,1, 43 Y. Kanemura,1
Y. Kataoka,1 S. Miki,1 M. Miura,1, 43 S. Moriyama,1, 43 Y. Nagao,1 M. Nakahata,1, 43 S. Nakayama,1, 43 T. Okada,1
K. Okamoto,1 A. Orii,1 G. Pronost,1 H. Sekiya,1, 43 M. Shiozawa,1, 43 Y. Sonoda,1 Y. Suzuki,1 A. Takeda,1, 43
Y. Takemoto,1 A. Takenaka,1 H. Tanaka,1 S. Watanabe,1 T. Yano,1 S. Han,2 T. Kajita,2, 43 K. Okumura,2, 43
T. Tashiro,2 J. Xia,2 G. D. Megias,3 D. Bravo-Berguno,4 L. Labarga,4 Ll. Marti,4 B. Zaldivar,4 B. W. Pointon,6, 47
F. d. M. Blaszczyk,5 E. Kearns,5, 43 J. L. Raaf,5 J. L. Stone,5, 43 L. Wan,5 T. Wester,5 J. Bian,7 N. J. Griskevich,7
W. R. Kropp,7 S. Locke,7 S. Mine,7 M. B. Smy,7, 43 H. W. Sobel,7, 43 V. Takhistov,7, 43 J. Hill,8 J. Y. Kim,9
I. T. Lim,9 R. G. Park,9 B. Bodur,10 K. Scholberg,10, 43 C. W. Walter,10, 43 S. Cao,53 L. Bernard,11 A. Coffani,11
O. Drapier,11 S. El Hedri,11, ∗ A. Giampaolo,11, † M. Gonin,11 Th. A. Mueller,11 P. Paganini,11 B. Quilain,11
T. Ishizuka,12 T. Nakamura,13 J. S. Jang,14 J. G. Learned,15 L. H. V. Anthony,16 D. Martin,16 M. Scott,16
A. A. Sztuc,16 Y. Uchida,16 V. Berardi,17 M. G. Catanesi,17 E. Radicioni,17 N. F. Calabria,18 L. N. Machado,18
G. De Rosa,18 G. Collazuol,19 F. Iacob,19 M. Lamoureux,19 M. Mattiazzi,19 N. Ospina,19 L. Ludovici,20
Y. Maekawa,21 Y. Nishimura,21 M. Friend,23 T. Hasegawa,23 T. Ishida,23 T. Kobayashi,23 M. Jakkapu,23
T. Matsubara,23 T. Nakadaira,23 K. Nakamura,23, 43 Y. Oyama,23 K. Sakashita,23 T. Sekiguchi,23 T. Tsukamoto,23
Y. Kotsar,24 Y. Nakano,24 H. Ozaki,24 T. Shiozawa,24 A. T. Suzuki,24 Y. Takeuchi,24, 43 S. Yamamoto,24 A. Ali,25
Y. Ashida,25, ‡ J. Feng,25 S. Hirota,25 T. Kikawa,25 M. Mori,25 T. Nakaya,25, 43 R. A. Wendell,25, 43 K. Yasutome,25
P. Fernandez,26 N. McCauley,26 P. Mehta,26 K. M. Tsui,26 Y. Fukuda,27 Y. Itow,28, 29 H. Menjo,28 T. Niwa,28
K. Sato,28 M. Tsukada,28 J. Lagda,30 S. M. Lakshmi,30 P. Mijakowski,30 J. Zalipska,30 J. Jiang,31 C. K. Jung,31
C. Vilela,31 M. J. Wilking,31 C. Yanagisawa,31, § K. Hagiwara,32 M. Harada,32 T. Horai,32 H. Ishino,32 S. Ito,32
H. Kitagawa,32 Y. Koshio,32, 43 W. Ma,32 N. Piplani,32 S. Sakai,32 G. Barr,33 D. Barrow,33 L. Cook,33, 43
A. Goldsack,33, 43 S. Samani,33 D. Wark,33, 38 F. Nova,34 T. Boschi,22 F. Di Lodovico,22 J. Gao,22 J. Migenda,22
M. Taani,22 S. Zsoldos,22 J. Y. Yang,35 S. J. Jenkins,36 M. Malek,36 J. M. McElwee,36 O. Stone,36 M. D. Thiesse,36
L. F. Thompson,36 H. Okazawa,37 S. B. Kim,39 J. W. Seo,39 I. Yu,39 K. Nishijima,40 M. Koshiba,41, ¶ K. Iwamoto,42
K. Nakagiri,42 Y. Nakajima,42, 43 N. Ogawa,42 M. Yokoyama,42, 43 K. Martens,43 M. R. Vagins,43, 7 M. Kuze,44
S. Izumiyama,44 T. Yoshida,44 M. Inomoto,45 M. Ishitsuka,45 H. Ito,45 T. Kinoshita,45 R. Matsumoto,45
K. Ohta,45 M. Shinoki,45 T. Suganuma,45 A. K. Ichikawa,54 K. Nakamura,54 J. F. Martin,46 H. A. Tanaka,46
T. Towstego,46 R. Akutsu,47 V. Gousy-Leblanc,47, ‖ M. Hartz,47 A. Konaka,47, ‖ P. de Perio,47 N. W. Prouse,47
S. Chen,48 B. D. Xu,48 Y. Zhang,48 M. Posiadala-Zezula,49 D. Hadley,50 M. O’Flaherty,50 B. Richards,50
B. Jamieson,51 J. Walker,51 A. Minamino,52 K. Okamoto,52 G. Pintaudi,52 S. Sano,52 and R. Sasaki52
(Super-Kamiokande Collaboration)1Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan
2Research Center for Cosmic Neutrinos, Institute for Cosmic RayResearch, University of Tokyo, Kashiwa, Chiba 277-8582, Japan
3Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan4Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
5Department of Physics, Boston University, Boston, MA 02215, USA6Department of Physics, British Columbia Institute of Technology, Burnaby, BC, V5G 3H2, Canada
7Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA8Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USA
9Institute for Universe and Elementary Particles, Chonnam National University, Gwangju 61186, Korea10Department of Physics, Duke University, Durham NC 27708, USA
11Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France12Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
13Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan14GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
15Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA16Department of Physics, Imperial College London , London, SW7 2AZ, United Kingdom
17Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Universita e Politecnico di Bari, I-70125, Bari, Italy18Dipartimento di Fisica, INFN Sezione di Napoli and Universita di Napoli, I-80126, Napoli, Italy
19Dipartimento di Fisica, INFN Sezione di Padova and Universita di Padova, I-35131, Padova, Italy20INFN Sezione di Roma and Universita di Roma “La Sapienza”, I-00185, Roma, Italy
21Department of Physics, Keio University, Yokohama, Kanagawa, 223-8522, Japan22Department of Physics, King’s College London, London, WC2R 2LS, UK
23High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan24Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
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25Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan26Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom
27Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan28Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
29Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, Aichi 464-8602, Japan30National Centre For Nuclear Research, 02-093 Warsaw, Poland
31Department of Physics and Astronomy, State University of New York at Stony Brook, NY 11794-3800, USA32Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
33Department of Physics, Oxford University, Oxford, OX1 3PU, United Kingdom34Rutherford Appleton Laboratory, Harwell, Oxford, OX11 0QX, UK
35Department of Physics, Seoul National University, Seoul 151-742, Korea36Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, United Kingdom
37Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan38STFC, Rutherford Appleton Laboratory, Harwell Oxford, and
Daresbury Laboratory, Warrington, OX11 0QX, United Kingdom39Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
40Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan41The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
42Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan43Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University ofTokyo Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8583, Japan
44Department of Physics,Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan45Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan
46Department of Physics, University of Toronto, ON, M5S 1A7, Canada47TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3, Canada
48Department of Engineering Physics, Tsinghua University, Beijing, 100084, China49Faculty of Physics, University of Warsaw, Warsaw, 02-093, Poland
50Department of Physics, University of Warwick, Coventry, CV4 7AL, UK51Department of Physics, University of Winnipeg, MB R3J 3L8, Canada
52Department of Physics, Yokohama National University, Yokohama, Kanagawa, 240-8501, Japan53Institute For Interdisciplinary Research in Science and Education, ICISE, Quy Nhon, 55121, Vietnam
54Department of Physics, Faculty of Science, Tohoku University, Sendai, Miyagi, 980-8578, Japan(Dated: September 24, 2021)
A new search for the diffuse supernova neutrino background (DSNB) flux has been conducted atSuper-Kamiokande (SK), with a 22.5 × 2970-kton·day exposure from its fourth operational phaseIV. The new analysis improves on the existing background reduction techniques and systematicuncertainties and takes advantage of an improved neutron tagging algorithm to lower the energythreshold compared to the previous phases of SK. This allows for setting the world’s most stringentupper limit on the extraterrestrial νe flux, for neutrino energies below 31.3 MeV. The SK-IV resultsare combined with the ones from the first three phases of SK to perform a joint analysis using22.5 × 5823 kton·days of data. This analysis has the world’s best sensitivity to the DSNB νe flux,comparable to the predictions from various models. For neutrino energies larger than 17.3 MeV,the new combined 90% C.L. upper limits on the DSNB νe flux lie around 2.7 cm−2·sec−1, stronglydisfavoring the most optimistic predictions. Finally, potentialities of the gadolinium phase of SKand the future Hyper-Kamiokande experiment are discussed.
∗ Corresponding author: [email protected]† Corresponding author: [email protected]‡ Corresponding author: [email protected]§ also at BMCC/CUNY, Science Department, New York, NewYork, 1007, USA.
¶ Deceased.‖ also at University of Victoria, Department of Physics and Astron-omy, PO Box 1700 STN CSC, Victoria, BC V8W 2Y2, Canada.
I. INTRODUCTION
A. Diffuse supernova neutrino background
Core-collapse supernovae (CCSNe) are among themost cataclysmic phenomena in the Universe and are es-sential elements of dynamics of the cosmos. Their un-derlying mechanism is however still poorly understood,as characterizing it would require intricate knowledge ofthe core of the collapsing star. Information about thiscore could be accessed by detecting neutrinos emitted bysupernova bursts, whose luminosity and energy spectraclosely track the different steps of the CCSN mechanismin a neutrino-heating scenario (see Refs. [1–3], for exam-
3
ple). Existing neutrino experiments, however, are mostlysensitive to supernova bursts occurring in our galaxy andits immediate surroundings, that are extremely rare (afew times per century in our galaxy [4, 5]). Learningabout the aggregate properties of supernovae in the Uni-verse hence requires observing the accumulation of neu-trinos from all distant supernovae. The integrated fluxof these neutrinos forms the diffuse supernova neutrinobackground, or DSNB (DSNB neutrinos are also referredto as supernova relic neutrinos (SRNs) in various publi-cations).
The DSNB is composed of neutrinos of all flavorswhose energies have been redshifted when propagating toEarth. Its spectrum therefore contains unique informa-tion not only on the supernova neutrino emission processbut also on the star formation and Universe expansionhistory. Spectra predicted from various models areshown in Fig. 1. Their overall normalization is mostlydetermined by the supernova rate, related to the cosmicstar formation rate. While this redshift-dependent ratealso impacts the DSNB spectral shape, the latter ismainly affected by the effective energies of supernovaneutrinos. Other factors shaping the DSNB spectruminclude the neutrino mass ordering, the initial massfunction of progenitors, the equation-of-state of neutronstars, the fraction of black-hole-forming supernovae, therevival time of the shock wave, etc. Possible combina-tions of these factors were systematically studied in theNakazato+15 model [6], the maximal and minimal fluxesof which are shown in the figure. The minimal predictionfrom this model and the Malaney97 gas infall model [7]give the lower bounds on the DSNB flux. Converselythe Totani+95 model [8] can be considered an upperbound on the expected DSNB flux, on par with the mostoptimistic predictions of the Kaplinghat+00 model [9],also shown in the figure. Between these bounds, theDSNB flux can vary over one order of magnitude andits spectral shape bears the imprint of a wide range ofphysical effects. Black-hole-forming supernovae notablymake the DSNB spectrum harder, as can be seen withthe Lunardini09 model [10], that assumes that 17% ofcore-collapse supernovae lead to black-hole formation.Similarly, the Horiuchi+18 model [11] incorporates afraction of black-hole-forming supernovae determinedusing the stars’ compactness. Aside from accountingfor black-hole formation, the Kresse+21 model [12],on the other hand, uses state-of-the-art supernovasimulations to model contributions from helium starsto the DSNB. Another recent study (Horiuchi+21 [13])discusses the impact of interactions in binary sys-tems, such as mergers, and mass transfer, on theDSNB flux. Detecting the DSNB would hence providevaluable insights into a wide array of physical processes.
B. Experimental searches
While a significant fraction of DSNB neutrinos are ex-pected to have energies lower than 10 MeV —as shownin Fig. 1—, the O(1) MeV region is hard to probe bycurrent experiments due to overwhelming backgroundsfrom reactor antineutrinos, solar neutrinos, and radioac-tivity. Experimentally the DSNB signal has thereforebeen searched for at energies of O(10) MeV. At theseenergies, the dominant detection channel in most exper-iments is the inverse beta decay (IBD) of electron an-tineutrinos (νe + p → e+ + n), and contributions fromsubleading channels such as electron neutrino elastic scat-tering or charged current interactions on oxygen can beneglected. This process produces an easily identifiablepositron and a neutron (Fig. 2). Here the neutron doesnot emit Cherenkov or scintillation light directly but itscapture on a proton leads to emission of a 2.2 MeV pho-ton. In pure water, the characteristic timescale for neu-tron moderation and capture is of 204.8 ± 0.4 µs [20].Pairing the “prompt” positron signal with the “delayed”photon emission from neutron capture is hence a keycomponent of many analyses.
Up to now, no evidence for the DSNB signal has beenconfirmed and upper limits have been set by variousunderground experiments, such as Super-Kamiokande(SK) [21–23], KamLAND [24], SNO [25, 26] and Borex-ino [27]. Note that, unlike other searches, the SNO anal-ysis is sensitive to electron neutrinos and, due to theirreducible solar neutrino background, its effective en-ergy threshold lies around the hep solar neutrino fluxendpoint, around 19 MeV. Among all past analyses, theSK and KamLAND experiments placed the most strin-gent upper limits on the DSNB νe flux. At SK the firstDSNB search was carried out in 2003 using a 22.5×1496-kton·day data set [21]. Using spectral shape fitting forsignal and atmospheric neutrino backgrounds, it placedan upper limit on the DSNB flux for a wide variety ofmodels in the 19.3−83.3 MeV neutrino energy range.This analysis already allowed to disfavor the most op-timistic DSNB predictions, in particular the Totani+95model [8], and constrain the parameter space of theKaplinghat+00 model [9]. In 2012, an improved analysiswas performed at SK, using a 22.5×2853-kton·day expo-sure, a lower neutrino energy threshold of 17.3 MeV, andnew event selection cuts allowing a 50% increase in sig-nal efficiency [22]. Below 17.3 MeV, large backgroundsfrom cosmic muon spallation and solar neutrino inter-actions make it extremely difficult to search for DSNBantineutrinos based on positron identification alone. Asearch for extragalactic antineutrinos performed at Kam-LAND in 2012 [24] probed neutrino energies ranging from8.3 to 31.8 MeV by investigating coincident positronand neutron capture signals. While neutron identifica-tion in a liquid scintillator detector such as KamLANDis significantly easier than in pure water, KamLAND’ssmall fiducial volume only allowed for an exposure of4.31 kton·year. In 2015, a new SK analysis including
4
Energy [MeV]eν10 20 30 40 50 60 70 80
/sec
/MeV
]2
Flu
x [/
cmeν
DS
NB
4−10
3−10
2−10
1−10
1
10=0.1, NH)λαHoriuchi+21 (Extrapolated,
Tabrizi+21 (NS+BH, NH)
Kresse+21 (High, NH)
= 0.1)2.5,crit
ξHoriuchi+18 (
Nakazato+15 (Max, IH)
Nakazato+15 (Min, NH)
Galais+10 (NH)
Horiuchi+09 (6 MeV, Max)
Lunardini09
Ando+03 (updated at NNN05)
Kaplinghat+00
Malaney97
Hartmann+97
Totani+95
FIG. 1. DSNB νe flux predictions from various theoretical models (Horiuchi+21 [13], Tabrizi+21 [14], Kresse+21 [12],Horiuchi+18 [11], Nakazato+15 [6], Galais+10 [15], Horiuchi+09 [16], Lunardini09 [10], Ando+09 [17], Kaplinghat+00 [9],Malaney97 [7], Hartmann+97 [18], and Totani+95 [8]). Refer to each publication for the detailed descriptions of model. Inthe legend, “NH” and “IH” represent neutrino normal and inverted mass orderings assumed in the calculation, respectively.For the Horiuchi+09 model with a 6 MeV temperature, only the maximal flux prediction is shown. The prediction for theGalais+10 model here is extrapolated up to 50 MeV as the original publication was served up to 40 MeV. The prediction byNakazato+15 is only available up to 50 MeV. The values of the flux used in this analysis for the Ando+03 model are the onesreleased at the NNN05 conference [19]. The corresponding flux is larger by a factor of 2.56 than in the original publication [17].
neutron identification led to stronger constraints downto 13.3 MeV neutrino energies [23]. Since the SK trig-gers did not allow to record the neutron capture signaluntil 2008, this analysis could only be performed on asmall part of the SK data set, with a total livetime of22.5 × 960 kton·days. Due to this low exposure andthe low neutron tagging efficiency in water, this searchhowever yielded weaker limits than the SK-I,II,III anal-ysis [22] above 17.3 MeV.
In this study, we draw on the previous SK analysesto present two DSNB searches for antineutrino energies
ranging from 9.3 to 81.3 MeV, with significantly im-proved background modeling and reduction techniques.In the 9.3 to 31.3 MeV range, we derive differential up-per limits on the νe flux independently from the DSNBmodel, following the strategy outlined in Ref. [23] usinga 22.5×2970-kton·day data set. In the 17.3 to 81.3 MeVrange we constrain a wide variety of DSNB models usingspectral fits analogous to the ones described in Ref. [22].We then combine the results of this analysis with theones obtained in Ref. [22] for the former SK phases, thusanalyzing 22.5 × 5823-kton·days of data. This unprece-
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FIG. 2. Schematic illustration of an IBD process and the sub-sequent neutron capture on another proton. The characteris-tic neutron capture time in water is τ = 204.8± 0.4 µs [20].
dented exposure will allow to probe the DSNB with anunmatched sensitivity.
The rest of this article proceeds as follows. First, theSK detector and the specific features of its data acqui-sition system are described in Section II. Then, detailsabout modeling of the DSNB signal and the differentbackgrounds are given in Sections III and IV, respec-tively. We then describe the data reduction process inSection V. The procedures associated with the DSNBmodel-independent and spectral analyses are described inSections VI and VII, respectively. Finally we discuss thecurrent constraints on the DSNB flux and future oppor-tunities at SK with gadolinium and Hyper-Kamiokandein Section VIII before concluding in Section IX.
II. SUPER-KAMIOKANDE
Super-Kamiokande is a 50-kton water Cherenkov de-tector located in the Kamioka mine, Japan. It is struc-tured by a cylindrical stainless steel tank with a diame-ter of 39.3 m and height of 41.4 m and consists of twoparts: an outer detector (OD) that serves as a muonveto and an inner detector (ID) where neutrino detec-tion takes place. In order to reduce backgrounds due toradioactivity near the detector wall, most analyses con-sider only events reconstructed at least 2 m away fromthe ID wall, thus defining a 22.5-kton fiducial volume(FV). It is located 1000 m underground, that allows re-duction of the cosmic ray muon flux by a factor of 105.In order to ensure a high-quality data taking, conditionsinside SK are tightly controlled; water is constantly re-circulated and purified, and the ID wall is covered with11,129 20-inch photomultipliers (PMTs) with a 3-ns timeresolution, corresponding to a 40% photocathode cover-age. These features allow SK to detect particles withenergies ranging from a few MeV to a few TeVs. TheOD includes 1,885 8-inch PMTs, facing outwards, to de-
tect the Cherenkov light from muons. Further detaileddescriptions of the SK detector and its calibration can befound in Refs. [28–32].
SK is currently undergoing its sixth data taking phasesince it started functioning in 1996. The first phase lasted1497 days and ended for a scheduled maintenance. Dueto an accident following the maintenance, which resultedin a loss of 60% of the ID PMTs, SK operated with areduced photocathode coverage for 794 days (phase II).The coverage was brought back to its nominal value forphase III, that lasted 562 days. SK’s previous spectralanalysis of the DSNB [22] used data from all these threephases. Since 2008, the front-end electronics has beenreplaced [33] and a new trigger system that allows forneutron tagging has been set up [34]. SK operated withthis new electronics during phase IV, for 2970 days, untilbeing stopped for refurbishment work in May 2018. Afterthe maintenance, SK operated for a short time with purewater for calibration and monitoring purposes (phase V)since January 2019, before being loaded with gadolinium(phase VI) in July 2020. This study will primarily focuson phase IV, and will present a combined analysis of theSK-I to IV data. Additionally, we will briefly discuss theopportunities offered by the gadolinium lodaded SK andby the future Hyper-Kamiokande experiments.
Data processing in SK makes use of multiple triggers,corresponding to different thresholds on the number ofPMT hits found in a 200-ns window. In SK-I to III, allPMT hits in a 1.3-µs window around the main activitypeak were stored, using hardware triggers. Since SK-IV, the new data acquisition system acquires every PMTsignal and a software trigger system defines events. Toidentify positrons from IBD processes, we use the super-high-energy (“SHE”) trigger, which requires 58 PMT hits(70 hits before September 2011) in 200 ns. The data ina [−5,+35]-µs window around the main activity peak iscollected with this trigger. This window is too short tocontain the delayed neutron capture signal after IBDs.In order to identify this signal, a 500-µs (350 µs be-fore November 2010) after trigger (“AFT”) window fol-lows each SHE trigger that is not associated with a pre-determined OD trigger. The trigger conditions for thedifferent periods in SK-IV are summarized in Table I. Inthe rest of this paper, we will describe the analysis of hitpatterns in these large SHE+AFT windows to identifythe coincident production of a positron and a neutron.
The prompt positron event is reconstructed using thededicated solar neutrino [35–38] and muon decay elec-tron vertex and direction fitter, which is then used toreconstruct the event energy [39]. For this SK phase, wefollow the convention introduced in Ref. [38] and subtractthe 0.511 MeV electron mass from this energy to obtainthe electron equivalent kinetic energy Erec. This quan-tity can also be interpreted as the total reconstructedpositron energy, and will be used to present the resultsof this study.
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TABLE I. Summary on the SHE and AFT trigger conditionsand livetime for the different three periods in SK-IV.
SHE-threshold AFT-window Livetime70 hits 350 µs 25.0 days70 hits 500 µs 869.8 days58 hits 500 µs 2075.3 days
III. SIGNAL MODELING
A. DSNB spectra and kinematics
In this analysis we consider both the DSNB modelswhose fluxes are shown in Fig. 1 and models where wevary specific physical parameters. For these parameter-ized models we compute the DSNB flux using the follow-ing formula:
Φ(Eν) =c
H0
∫ ∑s
RSN(z, s)∑νi,νi
Fi (Eν(1 + z), s)
× dz√ΩM (1 + z)3 + ΩΛ
, (1)
where Eν is the neutrino energy, c is the speed of lightin vacuum, H0 is the Hubble constant, z is the red-shift, RSN(z) is the redshift-dependent supernova rate,and Fi is the supernova neutrino emission spectrum fora given flavor i. The index s represents the different pos-sible classes of supernovae —e.g. supernovae collapsinginto neutron stars or black-holes— associated with spe-cific neutrino emission spectra. The last factor accountsfor the Universe expansion, with ΩM and ΩΛ being thematter and dark energy contributions to the energy den-sity of the Universe, respectively. We evaluate the su-pernova rate using a phenomenological model describedin Ref. [16], which extracts the redshift dependence ofthe cosmic star formation history by fitting observationsand uses the Salpeter initial mass function [40] to obtainthe fraction of supernova progenitors. We then considerblackbody neutrino emission spectra, where the effectivetemperature Tν takes into account neutrino oscillationeffects. For a given neutrino flavor i the spectrum for amodel with effective temperature Tν is thus given by:
Fi(Eν) = fν,iEtotν
120
7π4
E2ν,i
T 4ν,i
(eEν,i/Tν,i + 1
)−1
, (2)
where Etotν is the total energy of the neutrinos emitted
by the supernovae and fν,i represents the fraction of neu-trinos or antineutrinos with flavor i and can be roughlyapproximated by 1/6 for a given species. The blackbodymodel therefore only depends on the neutrino tempera-tures and luminosities. In what follows, we will refer toblackbody models with a neutrino effective temperature
T as Horiuchi+09 T MeV models. Note that, due to neu-trino scattering in the densest regions of the collapsingstar, supernova neutrino emission is better modeled us-ing a more sharply peaked, “pinched”, Fermi-Dirac spec-trum [41]; however, the current exposure at SK does notallow to probe this pinching effect. In this analysis weneglect the effects of degeneracies between the pinchingparameter and e.g. the neutrino temperature on the finalconstraints on neutrino emission spectra.
This analysis exclusively focuses on the detection ofelectron antineutrinos via IBD processes. In the rest ofthis paper, we model these processes using the Strumia-Vissani IBD calculation [42], that approximates the IBDcross section more precisely than the Beacom-Vogel cal-culation used for previous SK analyses [22].
B. Detector simulation
SK-IV has been the longest data taking phase of theexperiment, lasting about 10 years. During this term,the PMT gain has steadily increased by about 15% overthe whole SK-IV period. Additionally, since the energyscale change due to the gain change for this analysis wasabout 3 %, that effect was corrected in order to maintainthe stability of the detector. A key ingredient of ourDSNB study is therefore a simulation of antineutrino IBDprocesses that accounts for the evolution of the detector’sproperties throughout the entire SK-IV period.
In this study we simulate IBD processes uniformly dis-tributed in the entire inner detector, in order to accountfor events close to the ID wall being misreconstructedinside the fiducial volume. For each vertex we gener-ate a set of three momentum vectors corresponding toan antineutrino, a positron, and a neutron. In a viewof the wide diversity of DSNB models, we generate uni-formly distributed positron energies in 1−90 MeV andrenormalize events later to model specific spectra. Thisprocedure will also allow to use this simulation to modelbackgrounds associated to other IBD processes or β de-cays, as will be mentioned later. We then simulate de-tection signals using a dedicated simulation, based onGEANT3 [43], that reproduces the properties of the wa-ter in SK, as well as models the PMT properties andelectronic response. Detector properties such as watertransparency and PMT noise are being measured daily,allowing to accurately model the time-dependent noisecontamination of the positron signal. Neutron capture,however, produces a 2.2 MeV γ ray whose light yieldis below the SK trigger threshold and particularly diffi-cult to distinguish from PMT dark noise and low energyradioactive decays. In order to develop robust neutronidentification techniques we therefore collect noise sam-ples from data using a random wide trigger, and injectthem into simulation results, after the positron activitypeak.
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IV. BACKGROUND SOURCES
A. Atmospheric neutrinos
Atmospheric neutrinos are an important backgroundin the present DSNB searches. Below about 15 MeV,neutral-current quasielastic (NCQE) interactions, whichinduce nuclear γ ray emission [44–47], form the mainatmospheric neutrino background. On the other hand,charged-current quasielastic (CCQE) interactions andpion production dominate at higher energies. A typicalvisible signature for these interactions is the Cherenkovlight from electrons produced by muon and pion decays.Hence, the associated reconstructed energies will followa Michel spectrum for reconstructed energies of about 15to 50 MeV. Atmospheric neutrino events are simulatedusing the HKKM 2011 flux [48–50] as an input to theneutrino event generator NEUT 5.3.6 [51] to model in-teractions. Details about the model parameters used inthis analysis can be found in Ref. [52]. The nuclear de-excitation γ’s are simulated based on the spectroscopicfactors for the p1/2, p3/2, and s1/2 states calculated inRef. [44]. More detailed descriptions of the excited statescan be found in Refs. [45, 47] for the T2K NCQE mea-surement. One difference between our procedure andRef. [47] is treatment of the others state —a state af-fected by short-range correlations or with a very highexcitation energy—. This state is treated as the highestexcitation state (s1/2) in Ref. [47] while it is included inthe ground state (p1/2) in the present analysis as it isfrom the latest atmospheric neutrino analysis in SK [53].The systematic uncertainty regarding this treatment isconsidered in the scaling factor used in Section VI A.
The detector simulation for atmospheric neutrinoevents is performed using the same GEANT3-based sim-ulation tool as for the signal, but without corrections forthe PMT gain shift on the primary event. The associ-ated systematic error is estimated in Section VI A andfound to be subdominant. Finally, random trigger dataare overlaid on top of neutron capture signals in order tosimulate background for neutron tagging, following theprocedure described in Section III B. Note that for thislast step the time evolution of the detector properties istaken into account.
B. Cosmic ray muon spallation
In spite of its 2700-m water-equivalent overburden, SKis still exposed to cosmic ray muons with a rate of ∼2 Hz.Interactions of these muons in water produce electromag-netic and hadronic showers. Spallation of oxygen nucleiinduced by the muons or by secondary particles can thenlead to the production of radioactive isotopes, whose de-cays can be misidentified as IBD events in the DSNBsearch window. Below about 20 MeV, the associatedbackground is 106 times higher than the DSNB flux pre-dictions, making spallation reduction an essential aspect
of this analysis. Since most spallation isotope decaysonly produce β and γ rays, spallation backgrounds canbe significantly reduced using neutron tagging. Nonethe-less, accidental pairing between prompt β or γ events andPMT hits due to dark noise or intrinsic radioactivity willallow a sizable number of spallation events to pass asIBDs. Furthermore, a few isotopes undergo a β+n de-cay that mimics the IBD signal, and thus cannot be re-moved using neutron tagging. Efficient spallation reduc-tion therefore requires both dedicated spallation reduc-tion techniques tailored to the properties of the differentisotopes, and neutron tagging cuts.
Relevant spallation isotopes and their visibility in wa-ter have been studied with the FLUKA simulation [54] inRefs. [55–57]. The isotope lifetimes and the end-point en-ergies of their decays are summarized in Fig. 3. The high-est end-point is 20.6 MeV, from 14B and 11Li. The spal-lation cuts used in this analysis will therefore be appliedup to 23.5 MeV reconstructed kinetic electron energy inorder to account for energy resolution effects. Note alsothat the isotope half-lives range from O(0.01) sec to a fewtens of seconds. Given the high rate of cosmic ray muons,pairing a given isotope decay with its parent process is aparticularly difficult endeavour.
8 10 12 14 16 18 20 22
End-point energy [MeV]
10 2
10 1
100
101
Half-
life
[sec
]
16N
16C
15C
14B
13O
13B 12N
12B 12Be
11Be
11Li
9C 9Li
8B 8Li
8He
FIG. 3. End-point energies and half-lives of the β decay iso-topes produced by cosmic ray muon spallation in water, whosedecay products are found in the DSNB search window. Theisotopes represented by a red circle (a black square) decaywith (without) neutrons.
Isotopes that undergo β+n decays cannot be rejectedusing neutron tagging and therefore need to be mod-eled with particular care. This is notably the case for
8
8He, 11Li, 16C, and 9Li. Here 11Li is particularly short-lived and therefore easy to eliminate using mild spalla-tion cuts. Its production yield is also expected to beparticularly low (around 10−9 µ−1·g−1·cm2 [55]). In ad-dition, 8He and 16C will remain subdominant due totheir low production yields (around 0.23 and 0.02 ×10−7 µ−1·g−1·cm2 [55]) and endpoint β decay energies.On the other hand, 9Li has a non-negligible yield (around1.9×10−7 µ−1·g−1·cm2 [55]), a medium half-life of about0.18 sec, and decays into a β+n pair with a branchingratio of 50.8%. The associated β spectrum is shown inFig. 4, and extends up to 13.5 MeV reconstructed energywhen accounting for resolution effects. The β+n decayof 9Li is hence similar to the IBD of a DSNB neutrino,except that the β from 9Li is an electron and the neu-tron energy is higher than that from IBDs. Since SKdoes not distinguish electrons from positrons and doesnot allow to measure the neutron energy, we model 9Lidecay using the IBD Monte-Carlo simulation, renormal-izing events to reproduce the 9Li β+n spectrum. Finally,we estimate the total expected number of 9Li β+n de-cays in the DSNB search window by using an earlier SKmeasurement [58] that estimated the 9Li production rateto be 0.86± 0.12(stat.)± 0.15(syst.) kton−1·day−1. Notethat the difference in neutron energies with respect toIBD processes leads to a systematic uncertainty. How-ever, this uncertainty is taken into account when cali-brating neutron tagging efficiencies, as neutrons from thecalibration source have similar energies to the 9Li decayproducts. More details about this calibration procedureare given in Section V D.
FIG. 4. True electron kinetic energy (blue) and reconstructedkinetic energy (orange) spectra from the 9Li β+n decay.
C. Reactor neutrinos
Antineutrinos emitted from nearby nuclear reactorscan undergo IBDs in SK and therefore be mistaken as
the DSNB signal at low energies. We estimate the re-actor antineutrino flux using the SKReact code [59] de-veloped for the SK reactor neutrino analysis. This codeuses the reactor neutrino model from Ref. [60] based onIAEA records [61] to evaluate the electron antineutrinofluxes for any reactor in the world, and simulates oscilla-tion effects. The resulting flux prediction also accountsfor the time dependence of the reactor antineutrino fluxdue to changes in reactor activity. The expected totalreactor neutrino flux at SK can thus be predicted up toEmaxν = 9.2 MeV. The expected reactor neutrino spec-
trum is obtained from this predicted flux using the IBDsimulation, as shown in Fig. 5. Due to energy resolutioneffects, this spectrum extends up to ∼10 MeV recon-structed energy and dominates over DSNB predictionsthere. In the 7.5−9.5 MeV reconstructed kinetic elec-tron energy range, for example, the reactor antineutrinobackground is about 6 times higher than the DSNB signalpredicted by the Horiuchi+09 6 MeV model [16]. Reac-tor antineutrino backgrounds thus effectively set a lowerenergy threshold for the DSNB search.
FIG. 5. True positron kinetic energy (blue) and reconstructedkinetic energy (orange) spectra from reactor neutrino IBD in-teractions. The y-axis shown the average number of eventsper year at SK-IV. The event rate is not constant with timedue to reactors being powered on during the data taking pe-riod.
D. Solar neutrinos
Electron neutrinos from the Sun cause elastic interac-tions with electrons in SK. In the DSNB search window,the 8B and hep solar neutrino fluxes represent an im-portant background up to ∼20 MeV. This backgroundcan be drastically reduced by neutron tagging, althougha small fraction of electrons from solar neutrinos will beaccidentally paired with background fluctuations or ra-dioactive decays, like for the spallation backgrounds. In
9
the absence of neutron tagging, a solar neutrino interac-tion can still be identified by comparing the reconstructeddirections of the scattered electron to the direction of theSun at the detection time. The angle between these twodirections, called the opening angle, is expected to beclose to zero for solar electron neutrinos scattering elas-tically. It is however smeared by reconstruction effectsthat need to be modeled accurately. In this study, we usethe simulation designed for the latest SK-IV solar neu-trino analysis [38] to model solar neutrino spectra andevaluate the impact of opening angle cuts.
Finally, note that in this analysis we do not study theimpact of solar antineutrino production, since the ratepredicted by the Standard Model (SM) is negligible. An-tineutrino production via beyond the SM processes wouldyield a signal that can only be distinguished from theDSNB signature by spectral shape studies. So far, onlyupper limits on the solar antineutrino flux have been de-rived at SK, notably in Ref. [52].
V. DATA REDUCTION
We apply reduction cuts to the data taken by theSHE trigger in SK-IV, corresponding to an exposure of22.5 × 2970.1 kton·days. The SHE trigger efficiency isclose to 100% over the entire analysis window. The fol-lowing sections describe the four reduction steps used inthis analysis: noise reduction in Section V A, spallationreduction in Section V B, DSNB positron candidate selec-tion in Section V C, and neutron tagging in Section V D.
A. Search energy range and noise reduction
The lower energy threshold for this analysis is the SHEtrigger threshold, which corresponds to Erec > 7.5 or9.5 MeV depending on the observation time (see Ta-ble I). The upper bound of the DSNB analysis window isset to 29.5 MeV for the model-independent analysis and79.5 MeV for the spectral analysis.
We first select SHE-triggered events with Erec below79.5 MeV and apply a set of cuts aimed at removingPMT noise, calibration events, radioactivity from thesurrounding rock and the detector wall, and cosmic rayactivity. In particular, we require candidate events to belocated at least 2 m away from the ID wall, thus defininga fiducial volume (FV) of 22.5 kton. Additionally, weremove events associated with an OD trigger, or within50 µs of another event with reconstructed electron kineticenergy larger than 6 MeV, in order to remove electronsproduced by the decay of low energy cosmic ray muonsstopping in the detector. In addition, we apply fit qualitycuts to eliminate noise-like events. Inside the FV thesenoise reduction cuts have a signal efficiency larger than99% as confirmed by the IBD Monte-Carlo simulation.Finally, we require all SHE events to be followed by anAFT trigger to allow for neutron tagging. Due to occa-
sional deadtime induced by trigger software failure, thisstep is associated with a ∼94% signal efficiency. Eventspassing these criteria will be subsequently referred to as“DSNB candidates”.
B. Spallation reduction
Spallation backgrounds largely dominate over putativeDSNB signals for reconstructed electron kinetic energieslower than 23.5 MeV. Here, we present a set of dedicatedcuts that will allow for a substantial reduction of thesebackgrounds, even in the absence of neutron tagging.
1. Spallation preselection
We apply two sets of preselection cuts to reduce con-tributions from the most energetic muons and some long-lived spallation isotopes such as 16N, with minimumharm to the signal efficiency.
First, since energetic muons could induce the produc-tion of multiple radioactive isotopes, we remove all DSNBcandidates observed within 60 sec and 4.9 m from at leastone other low energy event with Erec in the 5.5-24.5 MeVrange [62]. The 60 sec time window has been chosen toinclude decays of abundant and long-lived isotopes suchas 16N while the 4.9-m distance cut provides optimal sig-nal over background separation. We estimate the signalefficiency of this so-called “multiple spallation cut” usinga sample of low energy events from radioactive decaysat SK (4 < Erec < 5 MeV), whose reconstructed verticeshave been replaced by random vertices inside the ID. Thecut parameters introduced above allow to remove about45% of the background with a 98% signal efficiency, ascan be seen in Fig. 6. Since this cut removes low energyevents clustered in space and time, it also removes lowenergy muons that are misclassified as electrons with tensof MeV energies. Consequently, in this study, we will ap-ply this cut over the whole energy range for each of ouranalyses, including the spallation-free Erec > 23.5 MeVregion.
In addition to removing multiple spallation events, welocate muon-induced showers by identifying neutron cap-tures observed less than 500 µs after muons. These neu-tron clusters, called “neutron clouds”, are often producedin muon-induced hadronic showers, that are the birth-places of spallation isotopes. Neutron capture events fol-lowing muons are collected separately from DSNB can-didates, using a specific trigger called the Wideband In-telligent Trigger (WIT) [63–65]. This trigger, in additionto setting a threshold on the number of PMT hits, ap-plies cuts on the event quality and distance of the recon-structed vertex to the ID wall. Events triggered by WITless than 500 µs after a given muon are considered asneutron captures if their reconstructed vertex is within5 m of the reconstructed muon track. If multiple neutroncaptures are observed after a muon event, we define a
10
FIG. 6. Minimal distance between a given DSNB candidate(blue) or SK low energy event with a random vertex (orange)and a well-reconstructed event with Erec > 5.5 MeV observedwithin 60 sec of it. The DSNB candidates are defined asall the SK-IV events with Erec > 7.5 MeV passing the noisecuts. Here we also show the 4.9 m separation required in thisanalysis with a red vertical line.
neutron cloud using the criteria from Ref. [62]. We thenremove DSNB candidates that are found close in timeand space to these neutron clouds, following the proce-dure introduced in Ref. [62]. More details about the cutcriteria are given in Appendix A. To estimate the signaland background efficiencies of the neutron cloud cut, wepair muons with DSNB candidates in data, defining twosamples: a “pre-sample”, including muons found up to60 sec before a DSNB candidate, and a “post-sample”,with muons found up to 30 sec after a candidate. Whilethe pre-sample contains a mixture of correlated and un-correlated pairs, the post-sample contains only uncor-related pairs. This sample can hence be used to bothreadily estimate signal efficiencies and characterize theproperties of the pairs formed by each isotope decay andtheir parent muon in the pre-sample. An example ofhow to extract the distribution of the distances betweenspallation events and the neutron clouds of their parentmuons is shown in Fig. 7. We optimize the neutron cloudcut by estimating the shape of the neutron clouds fromdata and maximizing the statistical significance of thesignal over the spallation background. The performanceof this cut is however currently limited by the weaknessof the neutron capture signal and the fact that the WITtrigger has only been available only during the last 388live days of SK-IV. While the signal efficiency is largerthan 99% this cut only removes about 10% of the spal-lation background in this analysis. Over the 388 days ofthe WIT trigger livetime, however, it removes about 40%of spallation isotope decays.
Finally, it should be noted that the multiple spallationand the neutron cloud cuts described above are expectedto overlap since muons associated with large hadronicshowers are also likely to lead to the production of mul-tiple isotopes. Accounting for this overlap, these prese-
FIG. 7. Distributions of distance between DSNB candidatesand neutron clouds for pre- and post-samples, where the se-lected neutron clouds have been observed up to 60 sec beforeand after the DSNB candidates respectively. The distribu-tion for the post-sample has been rescaled by assuming thatcontributions from spallation pairs beyond 20 m are negli-gible. Contributions from pairs formed by spallation isotopedecays and neutron clouds associated with their parent muonsappear as a peak in the pre-sample below 10 m. The associ-ated distribution can be extracted by subtracting the rescaledpost-sample from the pre-sample.
lection cuts allow to remove about 55% of the spallationbackground when neutron cloud data are available.
2. Searching for parent muons
Since preselection cuts remove only about half of thespallation background, a more in-depth study of the cor-relations between muons and DSNB candidates is neces-sary. In particular, in order to identify the decays of spal-lation isotopes, it is crucial to associate each isotope withits parent muon. Due to the long half-lives of isotopessuch as 11Be and 16N, we need to investigate all possiblepairings between DSNB candidates and muons observedup to 30 sec before them. This window size allows toaccommodate most decay products, without processinga prohibitively high number of muons. As with neutroncloud cut optimization, we define pre- and post-samplesin order to extract the observable distributions associatedwith spallation pairs and estimate signal efficiencies.
We define candidate muons by selecting events associ-ated with more than 31 PMT hits (34 before May 2015)in 200 ns and depositing more than 500 p.e. in the ID.Additionally, since the SK trigger windows can containmultiple events, we also look for muons around the mainactivity peak in these windows. For the same reason,calibration trigger windows are also thoroughly investi-gated. The properties of the muon candidates, such asthe charge deposited in the detector, the entry point,and the direction of the track, are then extracted using
11
a dedicated fitter [22, 66, 67]. This fitter classifies muonsinto five categories: misfits (1.0%), single through-goingmuons (82.2%), stopping muons (4.9%), multiple-trackmuons (7.6%), and corner clippers (4.3%); the fractionsof the different categories in the SK-IV data are shownin parentheses. Misfit muons with a charge lower than1000 p.e. are removed in order to reject non-muonic highenergy events. This cut does not affect removing spal-lation background because the track length of these lowcharge muons through the ID is typically less than 50 cm.
After having paired DSNB candidates with the muonsselected above, we extract the following observables, re-lated to the intrinsic properties of the muons and theircorrelations with DSNB candidates.
• dt: time difference between a muon and the DSNBcandidate. For spallation events, this observablereflects the half-lives of the produced isotopes.
• `t: transverse distance of the DSNB candidate tothe muon track (see Fig. 8). This observable is re-lated to the path lengths of the secondary particlesfrom muon showers. For well-fitted single through-going muons paired with their associated spallationisotope decays, `t is typically no larger than a fewmeters.
• `l: longitudinal distance to the point of the muontrack associated with the maximal energy depo-sition (see Fig. 8). The energy deposition alongthe muon track is determined by projecting backthe light seen by each PMT to a point on themuon track, following the procedure described inRef. [22]. So `l provides an estimate of the dis-tance between the low energy event and the originof the particle shower and, if the shower position iscorrectly identified, should also not be larger thana few meters for spallation pairs.
• Qµ: total charge deposited by muons in the detec-tor. Higher values of this observable are expectedwhen a shower is produced.
• Qres: residual charge deposited by a muon com-pared to the value expected from the minimum ion-ization. This observable can be expressed as:
Qres = Qµ − qMI · L,
where qMI and L are the number of p.e. per cen-timeter expected from the minimum ionization andthe track length, respectively. Here qMI dependson detector properties, such as water transparency,that vary with time and is therefore recomputed foreach run. For muons with multiple tracks, L is thelength of the first track. This observable allows todetermine how likely a given muon is to induce ashower.
An example set of these spallation variables for singlethrough-going muons is shown in Appendix A. The dis-tributions associated with corner clipping muons show
DSNB candidate
position where dE/dx is largest
lt
ll
muon track
FIG. 8. Schematic of the spallation observables `t and `l. Thecylindrical shape represents the SK ID.
no evidence for spallation. Moreover, as discussed inRef. [62], spallation background events associated withcorner clipping muons are expected to represent less than10−5 of the total number of spallation events. In the restof this study, we will therefore neglect contributions fromthese muons to spallation backgrounds.
Showers induced by muon spallation can be extremelyenergetic and involve up to thousands of particles, no-tably neutrons and pions. Such neutrons cause nuclearreactions and possibly produce deexcitation γ rays, andare later captured at a timescale up to ∼500 µs. TheMeV-scale γ rays or β particles —produced by the ini-tial neutron, secondary nuclear reactions, or the decayproduct of a short-lived isotope, followed by a 2.2 MeVγ ray from neutron capture can mimic an IBD signa-ture. To prevent these from leaking into the sample, werequire DSNB candidates to be more than 1 ms awayfrom any muon. The impact of this cut on the signal ef-ficiency is negligible. Additionally, we apply a set of cutson dt and `t for different energy ranges, exploiting thedependence of the isotopes’ half-lives in their endpointenergies shown in Fig. 3. Detailed descriptions of theserectangular cuts are given in Appendix A. These cutsare particularly efficient above 15.5 MeV where short-lived isotopes dominate. In 15.5−19.5 MeV, notably,they allow to remove about 85% of the spallation back-ground while keeping 88% of the signal events. Finally,in order to further eliminate spallation backgrounds, weuse distributions of the different observables consideredhere to define log-likelihood ratios. First, we preparetwo probability density functions (PDFs): the spallationPDF (PDFispall) and the random PDF (PDFirandom), foreach variable i = dt, `t, `l, Qµ, Qres. We isolate contri-butions from spallation events by subtracting the post-sample distributions from the corresponding pre-sampledistributions and obtain PDFispall after area normaliza-
tion of these subtracted distributions. For PDFirandom wenormalize post-sample distributions by their areas. Werepeat this procedure for each category of muons. For sin-
12
gle through-going and multiple track muons, that gener-ate most of the spallation background, we tune the PDFsin dt and `t bins. These bins, adjusted by considering theisotopes’ typical half-lives and the `t distributions, ac-count for the correlations between these observables. Foreach set of PDFs, we then define log-likelihood ratios as:
Lspall = log
(∏i
PDFispall
PDFirandom
). (3)
Separate likelihoods are defined for each muon category,except for corner clippers, whose contributions to spal-lation backgrounds are negligible as mentioned above.Note that for misfit muons only dt is used to calculatelog-likelihood ratios, as the other observables are not reli-able. An example distribution of the log-likelihood ratiois given as Fig. 33 in Appendix A. We finally determinecut conditions for each likelihood ratio, accounting forcomplex correlations between spallation observables, ge-ometrical and muon reconstruction effects.
The signal efficiencies and background rejection ratesof the resulting cuts are estimated using the randomsample introduced in this section, as well as spallation-dominated data samples. These samples as well as ourmethodology to estimate the spallation cut performanceare described in detail in Appendix A. The current cutsachieve significant improvement over the previous cutsused in Refs. [22, 23], especially at low energies; for thesame spallation remaining rate, the signal efficiency isincreased by up to 60% for Erec < 11.5 MeV, 20% for11.5 < Erec < 13.5 MeV, and comparable for higher en-ergies.
C. DSNB positron candidate selection
In the region above ∼20 MeV, spallation backgroundscan be reduced to negligible levels using a series of spal-lation cuts while keeping most of the signal. However,significant backgrounds from atmospheric neutrino inter-actions and radioactive decays remain. To identify them,we define the following discriminating observables, aimedat characterizing the prompt event.
1. Incoming event cut
Radioactivity near the detector wall as well as muonspallation in the rock surrounding the detector, can leadto electrons or γ rays entering FV. Instead of tighten-ing the FV cut, we consider the effective distance ofeach event to the ID wall deff [22, 35]. This observableis computed by following the reconstructed direction ofeach event backwards from its reconstructed vertex to theID wall, and can be interpreted as the minimal distanceneeded for a radioactive particle produced near the wallto travel to the event vertex, as shown in Fig. 9. The deff
distributions for the DSNB signal and for the events se-lected using the cuts outlined in Section V A are shown inFig. 10, for the reconstructed energy ranges correspond-ing to the model-independent analysis, 7.5 to 29.5 MeV,and the spectral analysis, 15.5 to 79.5 MeV. In this studywe impose lower thresholds on deff ranging from 3 to 5 mdepending on the reconstructed energy:
deff > max
300, 500− Erec − 15.5 MeV
1 MeV× 50
cm.
FIG. 9. Views of the ID, showing the effective distance ofa reconstructed event to the detector wall. The deff is thedistance that a particle emitted near the ID wall —e. g. fromby a radioactive decay— needs to travel to give the observedsignal.
2. Pre- and post-activity cuts
Atmospheric neutrino interactions can produce bothprompt signals from photons, electrons, or energeticheavy particles, and delayed signals from decay of muonsand pions to electrons. These signals will be typicallyseparated by a few microseconds and can therefore sharethe same trigger window. Depending on which parti-cle deposits most light, unusually high activity can benoticed either before or after the main peak. For pre-activity we compute the maximal number of hits, Nmax
pre ,in a 15-ns time-of-flight subtracted window between 5 µsand 12 ns before the main peak. We apply a similar pro-cedure to post-activity, using an algorithm developed forother analyses in SK and T2K that computes the num-ber of electrons from muon and pion decay Ndecay-e [68].The Ndecay-e distributions for low and high energy eventsare shown in Fig. 11. In the analyses discussed here werequire Nmax
pre < 12 and Ndecay-e = 0.
3. Cherenkov angle
The opening angle of the Cherenkov light cone (θC)emitted by highly relativistic particles, electrons andpositrons in the current context, in pure water is around42. Conversely, at the O(10) MeV energies consideredhere, heavier particles like muons and pions will be typ-ically observed near the Cherenkov threshold, leading to
13
500 1000 1500 2000 2500 3000 3500 4000 [cm]effd
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FIG. 10. The deff distributions for the observed data and IBD Monte-Carlo simulation, for events with Erec ∈ [7.5, 29.5] MeV(left) and Erec ∈ [15.5, 79.5] MeV (right). The rate of IBD Monte-Carlo simulation events has been scaled to match the numberof events observed in the data for deff > 1000 cm. The lower panels show the relative difference between the numbers ofdata and IBD simulation events. We consider only events reconstructed in the FV and passing the noise reduction cuts. Theassumed DSNB spectrum is taken from the Horiuchi+09 6 MeV model [16].
0 1 2 3decay-e N
0
100
200
300
400
500
600
Eve
nts CCQE-like
πCC1
CC otherNCQE
πNC1NC other
0 1 2 3decay-e N
0
200
400
600
800
1000
1200
1400
Eve
nts CCQE-like
πCC1CC otherNCQE
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FIG. 11. The Ndecay-e distributions for the atmospheric neutrino Monte-Carlo simulation, for events with Erec ∈ [7.5, 29.5] MeV(left) and Erec ∈ [15.5, 79.5] MeV (right). We consider only events reconstructed in the FV and passing the noise reductioncuts.
cones with smaller angles in the current analysis range.In addition, NCQE interactions with multiple photonemission can produce multiple overlapping Cherenkovcones, that will be reconstructed as a single cone with aparticularly large opening angle [45, 47]. Consequently,θC is one of the most powerful observables for reduc-ing both NCQE and µ/π-producing atmospheric back-grounds. The Cherenkov angle distributions for the sig-nal and atmospheric neutrino events are shown in Fig. 12for the energy ranges of the model-independent analysisand the spectral analysis. In what follows we will re-quire the Cherenkov angle in the signal regions to be in[38, 50]. In the spectral analysis, we will also use thisangle to define sidebands to evaluate atmospheric back-
grounds.
4. Ring clearness
Electrons and positrons do not follow a straight trajec-tory in SK due to scattering and bremsstrahlung, whichleads to fuzzy Cherenkov rings. Pions, on the other hand,lead to well-delineated ring patterns. In order to char-acterize this property we consider a 15-ns time-of-flightsubtracted window around the main activity peak andcompute the opening angles of the cones formed by thedirections of all possible 3-hit combinations. We thenidentify the peak of this opening angle distribution θ0
14
20 30 40 50 60 70 80 90 [degree]Cθ
0
50
100
150
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350E
ven
ts/2
.7-d
egre
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400
600
800
1000
1200
Eve
nts
/2.7
-deg
ree
CCQE-likeπCC1
CC otherNCQE
πNC1NC otherIBD signal
FIG. 12. The θC distributions for the atmospheric neutrino and IBD Monte-Carlo simulations, for events with Erec ∈[7.5, 29.5] MeV (left) and Erec ∈ [15.5, 79.5] MeV (right). We consider only events reconstructed in the FV and passingthe noise reduction cuts. The assumed DSNB spectrum is taken from the Horiuchi+09 6 MeV model [16]. The signal andbackground distributions are normalized to the same area.
and estimate the “clearness” of the ring by computing:
Lclear =Ntriplets(θ0 ± 3)
Ntriplets(θ0 ± 10). (4)
The Lclear distributions from the atmospheric and IBDMonte-Carlo simulations are shown in Fig. 13. Eventswith lower Lclear have fuzzier rings. For the analysespresented here we require Lclear < 0.36.
5. Average charge deposit
Energetic muons scatter less than electrons and henceoften deposit more charge in individual PMTs thanO(10) MeV electrons and positrons. We exploit thisfeature by considering a 50-ns time-of-flight subtractedwindow around the main activity peak and calculate theaverage charge deposited per PMT hit (q50/n50) in thiswindow. The distributions are given in Fig. 14. We re-quire q50/n50 to be less than 2 in the analysis.
6. Cut efficiencies and systematic uncertainties
We estimate the signal efficiencies of most of the cutsdetailed above using the IBD Monte-Carlo simulation.Hence, the main source of systematic uncertainties onthe cut efficiencies stems from the modeling of the SKdetector and particle propagation in water. We estimatethese uncertainties using calibration data taken by in-jecting a monoenergetic electron beam produced by aLINAC at different positions inside the detector [31]. Fora given cut, we compare the measured and predicted ef-ficiencies using a dedicated Monte-Carlo simulation, anddefine the systematic uncertainty as the maximum dis-crepancy over all calibration tests. LINAC calibrationthus allows to estimate uncertainties for ring clearness,
the average charge, and Cherenkov angle cuts. Con-versely, for the incoming event cut —that requires con-sidering uniformly distributed events— we use a strategydeveloped for the SK solar neutrino analyses [35–38]: wemeasure the variation of the deff cut efficiency after shift-ing the event directions and vertices in the IBD Monte-Carlo simulation. The vertex and direction shifts usedfor these estimates are obtained from calibration studiesusing a nickel source [30]. Finally, efficiencies for the pre-and post-activity cuts can be directly estimated using aspallation-dominated sample of low energy events, withnegligible systematic uncertainty. Overall, positron can-didate selection cuts allow to remove a large fraction ofatmospheric backgrounds while keeping up to 85% of thesignal. The total systematic uncertainty computed forpositron candidate selection cuts using these proceduresare of a few percent.
D. Neutron tagging
The introduction of a new trigger scheme at SK-IV hasmade characterizing IBDs via neutron tagging possible,by requiring the prompt and delayed signals be detectedwithin 500 µs of each other. In what follows, we willdevise a neutron tagging algorithm tailored to the DSNBanalysis, inspired by previous SK studies from Refs. [69,70].
1. DSNB candidate selection and neutron preselection
As explained in Section II, most SHE triggered eventsare followed by a 500 µs AFT trigger window in orderto record the neutron capture signal. Before attemptingto identify neutron candidates in this combined triggerwindow, we apply a cut on the maximum hits inside a200-ns window: N200 < 50 to eliminate SHE+AFT trig-
15
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6ring clearness
0
20
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60
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100E
ven
ts/0
.005 CCQE-like
πCC1CC otherNCQE
πNC1NC otherIBD signal
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6ring clearness
0
50
100
150
200
250
300
Eve
nts
/0.0
05 CCQE-likeπCC1
CC otherNCQE
πNC1NC otherIBD signal
FIG. 13. The Lclear distributions for the atmospheric neutrino and IBD Monte-Carlo simulations, for events with Erec ∈[7.5, 29.5] MeV (left) and Erec ∈ [15.5, 79.5] MeV (right). We consider only events reconstructed in the FV and passingthe noise reduction cuts. The assumed DSNB spectrum is taken from the Horiuchi+09 6 MeV model [16]. The signal andbackground distributions are normalized to the same area.
1 1.5 2 2.5 3 3.5 4Q50/N50
0
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120
Eve
nts
/0.5
CCQE-likeπCC1
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1 1.5 2 2.5 3 3.5 4Q50/N50
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50
100
150
200
250
300
350
Eve
nts
/0.5
CCQE-likeπCC1
CC otherNCQE
πNC1NC otherIBD signal
FIG. 14. The q50/n50 distributions for the atmospheric neutrino and IBD Monte-Carlo simulations, for events with Erec ∈[7.5, 29.5] MeV (left) and Erec ∈ [15.5, 79.5] MeV (right). We consider only events reconstructed in the FV and passing the noisereduction cuts. The assumed DSNB spectrum is taken from the Horiuchi+09 6 MeV model [16]. The signal and backgrounddistributions are normalized to the same area.
ger windows containing muons. This cut is associatedwith a signal efficiency larger than 99%. After applyingthe N200 cut we scan the SHE+AFT trigger windows ofthe remaining events to select hit clusters that could beassociated with neutron captures. Here, we take advan-tage of the fact that a typical neutron capture vertex iswithin a few tens of centimeters of the well-reconstructedIBD vertex. Since the SK resolution is about 50 cm forO(10) MeV events, this proximity allows to reliably es-timate the required photon emission time for each PMThit to be the result of the neutron capture. A neutroncandidate is therefore defined as a group of hits that isclustered in emission time. We then look for clustersmaximizing N10, the number of hits in a 10-ns window.
In previous SK-IV searches, neutron candidates weredefined as clusters of hits satisfying N10 ≥ 7 [69]. Thispreselection cut has an efficiency of around 35% and wasmotivated by the energy range of these searches, wherespallation backgrounds were largely dominating. In thisstudy, we modify this preselection step as follows. First,
we apply a cut to reduce the continuous PMT dark noise,likely due to scintillation in the PMT glass, that causesa single PMT to flash more than once in rapid succes-sion with a timescale of ∼10 µs. To do so, for each PMTwe remove hit pairs separated by less than 6 (12) µs forN10 > 6 (N10 ≤ 6). After applying this cut, we de-fine neutron candidates as hit clusters verifying N10 ≥ 6.This preselection cut will allow loosening of the neutrontagging cut in energy regions where spallation no longerdominates, in particular for the spectral analysis. Finally,since the continuous dark noise cut relies on investigat-ing PMT hit pairs, its efficiency sharply increases nearthe edge of the SHE+AFT trigger window. We restrictthe neutron search window to [14, 523] µs ([14, 373] µs forevents with a 350-µs AFT trigger window). After thesedifferent steps, neutron candidate preselection is associ-ated with an efficiency of 44.7%.
16
2. Boosted Decision Tree
After preselection, we are still left with a large back-ground from e. g. dark noise fluctuations and radon de-cays [71], totaling about 7 neutron candidates per event.To further reduce this background, for each neutron can-didate, 22 discriminating variables are calculated. Thesevariables are related to specific features of noise events(such as clustered PMT hits), the Cherenkov light pat-tern of the neutron candidate, and its position with re-spect to the primary event vertex. These 22 observablesare then used in a Boosted Decision Tree (BDT) imple-mented using the xgboost Python library [72]. The BDTis trained using a data set of 2.8 × 108 neutron candi-dates. In this sample, about 2× 106 candidates are neu-tron captures simulated using the procedure describedin Section III B and the rest is composed of low energyaccidental coincidences from random trigger events. Ta-ble II summarizes the BDT training parameters. Thefinal BDT performance is shown in Fig. 15. Even ac-counting for preselection cuts, this neutron tagging algo-rithm allows reduction the background rate by a factorof 7 compared to the analysis presented in Ref. [70] forthe same signal efficiency.
TABLE II. Parameters used for the training of the neutrontagging BDT in the xgboost Python library framework.
Parameter Valuelearning rate 0.02522
subsample 0.97max depth 10
tree method approx
max iterations 1500best iteration 1170
3. Systematic uncertainty on neutron tagging efficiency
To estimate the systematic uncertainty on the BDTefficiency associated with mismodeling of neutron propa-gation in water and the 2.2 MeV photon emission, wecompare the efficiencies predicted by the IBD Monte-Carlo simulation to measurements performed using anamericium-beryllium (241Am/Be) radioactive source em-bedded in a BGO scintillator. A detailed description ofthis procedure is given in Ref. [34]. To calculate theneutron identification efficiency for data, we follow themethodology described in Ref. [74] and fit the timing dis-tribution of tagged neutrons by a decaying exponentialplus a constant term as shown in Fig. 16. True neutroncapture event counts decay exponentially in time fromthe detection time of the prompt event, while uncorre-lated backgrounds are constant in time. By comparingthe efficiency in data and simulation for BDT cut pointsrelevant in our analysis, as described in Appendix B, we
FIG. 15. Neutron identification efficiency and mistag rate ofBDT used for the current analysis. The red band depicts theuncertainty associated with the time-dependence of the noisein SK, as described in Section VI A 4. The fraction of remain-ing IBD neutrons and the number of accidental coincidencesper event after preselection, averaged over the entire SK-IVperiod, are 44.7% and 7, respectively. These values dependlinearly on the PMT noise [73], and hence vary by about 15%over the SK-IV period.
assign a relative uncertainty of 12.5% for all neutron tag-ging cuts.
0 100 200 300 400 500 600 700 800
T [ s]
0.000
0.005
0.010
0.015
0.020
Tim
ing
peak
s / e
vent
/ 20
s
Exp + constant fit, = 195.512 ± 6.100 = 0.229 ± 0.0052/dof = 1.266
Constant fitBG/event/ s = 9.575E05 ± 5.36E08
Am/Be data, Center location (2016)
FIG. 16. Exponential + constant fit of neutron candidatetimings in the 2016 241Am/Be sample collected at the centerof the SK tank. The resulting time constant, 195.5 ± 6.1 µs,is consistent with prior measurements.
17
E. Solar neutrino cut
Since even mild neutron tagging cuts can reduce so-lar neutrino backgrounds to negligible levels, dedicatedsolar neutrino cuts are not implemented for the DSNBmodel-independent analysis. For the spectral analysis,however, events with no tagged neutrons are also consid-ered in order to maximize the effective exposure. Whenconsidering these events, we hence apply additional cutsspecifically targeting solar neutrino backgrounds. Thesecuts are based on the opening angle θsun between thereconstructed direction of candidate events and the di-rection of the Sun. The cosine of this angle is peaked at1 for solar neutrino interaction products, and is smearedby kinematic and reconstruction effects. To estimate theimpact of the latter, an specific observable, the MultipleScattering Goodness (MSG) g has been designed for thesolar neutrino analysis [35–38]. Simulated opening angledistributions for solar neutrino events in different MSGbins are shown in Fig. 17.
FIG. 17. Opening angle distributions for simulated solar neu-trino events for the different MSG bins used in this analysis.Events with low MSG have wider opening angle distributionsdue to direction reconstruction issues.
In this analysis we use the method described inRef. [22] and apply cos θsun cuts in the four MSG binsshown in Fig. 17. We estimate the impact of these cutson DSNB signal events by assuming that these eventshave a uniformly distributed θsun, and we obtain the as-sociated MSG distributions using the IBD Monte-Carlosimulation. Conversely, to estimate the number of solarneutrino events above 15.5 MeV, we evaluate the numberof solar events in 13.5-15.5 MeV from data and extrap-olate the result to higher energies using the solar neu-trino MC simulation from Ref. [75], a procedure alreadyused in the DSNB search at SK-I,II,III [22]. Here, wecan safely assume the cos θsun distribution for non-solarevent to be uniform [38], and therefore approximate thenumber of solar events in 13.5-15.5 MeV by:
N solarlow = Nlow(cos θsun > 0)−Nlow(cos θsun < 0), (5)
using the data passing the noise, spallation, andpositron selection cuts described in Secs V A, 3, and V C.Using the solar neutrino MC simulation from Ref. [75],the predicted number of solar neutrino events above15.5 MeV will then be
N solar ≈ 0.12N solarlow . (6)
The impact of solar and neutron tagging cuts can thenbe assessed by rescaling N solar by the corresponding ef-ficiencies.
Finally, we evaluate the systematic uncertainties on thesignal efficiency with the solar event cut using the LINACcalibration results. Specifically, we compute the scalingfactor that allows to minimize the difference between thepredicted and observed MSG distributions for LINACevents. We then evaluate the impact of this rescaling onthe final efficiency to be of about 1%.
F. Cut optimization
In this study, we perform two types of analyses. Herewe adopt a common cut optimization procedure for bothanalyses.
1. DSNB positron candidate selection cuts
We determined the positron candidate selection cutsby comparing the IBD Monte-Carlo simulation with theatmospheric neutrino simulation for the ring clearness,average charge deposit, and Cherenkov angle, and theobserved data for the effective distance deff. Since theimpact of the positron candidate selection cuts dependsweakly on the DSNB model considered, we assumed theHoriuchi+09 spectrum [16]. As discussed in Section V C,we estimate systematic uncertainties using results fromthe solar neutrino analysis [35–38] and the LINAC cali-bration [31]. The final cuts are the following:
deff > max
300, 500− Erec − 15.5 MeV
1 MeV× 50
cm,
Nmaxpre < 12,
Ndecay-e = 0,
Lclear < 0.36,
q50/n50 < 2,
38 < θC < 50.
The efficiencies of these cuts are shown in Fig. 18 as afunction of Erec and vary between 70 and 85%. Overall,positron candidate selection cuts allow to remove 80%of the atmospheric neutrino backgrounds, and bring con-tamination from natural radioactivity to negligible levels.
18
2. Spallation and neutron tagging cuts
Unlike positron candidate selection cuts, spallationand neutron tagging cuts need to be optimized in multi-ple energy regions to account for the important variationsof the spallation and atmospheric background rates in theanalysis windows. While only events with one taggedneutron are used in the DSNB model-independent anal-ysis, the spectral analysis also considers events with zeroor more than one tagged neutron. Here, we first optimizespallation and neutron tagging cuts for the signal regionwhere exactly one tagged neutron is required. Using thethus optimized neutron tagging cuts, we then derive op-timal spallation cuts for events with 6= 1 tagged neutron.
a. Events with one tagged neutron: We devise acut optimization scheme common to both the model-independent and spectral analyses by simultaneouslyadjusting spallation and neutron tagging cuts in Erec
bins. For each energy bin, we select events with ex-actly one tagged neutron and find the spallation and neu-tron tagging cuts that yield optimal sensitivity under thebackground-only hypothesis. We define the sensitivity asthe predicted number of signal events after cuts over the90% C.L. upper limit on the number of signal events,computed using the Rolke method [76]. To simplify theinterpretation of the results presented in this paper, weapply the same cuts for both the model-independent andspectral analyses in the 15.5−29.5 MeV reconstructed en-ergy range, where the two analyses overlap. In particular,we require spallation and solar neutrino backgrounds tobe negligible above 15.5 MeV. The remaining rates ofthese backgrounds can be reliably evaluated by rescal-ing the number of events observed after noise reduction,spallation, and positron candidate selection cuts by theneutron mistag rate.
The signal efficiencies for our choice of cuts are shownin the top panel of Fig. 18 for each energy region. Foreach set of cuts we also present the associated systematicuncertainties, computed as described in Sections V B,V C, and V D, in Table III.
TABLE III. Systematic uncertainties for the reduction cuts,computed as described in Sections V B, V C, and V D. Thesystematic uncertainties for the AFT trigger, noise reduction,pre- and post-activity cuts are negligible. The solar neutrinocut is used only for the spectral analysis, when events have6=1 tagged neutrons.
Cut Relative systematic errorSpallation cut 0.1%deff cut 0.1%Lclear cut 0.2%q50/n50 cut 1.2%θC cut 0.7%Neutron tagging 12.5%Solar neutrino cut 1.0%
b. Events with zero or more than one tagged neu-trons: As previously discussed, the events rejected by
[MeV]recE
10 15 20 25 30
Sig
nal
Eff
icie
ncy
[%
]
0
20
40
60
80
100
SHE+AFT, precut
spallation cut
effwall, pre-/post-activity cuts
ring clearness cut
charge/hit cut
Cherenkov angle cut
neutron tagging (tagged-n =1)
[MeV]recE
16 18 20 22 24 26 28 30
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]
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SHE+AFT, precut
spallation cut
effwall, pre-/post-activity cuts
ring clearness cut
charge/hit cut
Cherenkov angle cut
neutron tagging (tagged-n =0 or >1)
solar neutrino cut
FIG. 18. DSNB signal efficiencies for the signal regions whereone tagged neutron (top) and 6= 1 tagged neutrons (bottom)are required, as started after the SHE+AFT trigger require-ment and the noise reduction cuts. While the one taggedneutron region is common to both the model-independent andspectral analyses above 15.5 MeV, the 6= 1 tagged neutron re-gion is used only in the spectral analysis. Here, we appliednoise reduction, spallation, third reduction, neutron tagging,and solar cuts sequentially and show cumulative efficienciesat each stage. The result in the final bin above 29.5 MeVcorresponds to the efficiency for the range through 29.5 to79.5 MeV, as calculated assuming the Horiuchi+09 6 MeVspectrum [16]. Note also that efficiencies for the solar neu-trino cut in the bottom are shown in 1-MeV bins.
the neutron tagging cuts obtained above can still be con-sidered in the spectral analysis. In the 23.5−79.5 MeVregion, that covers most of the spectral analysis win-dow, spallation and solar neutrino backgrounds are neg-ligible and only noise reduction and positron candidateselection cuts need to be applied to these events. Inthe 19.5−23.5 MeV region, solar neutrino backgroundsare still negligible and spallation backgrounds are mostlylinked to short-lived isotopes, that are easy to reject us-ing the cuts from Section V B. For these energies, wetherefore apply the spallation cut derived above, whose
19
efficiency is close to 90%. In the 15.5−19.5 MeV range,however, both solar neutrino and spallation backgroundslargely dominate and need to be reduced using the tar-geted reduction strategies described in Sections V B andV E. In this analysis, we remove the solar neutrino back-grounds using the cuts in Section V E with the cut pointsfrom Ref. [22]. The cut points and the correspondingsignal efficiencies are shown in Table IV for the differentmultiple scattering goodness and reconstructed kineticelectron energy regions. The remaining number of solarneutrino events after all cuts is less than 2 for the entireenergy region.
TABLE IV. Cuts on cos θsun (upper limits), and signal effi-ciencies for SK-IV. These cuts are only applied to events with6= 1 tagged neutron, in the spectral analysis. They depend onthe value of the multiple scattering goodness, g, and on thereconstructed kinetic electron energy. They are the same asthe ones applied for SK-I and III in Ref. [22]. The signal effi-ciency for SK-IV is within 1% of the one obtained in Ref. [22]for SK-I and III, which is similar to the associated systematicuncertainty.
Erec [MeV] 15.5−16.5 16.5−17.5 17.5−18.5 18.5−19.5g < 0.4 0.05 0.35 0.45 0.93
0.4 < g < 0.5 0.39 0.61 0.77 0.930.5 < g < 0.6 0.59 0.73 0.81 0.93
g > 0.6 0.73 0.79 0.91 0.93Efficiency 73.1% 82.2% 88.3% 96.6%
In contrast, the impact of spallation cuts is difficult toevaluate in the 15.5−19.5 MeV range . To optimize spal-lation cuts for the events considered here, we thereforeproceed as follows. First, we bring contributions fromshort-lived isotopes —with O(0.01) sec half-lives— to anegligible level, using the cuts shown. in Appendix A. Ascan be seen in Fig. 3, the remaining event sample will bedominated by decays from 8B and 8Li, that have a half-life close to 1 sec. We then optimize the spallation like-lihood cuts using the method described in Appendix A 4to compute the remaining amount of 8B and 8Li decays,and maximize S/
√B where B and S are the numbers
of spallation and non-spallation events respectively. Theefficiencies of the optimal cuts are of 65% and 63% in15.5−17.5 and 17.5−19.5 MeV, for a 8B+8Li remainingfraction of about 2.5%. The corresponding remainingnumber of spallation events, as well as the performanceof this cut will be discussed and compared to results fromthe previous SK DSNB analyses in Section VII E.
G. Selected events in the final data samples
Here we discuss the behavior of the observed data afterthe cuts. In particular, the impact of spallation, deff ,and the other positron candidate selection cuts on datais shown in Fig. 19. This figure allows to estimate theamount of spallation and radioactive backgrounds that
need to be removed, since these backgrounds cannot becurrently simulated.
To validate our background modeling and neutron tag-ging procedure we also compare the observed data to thebackground expectations after the noise reduction, mul-tiple spallation cuts, DSNB positron candidate selection,and neutron tagging cuts. To simplify the interpretationof the data, we impose the same neutron tagging cut,with a 20% signal efficiency, for all energies. While mostspallation cuts are removed in order to focus on neutrontagging, multiple spallation cuts are conserved in order toavoid contaminating the neutron detection window withisotope decays —an effect not accounted in the mistagrate predictions. The predicted and observed event spec-tra are shown in Fig. 20 and agree within uncertainties.
After the cuts derived in Section V F are ap-plied, we find 102 events with exactly one neutron in7.5−79.5 MeV. For these events, the distribution of thetime difference between the neutron and the promptevent is shown in Fig. 21. Fitting this distribution by anexponential plus a constant, as is done in the 241Am/Becalibration, yields a time constant of τ = 154 ± 104 µs,which is compatible with the expected neutron capturetime in water. In the 15.5−79.5 MeV region, that willbe used for the spectral analysis, we also find 248 eventswith zero neutrons and 9 events with more than one neu-tron. The observation times and reconstructed verticesfor these events are shown in Figs. 22 and 23. No eventtime cluster has been observed and the time-dependenceof the event rate is consistent with the livetime varia-tions over the SK-IV period. Events are also uniformlydistributed all over the FV, irrespective of the numberof neutrons. The space and time distributions of theselected events are therefore consistent with what is ex-pected for DSNB candidates.
10 15 20 25 30 [MeV]recE
10
210
310
410
510
610
Eve
nts
/2-M
eV
Noise reductionSpallation
effdPositron ID
FIG. 19. Data spectrum after noise reduction, spallation, deff ,and all other positron candidate selection cuts. Here the cutsare applied in the order shown above.
20
[MeV]recE
8 10 12 14 16 18 20 22 24 26 28
Eve
nts
/2-M
eV
0
100
200
300
400
500
600
700SK-IV Data
(non-NCQE)νAtmospheric- (NCQE)νAtmospheric-
Li9Spallation νReactor-
Accidental coincidence
FIG. 20. Predicted and observed spectra for events passingnoise reduction, multiple spallation, DSNB positron candi-date selection, and neutron tagging cuts. Here we apply auniform neutron tagging cut with a 20% signal efficiency forall energies. In the absence of most spallation cuts, the domi-nant backgrounds are accidental coincidences and 9Li decays.The systematic uncertainties are shown by the hatched lines.
FIG. 21. Time differences between reconstructed neutron cap-tures and their corresponding prompt events (positron candi-dates). Here we show the data for one tagged neutron. Thesolid orange curve shows the fit result by an exponential plusa constant, giving a time constant of τ = 154± 104 µs.
VI. DSNB MODEL-INDEPENDENT ANALYSIS
In this section we perform a DSNB model-independentsearch. Specifically, we divide the 7.5−29.5 MeV recon-structed energy range into 2-MeV bins and, in each ofthem, search for DSNB IBDs. In what follows, we de-scribe how to estimate the various backgrounds encoun-tered in this analysis, model their energy dependence,and estimate the corresponding uncertainties.
FIG. 22. Observation times for events with one neutron (top),and with zero or more than one neutron (bottom) after thecuts. Overlaid is the expected time distribution, where varia-tions of the data-taking rate over the SK-IV period are takeninto account.
A. Background estimation
1. Atmospheric neutrinos
In the high end of the analysis window (Erec >19.5 MeV), the atmospheric neutrino spectrum is domi-nated by decay of invisible muons or pions from CC orNC interactions, forming the well-known Michel spec-trum. Systematic uncertainties in this region will there-fore only affect the total number of predicted atmosphericneutrino events. Here, we estimate this number using thesideband region of 29.5 < Erec < 49.5 MeV, that has asimilar background composition. The number of eventsin this sideband is 88.8% of the atmospheric neutrinoMonte-Carlo prediction, and we therefore use this factorto rescale the non-NCQE backgrounds. The associateduncertainty is due to statistical fluctuations in the num-ber of events in the sideband and is around 19%. The
21
FIG. 23. Top (top) and transverse (bottom) views of reconstructed vertices for events with one neutron (left), and with zeroor more than one neutron (right) after the cuts. Events with more than one neutron are shown as red crosses. The solid anddashed gray lines show the ID and the FV, respectively.
resulting spectrum is labeled as “non-NCQE” in Fig. 24.
Below 19.5 MeV, the dominant atmospheric neutrinobackground arises from NCQE interactions. The crosssection measurements from T2K [47] are used to es-timate this background. In particular, the Monte-Carlo simulation predictions of neutrino and antineu-trino NCQE interactions are renormalized using thescaling factors from this measurement; fν-NCQE =
0.80 ± 0.08(stat.)+0.24−0.18(syst.) and fν-NCQE = 1.11 ±
0.18(stat.)+0.29−0.22(syst.), respectively. Note that this
rescaling provides an inclusive estimation of the NCQEand NC 2p2h interactions. The errors of these factorsare taken as cross section uncertainties.
Two additional flux uncertainties are considered forthe NCQE background: the atmospheric neutrino fluxuncertainty and the uncertainty due to the flux differencebetween the T2K beam and atmospheric neutrinos. Forthe former, a 15% uncertainty is taken from Refs. [48, 49].The latter uncertainty arises from the fact that the scal-ing factors above are measured for the T2K fluxes whilethe current focus is the atmospheric neutrino flux andthen the effect of cross section model uncertainties is dif-ferent. To estimate this uncertainty, the ratios of flux-
averaged events in the T2K beam and atmospheric neu-trino fluxes for different cross section models are calcu-lated. Here six models are considered: Spectral Function(SF) [77, 78], Relativistic Mean Field (RMF) [79–82], Su-perscaling (SuSA) [83, 84], Relativistic Green’s Function(RGF) [82, 85–87] with two functional forms for the po-tential (EDAI, Democratic), and Relativistic Plane WaveImpulse Approximation (RPWIA) [82]. The maximumdifferences are taken as systematic errors, 5% for neutri-nos and 7% for antineutrinos.
There are two systematic error sources related to neu-tron tagging for the NCQE background: tagging effi-ciency and neutron multiplicity. For the uncertainty onthe tagging efficiency, 12.5% is employed in this analysisas the maximum difference between the measured andpredicted efficiencies in the 241Am/Be calibration. Theneutron tagging efficiency will also depend on the dis-tance between the neutron emission and capture vertices.Indeed, neutrons produced in atmospheric interactionscan travel up to a few meters and are hence more diffi-cult to identify than neutrons produced in DSNB IBDs.The effect of the uncertainties in modeling the neutrontravel distance on the efficiency is of around 7% [46].In this analysis, the number of tagged neutrons is re-
22
quired to be one, therefore the model uncertainty affect-ing the neutron multiplicity has to be estimated. Herethe recent measurement of the neutron multiplicity af-ter (mostly CC) interactions of neutrinos from the T2Kbeam inside the SK tank is used [73]. This measure-ment allows to compare observations with Monte-Carlosimulation predictions for neutron multiplicity as a func-tion of the reconstructed squared momentum transferredto the nucleus, Q2, and could therefore be adjusted tostudy the NCQE background. We incorporate the maxi-mum difference between observed and predicted neutronmultiplicity in T2K for each Q2 range, and renormalizethe present Monte-Carlo simulation prediction to accom-modate this gap. This procedure gives variances of ap-proximately 40% in the number of events with the taggedneutron being one, both for neutrinos and antineutrinos.
The NCQE spectral shape is sensitive to the γ emissionmodel, affecting the current differential limit extraction.It is complicated to estimate the associated systematicuncertainty, as γ rays are produced at every stage of theNCQE process, from the primary neutrino interaction tothe secondary nuclear reaction. The modeling of theseγ emission is in particular a probable cause of the cur-rently observed discrepancy between the observed andpredicted Cherenkov angle distributions using neutrinosfrom the T2K beam [47]. One notable effect of thismismodeling is a smearing of the reconstructed energyanalogous to a resolution effect. To evaluate the associ-ated systematic uncertainty we model this smearing byconvolving the original spectrum with a Gaussian dis-tribution and using the energy-dependent ratio betweenthe smeared and unsmeared spectra to renormalize theMonte-Carlo events. We then compute the number ofrenormalized events in each energy bin after the reduc-tion steps described in Section V. The difference betweenthis result and the nominal prediction is then taken asthe systematic uncertainty associated to the γ emissionmodeling. For this study, we set the smearing parameterσ to 3 MeV for all energies; this value allows to coverthe discrepancy observed between the predicted and ob-served θC distributions in the T2K measurements men-tioned above. The resulting uncertainty ranges from 30%to 60% in the 7.5−29.5 MeV range.
Finally, we combine all the systematic uncertaintiesdescribed above by adding them in quadrature. The totalsystematic uncertainty on the NCQE background thenvaries from 60% to 80% for low to high energies. Thepredicted NCQE spectrum with the T2K scaling is shownin Fig. 24.
2. Spallation 9Li
The background rate of spallation 9Li can be estimatedby the following formula:
B9Li = R9Li × Tlive × 22.5 kton
×Br[9Li→ β + n]× fwindow × εreduc, (7)
where R9Li is the production 9Li rate measured at SK(0.86± 0.12(stat.)± 0.15(syst.) kton−1·day−1) [58], Tlive
is the operational livetime (2075.3 and 2970.1 days be-low and above Erec = 9.5 MeV, respectively), Br[9Li →β + n] = 0.508 is the branching ratio for β+n decay,fwindow is the fraction of the 9Li decay energy spectrumabove the search energy threshold, and εreduc is the re-duction efficiency. We estimate fwindow using the Monte-Carlo simulation elaborated for IBD events, renormalizedto fit the 9Li spectrum. This same simulation can be usedto estimate the efficiencies for the noise and positron re-ductions as well as the neutron tagging, that are the sameas for the DSNB signal. The spallation cut efficiency isestimated using the procedure outlined in Section V. Thedominant systematic uncertainty on the number of 9Lievents in each energy bin after cuts arises from estimat-ing the impact of spallation cuts. Indeed, as discussedin Appendix A 4, our method assumes that the time dif-ference between an isotope decay and its parent muonis the only isotope-dependent spallation observable. Inthis study, we account for the impact of other spallationobservables by defining a 50% uncertainty on the num-ber of 9Li events. The uncertainty on the event rate istaken from the previous SK study [58] as 22%. Other un-certainties come from the reduction, especially from thespallation cut and neutron tagging, that is 20% in total.The total uncertainty assigned for the 9Li backgroundestimation is therefore 60%.
3. Reactor neutrinos
Reactor neutrino backgrounds are estimated by renor-malizing the IBD Monte-Carlo simulation. They popu-lates only in the lowest energy bin, as seen in Fig. 24. Inthis analysis, a conservative 100% uncertainty is assignedto their estimated rate.
4. Accidental coincidences
A prompt SHE signal accidentally paired with a subse-quent dark noise fluctuation or a low energy radioactivedecay can look like an IBD signature. Since accidentalpairing can occur for both signal and background events,the resulting background can be readily estimated bycomputing the number of events left after noise reduc-tion, spallation, and positron reduction cuts Ndata
pre-ntag,and rescaling it by the neutron mistag rate:
Bacc = εmis ×Ndatapre-ntag. (8)
23
The associated systematic errors are highly cut-dependent and arise from the time dependence of thePMT dark noise and natural radioactivity. In order toevaluate its effect on the background rejection, we sepa-rate the random trigger data mentioned in section III Bover all the SK-IV period into 10 time bins of about eightmonths each. Then we evaluate the BDT mistag rate foreach bin separately and, for a given signal efficiency, takethe standard deviation from the average mistag rate assystematic error. The typical size of uncertainty is a fewto 30%, in the region of interest for the DSNB analyses,as shown in Fig. 15.
B. Differential upper limit
The observed data and expected background spectraare shown in Fig. 24. The corresponding p-values arecalculated for each energy bin by performing pseudo ex-periments as follows. We vary the number of expectedbackground events randomly based on Gaussian distri-butions with their widths being the 1σ systematic uncer-tainties from each background source. We then calculatep-values from the resulting distributions and the observednumber of events in each bin, as shown in Table V. Herethe most significant bins are found to be at 2σ level. Wetherefore conclude that no significant excess is observedin the data over the background prediction in any energybin, and place upper limits on the extraterrestrial νe fluxusing the pseudo experiments above. Here we obtain the90% C.L. upper bound on the number of signal (N limit
90 )as an excess of the observation over the background ex-pectation, by varying the number of observed events ineach energy bin by their statistical uncertainties as wellas varying the number of expected background events bytheir systematic uncertainties from each source. The 90%C.L. upper limit on the νe flux is then calculated as:
φlimit90 =
N limit90
t ·Np · σIBD · εsig, (9)
where t is the operational livetime [sec], Np is the num-ber of free protons in the SK’s FV, σIBD is the IBDcross section [10−41 cm2] at a mean neutrino energy inthe corresponding region (Eν), and εsig is the signal ef-ficiency. Note that the neutrino energy is obtained asEν = Erec + 1.8 MeV in IBD. For the expected sensi-tivity, the same procedure is applied while the numberof observed event is replaced with the number of nomi-nal background prediction. Here statistical uncertaintieson the backgrounds are considered instead. The expectedsensitivities and observed upper limits from this work aresummarized in Table V. These results are also comparedwith the previously published results and theoretical pre-dictions in Fig. 25. Note that the SK-I,II,III limits pre-sented in this figure have been obtained using a differentmethodology, more similar to the one used for the spec-tral analysis in Section VII. In addition, the SK-I,II,III
analysis not only used a higher energy threshold but alsodid not involve neutron tagging [22, 69]. Hence, we donot combine the SK-IV result with the SK-I,II,III one forthe model-independent differential limit. The sensitivi-ties obtained with this analysis are the world’s tightestover the search region [88]. The current limit disfavorsthe Totani+95 model [8] and the most optimistic pre-dictions of the Kaplinghat+00 model [9], and is reach-ing close to several other model predictions. Due to notonly a higher exposure but also higher cut efficienciesand more precise background estimation, this new anal-ysis considerably improves on the previous SK-IV DSNBmodel-independent search [69].
[MeV]recE
10 20 30 40 50 60 70
Eve
nts
/2-M
eV
0
5
10
15
20
25SK-IV Data
(non-NCQE)νAtmospheric-
(NCQE)νAtmospheric-
Li9
Spallation
νReactor-
Accidental coincidence
DSNB (Horiuchi+09 6-MeV, Maximum)
[MeV]recE
10 20 30 40 50 60 70
Eve
nts
/2-M
eV
1
10
SK-IV Data
(non-NCQE)νAtmospheric-
(NCQE)νAtmospheric-
Li9
Spallation
νReactor-
Accidental coincidence
DSNB (Horiuchi+09 6-MeV, Maximum)
FIG. 24. Reconstructed energy spectra after data reductionsfor the background expectation and observation including thesignal window and the sideband region with a linear (top)and a log (bottom) scale for the vertical axis. Color-filled his-tograms correspond to each background source with hatchedlines in the signal window representing the total systematicuncertainty. The red dashed line represents a DSNB signalexpectation from the Horiuchi+09 model [16] shown only forthe signal window.
24
TABLE V. Summary on the 90% C.L. expected sensitivities and observed upper limits as well as the corresponding p-valuesin each electron antineutrino energy bin (Eν = Erec + 1.8 MeV).
Eν [MeV] Expected [cm−2sec−1MeV−1] Observed [cm−2sec−1MeV−1] p-value9.3−11.3 4.44× 101 3.71× 101 0.346
11.3−13.3 1.14× 101 2.04× 101 0.88613.3−15.3 4.17× 100 9.34× 100 0.93815.3−17.3 1.87× 100 3.29× 100 0.83017.3−19.3 8.48× 10−1 5.08× 10−1 0.24319.3−21.3 4.64× 10−1 6.84× 10−1 0.68621.3−23.3 3.28× 10−1 1.27× 10−1 0.07323.3−25.3 2.11× 10−1 3.75× 10−1 0.59725.3−27.3 2.13× 10−1 7.77× 10−2 0.05127.3−29.3 1.98× 10−1 2.42× 10−1 0.60529.3−31.3 1.50× 10−1 7.09× 10−2 0.126
VII. SPECTRAL FITTING
In this section, we derive model-dependent limits onthe DSNB flux by fitting signal and background spectralshapes to the observed data in the 15.5−79.5 MeV range,and combine the results with the ones from previous SKphases [22] to achieve a 22.5 × 5823 kton·day exposure.While atmospheric neutrino backgrounds, notably fromdecays of invisible muons and pions, will dominate overmost of the analysis window, we also account for possibleresidual spallation in 15.5−19.5 MeV.
A. Signal and sideband regions
In order to evaluate the number of atmospheric neu-trino background events, we define three regions of pa-rameter space based on the reconstructed Cherenkov an-gle: one signal region with θC ∈ [38, 50], that will con-tain most of the signal and the irreducible backgrounds,and two sidebands with θC ∈ [20, 38] and θC ∈ [78, 90].The low Cherenkov angle region will be populated withmostly atmospheric backgrounds involving visible muonsand pions while the high angle region will be mostly pop-ulated by NCQE atmospheric neutrino events with mul-tiple γ rays. Finally, we separate events with exactlyone identified neutron from the others, thus defining an“IBD-like” and a “non IBD-like” region. Note that dueto the low efficiencies of the neutron tagging cuts the nonIBD-like region is expected to contain a sizable amountof signal. Our analysis will hence involve six regions ofparameter space: two signal regions with intermediatevalues of the Cherenkov angle, and four sidebands withlow and high Cherenkov angle values, as summarized inTable VI.
B. Spectral shape fitting
We perform a simultaneous fitting of the signal andbackground spectra to the observed data in all six regions
TABLE VI. Overview of the regions used in the spectral anal-ysis. We split the parameter space according to the recon-structed Cherenkov angle and the number of tagged neutrons.Regions with small and large Cherenkov angles are dominatedby the interactions producing visible muons and pions and byNCQE interactions, respectively. We assign numbers for eachregion.
Ntagged-n
θC 20−38 38−50 78−90
1 I II III6=1 IV V VI
of parameter space defined in Table VI using an extendedmaximum likelihood method. Performing this type ofanalysis requires knowing the shapes of the signal andbackground spectra in each of the regions. While the sig-nal spectrum can be reliably predicted by the IBD Monte-Carlo simulation for a given DSNB model, the treatmentof the atmospheric neutrino and spallation backgroundsis more complex. For this study, we follow the methoddescribed in Ref. [22] and divide these backgrounds intothe following five categories.
a. Invisible muons and pions: this category re-groups events with electrons produced by the decays ofinvisible muons and pions. The energy distribution ofthese electrons follows a Michel spectrum, whose shapeis independent of the Cherenkov angle and the neutronmultiplicity and will therefore be the same across all sixregions. For this study, we estimate the shape of theMichel spectrum at SK directly from data, using a sam-ple of electrons produced by cosmic ray muon decays(a similar sample for atmospheric and accelerator neu-trino oscillation and proton decay analyses is describedin Refs. [89, 90]). We then use the atmospheric neu-trino Monte-Carlo simulation to compute the fractionsof background events in the different signal and back-ground regions. Since electrons cannot be distinguishedfrom positrons at SK this background dominates in thesignal regions II and V and are negligible everywhere else.
25
Energy [MeV]eν
10 15 20 25 30
/sec
/MeV
]2
Flu
x U
pp
er L
imit
[/c
meν
1−10
1
10
210
SK-IV 2970 days, Observed 90% C.L. (This work)
SK-IV 2970 days, Expected 90% C.L. (This work)
SK-IV 960 days (Astropart Phys 60, 41, 2015)
SK-I/II/III 2853 days (Phys Rev D 85, 052007, 2012)
KamLAND 2343 days (Astrophys J 745, 2012)
DSNB Theoretical Predictions
FIG. 25. The 90% C.L. expected and observed upper limits on the extraterrestrial electron antineutrino flux from the presentwork, in comparison with previously published results from SK [22, 23] and KamLAND [24] and DSNB theoretical predictionsfrom Fig. 1 (in gray). The upper limit from Ref. [22] (blue) has been derived in Ref. [23].
b. νe CC interactions: in this category we find back-grounds arising from CC interactions of electron neutri-nos and antineutrinos, with no visible muons and pionsin the final state. Their contributions will dominate inthe signal regions II and V above 50 MeV. We estimatethe associated spectral shapes in all regions using theatmospheric neutrino Monte-Carlo simulation. Similarlyto Michel electrons, this background is negligible outsidethe regions II and V.
c. µ/π-producing interactions: visible muons andpions will be associated with low Cherenkov angles, asthese particles are significantly heavier than electrons.The associated background will therefore dominate inthe low Cherenkov angle regions I and IV, and, afterpositron candidate selection cuts, will be negligible in thesignal regions. We extract the associated spectral shapesby considering an atmospheric Monte-Carlo sample withonly CC interactions, visible muons and pions, and noelectrons.
d. NCQE interactions: unlike the other types of at-mospheric neutrino events the NCQE spectrum peaks atlow energies, similarly to the DSNB spectrum. Here wedefine spectral shapes using simulated NCQE events withno electrons. This background, often involving multipleγ rays, will dominate in the high Cherenkov angle regionsIII and VI, but will also contribute to all other regions.
e. Spallation backgrounds: these backgrounds arenegligible in the one-tagged-neutron regions I, II, andIII after the cuts. However, in the other regions, espe-cially in signal region V, residual spallation backgroundsfrom 8Li, 8B, and 9C decays could remain. Since 9C hasa shorter half-life and is produced closer to the muontrack than the other two isotopes, it is expected to besubdominant. To model the spallation spectrum and itsvariability we parameterize this spectrum and vary itsisotope composition as follows:
26
Sspall(E) =f0S9C(E) (10)
+ (1− f0) (f1S8B(E) + (1− f1)S8Li(E)) ,
with f0 ∈ [0, 0.5] and f1 ∈ [0, 1]
where Si(E) refers to the decay spectrum for a given iso-tope i, normalized to one in the spectral analysis energywindow, and f0 and f1 are the isotope fractions. Here, weconstrain 9C to always be less abundant than the othertwo isotopes after spallation cuts are applied. In whatfollows, we will take the nominal spallation spectrum tobe the average between the steepest and the least steepspectra and parameterize possible deviations from thishypothesis as systematic uncertainties. We evaluate theβ spectra using external measurements [91] for 8B decaysand GEANT4 for 8Li and 9C. As with 9Li, we then usethese spectra to renormalize events in the IBD Monte-Carlo simulation and thus model detector resolution ef-fects.
Although the first four background categories do notinclude all possible types of atmospheric neutrino interac-tions, their associated spectra can be linearly combinedto model other background categories. Pion-producingNC backgrounds can notably be treated as a superpo-sition of NCQE and decay electron backgrounds. Thefive categories described here hence allow to map all thebackground configurations relevant to this analysis.
For each background category we define probabilitydistribution functions (PDFs) which model the corre-sponding energy spectra in each of the six Cherenkov an-gle and neutron regions. These PDFs are normalized to 1across all regions. We apply a similar procedure to obtainsignal spectral PDFs associated to different DSNB mod-els, using the IBD Monte-Carlo simulation. For Nevents
observed events with energies E1, ..., ENevents we then
extract the most probable numbers of signal and back-ground events by performing an extended unbinned max-imum likelihood fit, using the following likelihood func-tion:
L(Nj) = e−∑5j=0Nj
Nevents∏i=1
5∑j=0
Nj PDF(r)j (Ei). (11)
Here, the index j = 0, ..., 5 refers to the signal and the fivebackground categories described above. Then Nj des-ignates the numbers of events for the signal and the dif-ferent background types, across all six Cherenkov angle
and tagged neutron regions. For each event, PDF(r)j (Ei)
is the PDF for the signal or background category j in theregion r (for the regions defined in Table VI).
C. Systematic uncertainties
One considerable advantage of using the likelihood de-fined in Equation 11 is that the sizes of the different back-
ground contributions can be treated as nuisance param-eters. This likelihood, however, does not account for theconsiderable uncertainties on the spallation and atmo-spheric background spectral shapes in the energy windowof the DSNB analysis. In this section, we outline howto incorporate systematic uncertainties on these shapesas well as on detector modeling and predicted cut effi-ciencies. We account for systematic uncertainties on thespallation and atmospheric neutrino background spec-tral shapes, energy reconstruction, and reduction effi-ciencies by convolving the likelihood introduced in Equa-tion 11 with suitable probability distributions. Here weneglect the systematic uncertainties associated with theµ/π background. The amounts of these background inthe signal regions II and V are indeed constrained to benegligible by observations from the low angle regions Iand IV, a result that is robust under large variations ofthe assumed spectral shapes in these regions. We also ne-glect the systematic uncertainties on the spectral shapeof the background associated with invisible muon andpion decays since this shape has been directly extractedfrom a large sample of SK-IV data. We then considerfive sources of systematic uncertainties: energy scale andresolution, spectral shape predictions for the spallation,NCQE, and νe CC backgrounds, and reduction cut effi-ciencies.
1. Energy scale and energy resolution
To estimate the impact of energy scale and energyresolution uncertainties on the signal and atmosphericbackground spectra, we follow the procedure described inRef. [22]. The energy scale and energy resolution uncer-tainties are obtained from the solar neutrino analysis andincreased to 2% and 3% respectively to account for thehigher energies studied here. We model the effect of theseuncertainties by distorting the signal and atmosphericbackground PDFs in Equation 11 using the energy reso-lution functions from Refs. [35–38]. We parameterize theamount of distorsion applied to these PDFs using thevariable ε such that ε = 1 represents a 1σ deviation inthe energy scale and resolution. The final likelihood canthen be expressed as:
L′ =
∫ +∞
−∞e−ε
2/2L(ε) dε, (12)
where L(ε) represents the likelihood from Equation 11with the PDFs distorted by an amount ε. These uncer-tainties have a negligible impact on the final result andare therefore not taken into account in the final fit.
While energy scale and resolution uncertainties on sig-nal and atmospheric background spectra can be neglectedin this analysis, the spallation background spectrum isparticularly steep and hence more sensitive to the mod-eling of energy reconstruction. In this analysis, we will
27
therefore account for the associated modeling uncertain-ties when estimating spallation spectral shape systematicuncertainty.
2. Spallation background spectral shapes
As discussed above, we consider two sources of sys-tematic uncertainties here: energy scale and resolutionuncertainties, and isotope composition. We estimate thelatter by varying the 8B, 8Li, and 9C fractions as shown inEquation 3. Then, we distort the steepest and least steepspectra found using this method in order to account forthe 2% and 3% energy scale and resolution uncertaintiesdiscussed above. We take these distorted spectra as our±1σ variations from the nominal spallation spectrum.Finally, we parameterize the total spectral distorsion as-sociated with the systematic uncertainty by using a thirdorder polynomial P3 such that:
PDFnew = PDFold ×N [1 + εP3(E)] , (13)
where ε is expressed in units of σ. More details aboutthese estimates are given in Appendix D. We then con-volve the likelihood L from Equation 11 with a Gaussianprior on ε:
L′ =
∫ 2
−2
L(ε)e−ε2
2 dε. (14)
3. Atmospheric νe CC spectral shapes
The shape of the νe CC background for electron ener-gies below about 100 MeV has not been studied in-depthto date, although Monte-Carlo simulations predict a lin-ear increase in the number of events with the electronenergy. In our analysis, we model this spectral shape un-certainty by allowing the slope of the νe CC spectrum tovary in the two signal regions. We then integrate the dis-torted PDF using pseudo-Gaussian weights. A detaileddescription of this procedure is provided in Ref. [22].
At this step of the analysis, we assume the spectralshape distortions in the =1 and 6=1 tagged neutron re-gions to be fully correlated and model the effect of neu-tron multiplicity uncertainties separately.
4. Relative normalization for NCQE events
The Cherenkov angle distribution of atmosphericNCQE events is associated with large uncertainties stem-ming from the modeling of γ ray emission. We incorpo-rate this uncertainty in the current analysis by allowingthe relative normalization of the NCQE PDFs betweenthe different Cherenkov angle regions to vary. Follow-ing the procedure outlined in Ref. [22], we define a 1σ
variation of this normalization to correspond to a 100%change of the number of NCQE events in the intermedi-ate Cherenkov angle region. Additionally, in order for theoverall normalization of the NCQE PDFs across regionsto remain constant, we reweight these PDFs as follows:
PDF’NCQEmed, n = PDFNCQE
med, n × (1 + ε), (15)
PDF’NCQEhigh, n = PDFNCQE
high, n × (1− fhighε), (16)
PDF’NCQElow, n = PDFNCQE
low, n × (1− flowε), (17)
where the “low”, “med”, and “high” indices refer tothe low (20−38), medium (38−50), and high (78−90)Cherenkov angle ranges from Table VI and n = 0, 1 forthe tagged neutron regions respectively. flow, fmed, fhigh
are scaling factors introduced to preserve the overall nor-malization of the PDFs. The ε parameterizes the PDFdistortion, in units of σ. We finally inject these distortedPDFs into Equation 11 and convolve the new likelihoodwith a weighted Gaussian prior, as with νe CC back-ground uncertainties.
5. Uncertainty on the neutron multiplicity
The fractions of signal and background events observedin the =1 and 6=1 tagged neutron regions depend on boththe neutron tagging efficiency and the true neutron multi-plicity of the observed events. As shown in the 241Am/Becalibration study, the efficiency of the neutron taggingcut for the DSNB spectral analysis is associated with asystematic uncertainty of around 6%. Conversely, the ac-tual neutron multiplicity for atmospheric neutrino inter-actions is poorly known. As discussed in Section VI A,neutron multiplicity uncertainties of up to ∼40% havebeen measured for reconstructed energies above 100 MeVusing the T2K neutrino beam [73]. In what follows, wetherefore consider a 40% systematic uncertainty on theneutron tagging.
We model the effect of neutron multiplicity uncertain-ties by varying the relative normalization of the PDFsin the =1 and 6=1 tagged neutron regions for the νe CC,NCQE, and invisible muon and pion backgrounds. Asmentioned at the beginning of this section we neglect thesystematic uncertainty associated with µ/π backgrounds,which are associated with negligible contributions in thesignal region. As discussed above, we set the 1σ varia-tion of the fraction of events with one tagged neutron toa conservative value of 40%. We then distort the PDFsin the =1 and 6=1 tagged neutron regions for each back-ground category as follows:
PDFIBDj,new = PDFIBD
j,old × (1 + αjε), (18)
PDFnon-IBDj,new = PDFnon-IBD
j,old × (1− αjfε), (19)
where αj is the relative 1σ systematic uncertainty forbackground category j, ε measures the magnitude of the
28
distortion in units of σ and f preserves the overall nor-malization of the PDFs. Finally, we incorporate this un-certainty into the final likelihood by integrating the initiallikelihood similarly to Equation 14.
6. Combining the background uncertainties
The three categories of systematic uncertainties onbackgrounds described above —spallation and νe CCspectral shapes, NCQE Cherenkov angle distribution,and neutron multiplicity— are incorporated into Equa-tion 11 using the modified likelihood defined in Equa-tion 14 and the modified PDFs defined in Ref. [22] aswell as in Eqs 17 and 19 with distorsion parameters ενeCC,εNCQE, and εn respectively. The final likelihood Lsyst canthen be written as:
Lsyst(Nj) =
∫ 3
−1
dενeCC
∫ 3
−1
dεNCQE
∫ 3
−2
dεn
∫ 2
−2
dεspall
× L(Nj, ενeCC, εNCQE, εn, εspall) (20)
×G(ενeCC)×G(εNCQE)× e−ε2n2
√π× e−
ε2spall2
√π
,
where L(Nj, ενeCC, εNCQE, εn, εspall) is the likelihooddefined in Equation 11 with distorted PDFs and G isthe weighted Gaussian introduced in Ref [22].
7. Energy-independent efficiency systematic error
Maximizing the likelihood Lsyst defined in Equation 20over the numbers of events in all five background cate-gories results in a marginalized likelihood Lopt(Ns) whereNs is the number of signal events. Using this likelihood toconstrain the total number of DSNB events that passedthrough the detector, R, requires rescaling Ns by the av-erage value of the signal efficiency over all analysis regionsand their associated energy windows, εsig. We thereforeneed to incorporate the systematic uncertainty on εsiginto Lopt, following a procedure similar to the treatmentof the background systematic uncertainty. Since the neu-tron tagging efficiency only affects the relative normaliza-tion between regions, the main sources of uncertaintieson εsig will arise from noise reduction and positron candi-date selection cuts. These uncertainties are summarizedin Table III. We also incorporate the uncertainties associ-ated to the fiducial volume cut, inverse beta decay crosssection, and livetime calculation, that have been takenfrom the solar neutrino analyses and are summarized inTable VII. Adding all these uncertainties in quadrature,we then rewrite the likelihood as:
L′(R) =
∫ 1
0
Lopt(εR)e−
(ε−εsig)2
2σ2sig dε, (21)
where σsig is the 1σ systematic uncertainty on εsig.
TABLE VII. Uncertainties associated with the fiducial vol-ume cut, the Strumia-Vissani IBD cross section calculation,and the livetime calculation for SK-I to IV. The uncertaintiesfor SK-I,II,III have been taken from the SK solar neutrinoanalyses [35–38]. For SK-IV the uncertainties have been ob-tained from the IBD Monte-Carlo simulation.
SK phase I II III IVFiducial volume 1.3% 1.1% 1.0% 1.5%
Cross section 1.0% 1.0% 1.0% 1.0%Livetime 0.1% 0.1% 0.1% 0.1%
Systematic uncertainties associated with reduction ef-ficiencies weaken the final limits by around 1%. Similarly,while the uncertainties associated with spallation and at-mospheric neutrino backgrounds are of order 100%, theiroverall effect on the final limits is of about 5%. The lim-ited impact of spectral shape uncertainties is due to thelarge dominance of backgrounds associated with invisiblemuon and pion decays, whose spectrum is well-known.The final analysis will hence be largely dominated bystatistical uncertainties, which will allow to easily com-bine SK-IV observations with results from previous SKphases.
D. Combination with SK-I,II,III
The methodology described above, based on an ex-tended maximum likelihood fit over signal and sidebandregions, is similar to the one described in Ref. [22], thatperformed a DSNB spectral analysis over the 22.5 ×2853 kton·days of data corresponding to the first threeSK phases. While this previous analysis did not includeneutron tagging and used slightly different backgroundcategories and reduction cuts, it is also dominated bystatistical uncertainties. Hence, the SK-I,II,III resultscan be readily combined with the SK-IV observations.
In order to study a wide variety of the discrete andparameterized models introduced in Section I, we buildsignal PDFs for all four phases of SK using Monte-Carlosimulation to model detector resolution effects over mostof the energy range. For SK-IV, we renormalize the IBDMonte-Carlo simulation by the predicted DSNB spec-trum for all energies. For SK-I,II,III, we renormalize thesimulations used in Ref. [22] —with events generated inEe+ in 10−90 MeV— and use the resolution functionsfrom Refs. [35–37] to extrapolate them to lower energies.For the Galais+10 [15] and the Nakazato+15 [6] models,for which DSNB fluxes are available only up to antineu-trino energies of 50 MeV, we assume the predicted fluxto be zero in the 50−81.3 MeV range. This assumptionis not expected to affect the spectral fit, as backgroundsfrom νe CC interactions largely dominate at these ener-gies. Finally, for each DSNB model, we fit the data sam-ples obtained in Ref. [22] for the first three SK phases.
29
Here, although we use the same cuts and search regionsas in Ref. [22], we account for possible residual spallationby modeling the spectra and associated systematic uncer-tainty using the same procedure as at SK-IV. We thencombine the four fit results by summing the correspond-ing likelihoods maximized over the nuisance parameters.
E. Results
We apply the procedure described in the previous sec-tions to the observed data collected during phases I to IVof SK for the Horiuchi+09 DSNB model [16]. The associ-ated spectral fits for SK-IV and for SK-I,II,III are shownin Figs. 26 and 27 for the DSNB signal and for the spalla-tion and atmospheric neutrino background categories in-troduced in Section VII B. Since neutron tagging was notpossible in the first three phases of SK, the correspondingfits span only three regions, defined by the low, medium,and high Cherenkov angle ranges defined in Table VI. ForSK-IV, the low energy bump in the predicted decay elec-tron spectrum for IBD-like events is due to the energydependence of the neutron tagging cut, that strongly de-pends on the background composition. As expected, thedominant backgrounds in the low and high Cherenkovangle sidebands are backgrounds with visible muons andpions and NCQE backgrounds, respectively. While mostof the signal region is dominated by backgrounds frominvisible muons and pions, νe CC contributions becomesizable above about 50 MeV. For SK-IV, the backgroundrates are extremely low in the IBD-like region, that willhence be particularly sensitive to IBD signals in spite ofthe low efficiency of the neutron tagging cut.
In spite of introducing spallation backgrounds in thespectral fits, the results shown in Fig. 27 for SK-I,II,IIIare highly similar to the ones shown in Ref. [22]. Thenumber of spallation events for each phase never exceed2, within the upper limit obtained in Ref. [22]. Sincethe current analysis uses a similar procedure with moreinclusive muon selection criteria and 20−25% lower sig-nal efficiencies, the spallation cut effectiveness at SK-IVshould remain on par with the ones observed at previ-ous SK phases. Yet, an important amount of spallationbackgrounds (∼8 events) is predicted below 19.5 MeVat SK-IV. The origin of this important spallation back-ground will be further studied in future SK analyses withan enhanced performance by gadolinium. Note that thiseffect was not observed in other SK searches probing asimilar energy range. These searches however used spe-cific cuts on e.g. the event timings or opening angles thatwe do not apply in this analysis.
Even accounting for possible residual spallation, thenumber of events observed in 17.5−19.5 MeV is higherthan the best-fit predictions from Fig. 26. While this canbe explained by statistical fluctuation, it led us to in-vestigating possible non-spallation sources for the excessobserved over atmospheric neutrino background predic-tions in 15.5−19.5 MeV. We first ruled out the possibility
of a strong DSNB signal, as it would be associated witha steeply falling spectrum and hence to an unrealisti-cally high supernova rate. The hypothesis of an isolatedastrophysical event is also strongly disfavored since theobserved events are uniformly distributed over the SK-IVperiod, as discussed in Section V G. A radioactive originfor the observed events is also highly unlikely, given theirhigh energies and their uniform spatial distribution. Theevent positions are notably not correlated with the loca-tions of calibration sources. Residual spallation thereforeremains the most plausible explanation for the high num-ber of events observed in 15.5−19.5 MeV at SK-IV.
The likelihoods associated to the SK-I to IV fits forthe Horiuchi+09 model are shown in Fig. 28 as a func-tion of the DSNB rate for the reconstructed equivalentelectron kinetic energies Erec > 15.5 MeV. This figurealso shows the likelihood for the combined analysis, witha total exposure of 22.5×5823 kton·days. The associatedlimits on the DSNB flux are shown in Table VIII. Theexpected sensitivities of the SK-I,II,III analysis changeby only ∼3% with the inclusion of the spallation back-grounds while the associated observed upper limits on theDSNB flux become tighter. The expected sensitivities ofthe SK-IV and the combined analyses to the DSNB fluxat 90% C.L. are 2.2 νe cm−2·sec−1 and 1.5 νe cm−2·sec−1,respectively. Hence, the predicted flux for this model,1.9 νe cm−2·sec−1, is well within the reach of the SK-I,II,III,IV analysis. The observed upper limits on theDSNB flux for SK-IV and for the combined analysis areof 4.6 νe cm−2·sec−1 and 2.6 νe cm−2·sec−1, respectively.The best-fit flux for the combined analysis is now of1.30+0.90
−0.85 νe cm−2·sec−1. The 1.5σ excess observed overthe background prediction is higher than the 0.9σ excessfrom the previous combined analysis [22]. While not sta-tistically significant, this result is compatible with a widerange of DSNB predictions with a flux comparable to theone of the Horiuchi+09 model [16].
VIII. DISCUSSION
A. Constraints on the DSNB parameter space
Over the two search strategies presented in this pa-per, the analysis described in Section VI gives a model-independent differential limit on the νe flux while themodel-dependent spectral analysis uses data from allphases of SK and yields the tightest constraints on DSNBmodels. In this section, we present the results of thisanalysis using both discrete DSNB models —most ofthem based on supernova simulations— and simplifiedparameterizations.
The 90% C.L. expected and observed upper limits onthe DSNB rate and flux for theoretical models are shownin Fig. 29 for the combined SK-I,II,III,IV analysis, withthe corresponding results being tabulated in Table VIII.With an exposure of 22.5×5823 kton·days, the sensitivityof the combined analysis at 90% C.L. is the tightest to
30
20 30 40 50 60 70 80Erec [MeV]
0.0
2.5
5.0
7.5
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17.5N
umbe
r of
eve
nts
afte
r cu
ts0
/ >1
neut
ron
tags
Sideband (20 < C < 38 )
e CCNCQEDecay e
/SpallationDSNBAll backgrounds
20 30 40 50 60 70 80Erec [MeV]
Signal region (38 < C < 50 )
20 30 40 50 60 70 80Erec [MeV]
Sideband (78 < C < 90 )
20 30 40 50 60 70 80Erec [MeV]
0.0
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5.0
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vent
s af
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1 ne
utro
n ta
g
e CCNCQEDecay e
/SpallationDSNBAll backgrounds
20 30 40 50 60 70 80Erec [MeV]
20 30 40 50 60 70 80Erec [MeV]
FIG. 26. Best-fit signal and background spectra for SK-IV, assuming the DSNB spectrum predicted by the Horiuchi+09model [16]. The six regions presented here include two signal regions and four sidebands in Table VI.
date and is on par with predictions from the Ando+03,Horiuchi+09 (Tν = 6 MeV), Galais+10, and Kresse+21models [12, 15–17]. One common feature of these opti-mistic models is that they use the highest cosmic star for-mation history allowed by observations. Additionally, theKresse+21 predictions [12] are based on neutrino emis-sion models derived from state-of-the-art supernova sim-ulations, and take a wide range of progenitors into ac-count. The ability of this analysis to probe such realisticmodels makes the prospects for future experiments par-ticularly promising. Currently, an excess of about 1.5σhas been observed in the data and the resulting 90% C.L.limits on the DSNB flux improve on the constraints ob-tained in Ref. [22] for SK-I,II,III. These results confirmthe exclusion of the Totani+95 model [8] and of the mostoptimistic predictions of the Kaplinghat model [9].
Another striking feature observed in Fig. 29 is the sta-bility of the observed and expected limits on the DSNBflux over all models. This stability results from the lim-ited sensitivity of the current analysis to the DSNB spec-tral shape. In order to translate flux limits into con-straints on astrophysical parameters, we therefore ignoresubtle effects associated with e.g. black-hole formation ormultiple classes of progenitors, and use the simple Fermi-
Dirac neutrino emission model described in Section III,as in Ref. [22]. The associated two-dimensional 90% C.L.limit on the neutrino emission temperature and on theDSNB rate for Eν > 17.3 MeV is shown in Fig. 30, forthe combined SK-I,II,III,IV analysis. This figure alsoshows the expected rates for different effective neutrinoemission temperatures. Here, the band accounts for thecurrent uncertainty on the cosmic star formation rate,using the low, fiducial, and high estimates from Ref. [16].Since we used two-dimensional exclusion contours insteadof computing limits for individual models, the limits ap-pear weaker than the ones shown in Fig. 29. These limitsare on par with the SK-I,II,III analysis [22]. In additionto the rate limits, whose interpretation is complicatedby the high SK analysis threshold, we also show 90%C.L. exclusion contours for the total νe energy and theeffective neutrino temperature in Fig. 31. This figurealso shows the regions of parameter space allowed by theKamiokande II and IMB experiments for the supernovaSN1987A [92]. While the neutrino temperature for thissupernova is particularly low, future experiments shouldbe able to probe at least the associated IMB region.
31
25 50 75Erec [MeV]
0.0
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e CCNCQEDecay e
/SpallationDSNBAll backgrounds
25 50 75Erec [MeV]
Signal region (38 < C < 50 )
25 50 75Erec [MeV]
Sideband (78 < C < 90 )
20 40 60 80Erec [MeV]
0
2
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12
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ber
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e CCNCQEDecay e
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20 40 60 80Erec [MeV]
Signal region (38 < C < 50 )
20 40 60 80Erec [MeV]
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25 50 75Erec [MeV]
0
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vent
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Sideband (20 < C < 38 )
e CCNCQEDecay e
/SpallationDSNBAll backgrounds
25 50 75Erec [MeV]
Signal region (38 < C < 50 )
25 50 75Erec [MeV]
Sideband (78 < C < 90 )
FIG. 27. Best-fit signal and background spectra for SK-I (top), II (middle), and III (bottom), assuming the DSNB spectrumpredicted by the Horiuchi+09 model [16]. The three regions presented here correspond to different range of the Cherenkovangle, as shown in Table VI. Since neutron tagging is not possible in SK-I,II,III, only these three Cherenkov angle regions areconsidered.
32
0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0DSNB [events/year]
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
0.00
Like
lihoo
d
SKISKIISKIIISKIVCombined
FIG. 28. Likelihoods associated with phases I to IV of SK, as well as the combined likelihood. As mentioned in the main text,we can neglect correlations between background systematic uncertainties when combining all phases of SK.
FIG. 29. The 90% C.L. upper limits, best-fit values, and expected sensitivities for the DSNB fluxes (left) and rates (right)associated with the models described in Section I. The best fit rates and fluxes are shown with their associated 1σ error bars.This figure also shows the predictions for each models, either as a range or as one value. Note the stability of the expected andobserved flux limits across all models.
33
TABLE VIII. Best-fit values and the 90% C.L. upper limits on the DSNB fluxes (in cm−2·sec−1) for the theoretical models forphases SK-I to IV as well as for the combined analysis. Here the upper limits are given for Eν > 17.3 MeV.
Best fit 90% CL limit Pred.Model SK4 All SK1 SK2 SK3 SK4 All
Totani+95 Constant 2.5+1.4−1.3 1.3+0.9
−0.9 2.3 6.3 7.0 4.5 2.6 4.67
Kaplinghat+00 HMA (max) 2.6+1.5−1.3 1.3+0.9
−0.9 2.3 6.7 7.1 4.7 2.6 3.00
Horiuchi+09 6 MeV, max 2.6+1.4−1.3 1.3+0.9
−0.9 2.4 6.0 7.0 4.6 2.6 1.94
Ando+03 (updated 05) 2.7+1.5−1.4 1.4+0.9
−0.9 2.3 6.6 7.2 4.7 2.7 1.74
Kresse+21 (High, NH) 2.7+1.5−1.3 1.4+0.9
−0.9 2.3 6.7 7.2 4.7 2.7 1.57
Galais+09 (NH) 2.5+1.4−1.3 1.3+0.9
−0.9 2.3 6.3 7.0 4.5 2.6 1.56
Galais+09 (IH) 2.6+1.4−1.3 1.3+0.9
−0.9 2.3 6.4 7.0 4.5 2.6 1.50
Horiuchi+18 ξ2.5 = 0.1 2.6+1.4−1.3 1.4+0.9
−0.9 2.4 6.1 7.1 4.6 2.7 1.23
Kresse+21 (High, IH) 2.7+1.5−1.3 1.4+0.9
−0.9 2.3 6.7 7.1 4.7 2.7 1.21
Kresse+21 (Fid, NH) 2.7+1.5−1.3 1.4+0.9
−0.9 2.3 6.8 7.2 4.7 2.7 1.20
Kresse+21 (Fid, IH) 2.7+1.5−1.3 1.4+0.9
−0.9 2.3 6.8 7.2 4.7 2.7 1.02
Kresse+21 (Low, NH) 2.7+1.5−1.4 1.4+0.9
−0.9 2.3 6.8 7.2 4.8 2.7 0.96
Tabrizi+21 (NH) 2.7+1.5−1.3 1.4+0.9
−0.9 2.4 6.6 7.1 4.7 2.7 0.92
Kresse+21 (Low, IH) 2.7+1.5−1.4 1.4+0.9
−0.9 2.3 6.8 7.2 4.8 2.7 0.84
Lunardini09 Failed SN 2.8+1.5−1.4 1.4+0.9
−0.9 2.4 6.8 7.3 4.8 2.8 0.73
Hartmann+97 CE 2.6+1.4−1.3 1.3+0.9
−0.9 2.3 6.5 7.1 4.6 2.6 0.63
Nakazato+15 (max, IH) 2.7+1.5−1.4 1.4+1.0
−0.9 2.4 6.5 7.2 4.8 2.7 0.53
Horiuchi+18 ξ2.5 = 0.5 2.7+1.5−1.4 1.3+0.9
−0.9 2.2 7.1 7.1 4.8 2.6 0.55
Horiuchi+21 2.1+1.3−1.2 1.2+0.9
−0.9 3.4 4.3 5.9 3.9 2.5 0.28
Malaney97 CGI 2.7+1.5−1.3 1.3+0.9
−0.9 2.3 6.8 7.1 4.7 2.6 0.26
Nakazato+15 (min, NH) 2.8+1.5−1.4 1.4+1.0
−0.9 2.3 6.8 7.2 4.8 2.7 0.19
TABLE IX. Best-fit values and the 90% C.L. upper limits on the DSNB rates (in events·year−1) for the theoretical models forphases SK-I to IV as well as for the combined analysis. Here the upper limits are given for Eν > 17.3 MeV.
Best fit 90% CL limit Pred.Model SK4 All SK1 SK2 SK3 SK4 All
Totani+95 Constant 4.5+2.5−2.2 2.3+1.6
−1.5 4.2 11.2 12.2 7.9 4.6 8.35
Kaplinghat+00 HMA (max) 4.4+2.4−2.2 2.2+1.5
−1.4 3.9 11.2 11.7 7.7 4.4 5.09
Horiuchi+09 6 MeV, max 4.6+2.5−2.3 2.4+1.7
−1.6 4.4 11.7 12.5 8.2 4.8 3.54
Ando+03 (updated 05) 4.7+2.5−2.4 2.4+1.6
−1.6 4.2 11.8 12.4 8.2 4.7 3.09
Kresse+21 (High, NH) 4.5+2.5−2.3 2.4+1.6
−1.5 4.1 11.7 12.2 8.1 4.6 2.76
Galais+09 (NH) 4.4+2.4−2.2 2.2+1.6
−1.4 4.0 11.0 11.9 7.8 4.5 2.74
Galais+09 (IH) 4.4+2.4−2.2 2.2+1.6
−1.4 4.0 11.0 11.9 7.7 4.5 2.62
Horiuchi+18 ξ2.5 = 0.1 4.8+2.6−2.4 2.5+1.7
−1.6 4.5 12.1 12.8 8.4 4.9 2.29
Kresse+21 (High, IH) 4.6+2.5−2.3 2.4+1.6
−1.5 4.1 11.7 12.2 8.1 4.6 2.14
Kresse+21 (Fid, NH) 4.5+2.5−2.2 2.3+1.5
−1.5 4.0 11.7 11.9 7.9 4.5 2.06
Kresse+21 (Fid, IH) 4.5+2.5−2.2 2.3+1.5
−1.5 4.0 11.6 11.9 7.9 4.5 1.75
Kresse+21 (Low, NH) 4.5+2.5−2.2 2.2+1.6
−1.4 3.9 11.6 11.8 7.9 4.5 1.65
Tabrizi+21 (NH) 4.6+2.5−2.3 2.4+1.6
−1.5 4.2 11.8 12.3 8.2 4.7 1.64
Kresse+21 (Low, IH) 4.5+2.5−2.2 2.2+1.6
−1.4 4.0 11.6 11.9 7.9 4.5 1.43
Lunardini09 Failed SN 5.0+2.7−2.5 2.6+1.7
−1.7 4.5 12.7 13.1 8.8 5.1 1.36
Hartmann+97 CE 4.4+2.4−2.2 2.2+1.6
−1.4 4.0 11.2 11.9 7.7 4.5 1.09
Nakazato+15 (max, IH) 5.0+2.7−2.5 2.5+1.8
−1.6 4.5 12.1 13.0 8.7 5.0 0.99
Horiuchi+18 ξ2.5 = 0.5 4.2+2.3−2.1 2.1+1.5
−1.4 3.5 11.4 10.9 7.4 4.1 0.87
Horiuchi+21 3.7+2.2−2.1 2.0+1.6
−1.6 6.0 7.5 10.2 6.8 4.2 0.49
Malaney97 CGI 4.3+2.4−2.1 2.2+1.5
−1.4 3.8 11.2 11.3 7.6 4.3 0.44
Nakazato+15 (min, NH) 4.7+2.5−2.4 2.4+1.6
−1.6 4.0 11.8 12.1 8.2 4.6 0.34
B. Prospects at future experiments
Recent doping of SK with gadolinium (SK-Gd) as wellas the advent of Hyper-Kamiokande (HK) in the moredistant future open new promising perspectives for the
DSNB search. Using gadolinium will notably allow toconsiderably improve neutron tagging and hence elimi-nate most spallation backgrounds and lower the thresh-old of the analysis. As shown in Fig. 24, however, mul-tiple backgrounds involving neutrons can still dominate
34
2 3 4 5 6 7 8
T [MeV]
0
1
2
3
4
5
6
7
8
9ev
ent /
22.5
kton
yr
> 16
MeV
90% C.L. upper limits for individual T s 2D Blackbody DSNB exclusionPredicted rates
FIG. 30. The 90% C.L. excluded region for the DSNB rate forEν > 17.3 MeV and the effective neutrino temperature, forthe blackbody models described in Section III (red surface).To guide the eye, we also show the one-dimensional exclusionlimit for individual neutrino temperatures. The blue bandshows the predictions for blackbody models, for the low, fidu-cial, and high star formation rates used in Ref. [16].
2 3 4 5 6 7 8
T [MeV]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
SN
e
ener
gy in
1053
erg
1e53
IMB
Kamioka
SK 1497+794+562+2970 Days
Excluded (E > 17.3 MeV)
90% C.L.
90% C.L. upper limits for individual T s 2D Blackbody DSNB exclusion
FIG. 31. The 90% C.L. excluded region for the total νe energyemitted during a supernova and the effective neutrino temper-ature, for the blackbody models described in Section III (redsurface). To guide the eye, we also show the one-dimensionalexclusion limit for individual neutrino temperatures. We alsoshow the 90% C.L. contours corresponding to the range ofparameters allowed for SN1987A.
over the DSNB up to about 15.5 MeV. Reactor antineu-trinos, in particular, provide an irreducible backgroundup to 9.5 MeV. Up to about 11.5 MeV, 9Li decays mightthen dominate, and spallation reduction will remain a keycomponent of future analyses. Locating muon-inducedshowers using neutrons will become especially powerful atSK-Gd. After eliminating spallation, atmospheric NCQEinteractions will dominate over a wide energy range andwill call for new dedicated reduction techniques. At SK-Gd, notably, the high visibility of the neutron capturesignal will allow to locate neutron capture without usingthe positron vertex, which could allow to use the neu-tron travel distance as a discriminating observable. Fi-nally, while HK may not be doped with Gd, this consid-erably larger detector coupled with the accelerator neu-trino beams will allow to improve the characterization ofthe NCQE rate, spectral shape, and neutron multiplic-ity, that are currently associated with large systematicuncertainties [47]. In the future, further studies usingthe upcoming Intermediate Water Cherenkov Detector(IWCD) will allow to considerably reduce neutron multi-plicity uncertainties by studying monochromatic beams,and will hence be a key piece of the DSNB search pro-gram at HK. The DSNB study will also be extended bysearches at lower energies, achieved at future large-scaleliquid scintillation detectors, such as JUNO [93], givingdeeper insights into spectrum shape over the wide energyrange in combination with HK.
IX. CONCLUSION
In this paper, we presented two analyses taking ad-vantage of the longest data taking phase of SK, the im-proved data reduction, and better background estimates.We developed improved spallation reduction and neutrontagging algorithms with respect to the previous analysesof SK-IV data, and constrained the DSNB flux in the7.5−29.5 MeV and 15.5−79.5 MeV energy ranges. Withthe model-independent analysis, we achieved the world’stightest upper limit on the extraterrestrial electron an-tineutrino flux. For the latter region, we notably ex-tended the spectral analysis developed for SK-I,II,III [22],and combined the results of the first four SK phases toreach an exposure of 22.5 × 5823 kton·days. This expo-sure yields SK a world-leading sensitivity to the DSNBflux at 90% C.L., comparable to the fluxes of several re-alistic models. A 1.5σ excess has been observed across allthe models probed and the final 90% C.L. limits on theDSNB flux are on par with the ones obtained in previousSK analyses [22, 69]. The last 20 years of data taking atSK have hence brought us to the doorstep of the DSNBparameter space. The enhanced neutron tagging capabil-ities at SK-Gd and the larger detector volume achievedat HK will allow to explore this parameter space, settingmeaningful constraints on astrophysical observables, withthe realistic prospect of a groundbreaking discovery.
35
ACKNOWLEDGMENT
We gratefully acknowledge the cooperation of theKamioka Mining and Smelting Company. The Super-Kamiokande experiment has been built and operatedfrom funding by the Japanese Ministry of Education,Culture, Sports, Science and Technology, the U.S. De-partment of Energy, and the U.S. National Science Foun-dation. Some of us have been supported by funds fromthe National Research Foundation of Korea NRF-2009-0083526 (KNRC) funded by the Ministry of Science,ICT, and Future Planning and the Ministry of Educa-tion (2018R1D1A3B07050696, 2018R1D1A1B07049158),the Japan Society for the Promotion of Science, the Na-tional Natural Science Foundation of China under GrantsNo. 11620101004, the Spanish Ministry of Science, Uni-versities and Innovation (grant PGC2018-099388-B-I00),the Natural Sciences and Engineering Research Council(NSERC) of Canada, the Scinet and Westgrid consor-tia of Compute Canada, the National Science Centre,Poland (2015/18/E/ST2/00758), the Science and Tech-nology Facilities Council (STFC) and GridPPP, UK, theEuropean Union’s Horizon 2020 Research and Innova-tion Programmeunder the Marie Sklodowska-Curie grantagreement no. 754496, H2020-MSCA-RISE-2018 JEN-NIFER2 grant agreement no.822070, and H2020-MSCA-RISE-2019 SK2HK grant agreement no. 872549.
Appendix A: Spallation cut
1. Neutron cloud cut
For each cloud, we define a specific coordinate systemwhose origin is the projection of the cloud barycenteron the muon track. For a given DSNB candidate recon-structed vertex, `l is defined as the distance to this originalong the muon track while `t is the transverse distanceto the track. For a given cloud multiplicity, a DSNB can-didate observed less than dt after the associated muon,and within the ellipse defined by `l and `t, is classified asspallation background. Conditions for the neutron cloudcut are summarized in Table X for different multiplicitiesof the cloud.
TABLE X. Conditions for the neutron cloud cut as a func-tion of the cloud multiplicity. A number followed by the ‘+’symbol represents a lower bound on this multiplicity.
Multiplicity 2+ 2+ 2 3 4−5 6−9 10+dt [sec] 0.1 1 30 60 60 60 60`l [cm] 1200 800 383 548 603 712 766`t [cm] 1200 800 219 268 379 490 548
2. Rectangular cuts
As mentioned in Section V B, we applied a series ofrectangular cuts based on spallation variables. The un-derlying idea is to remove isotopes with their half-livesdependent on the energy region and muon type. In par-ticular, for events with a number of tagged neutrons dif-ferent from one in the spectral analysis, we apply spe-cific rectangular cuts to entirely O(0.01) sec half-lives.The criteria are summarized in Tables XI and XII forevents with and without exactly one tagged neutron re-spectively.
3. Spallation PDFs and log-likelihood ratio
When producing the spallation and random PDFs, weseparate the dt and `t bins to account for the possi-ble correlations, 0−0.05, 0.05−0.5, and 0.5−30 sec fordt (determined by the isotope half-lives in Fig. 3), and0−300, 300−1000, 1000−5000 cm for `t. Fig. 32 showsPDFs for each spallation variable from single through-going muons. Here the results from the most spallation-rich region (0 < dt < 0.05 sec and 0 < `t < 300 cm) areshown. We calculate the spallation log-likelihood ratiowith the procedure described in Section V B. An exam-ple distribution is shown for single through-going muonsin Fig. 33. The cut criteria are tuned depending on thereconstructed energy as well as the dt and `t bins. Weuse the common binning for dt, 0−0.05, 0.05−0.5, and0.5−30 sec, independent of the muon type. In contrast,for `t, we separate bins only for most impactful muontypes, that is, single through-going and multiple muons:0−200, 200−300, 300−500, 500−1000, and >1000 cmfor single through-going, and 0−100, 100−200, 200−300,300−500, 500−700, 700−1000, 1000−2000, 2000−3000,>3000 cm for multiple muons.
4. Spallation cut performance estimation
In this section we present our methodology to estimatethe impact of spallation cuts on non-spallation “signal”events (DSNB, solar, reactor, and atmospheric neutrinointeractions), as well as on spallation backgrounds. Inwhat follows, we treat 9Li decays separately as they pro-vide the dominant β+n signature associated with spalla-tion.
As explained in Section V B, random event efficienciesfor multiple spallation and neutron cloud cuts are esti-mated to be 98% and 99.8%, respectively. We estimatethe signal efficiencies for the rectangular and likelihoodcuts described above by evaluating their impact on thepost-sample, as described in the previous section. Theassociated efficiency (εrandom) can thus be expressed as:
εrandom = Npost,after/Nbefore, (A1)
36
TABLE XI. Summary on the rectangular spallation cuts for events with exactly one tagged neutron. When a given cut hasrequirements on both dt and `t, at least one should be fulfilled.
Muon type Energy range dt requirement `t requirement
AllErec < 23.5 MeV dt > 0.001 sec -Erec < 23.5 MeV dt > 0.1 sec `t > 400 cm
Misfit 15.5 < Erec < 19.5 MeV dt > 1.5 sec -Well-fitted single through-going 15.5 < Erec < 17.5 MeV dt > 7 sec `t > 150 cm
Stopping 15.5 < Erec < 19.5 MeV dt > 0.05 sec -Poorly-fitted stopping 15.5 < Erec < 17.5 MeV dt > 6 sec -
All multiple 15.5 < Erec < 19.5 MeV dt > 0.05 sec -
TABLE XII. Summary on the rectangular spallation cuts for events with tagged neutrons different from one. When a givencut has requirements on both dt and `t, at least one should be fulfilled. Here tighter rectangular cuts are applied to themuon categories generating most of the spallation —single through-going and multiple muons— to remove contributions fromshort-lived isotopes.
Muon type Energy range dt requirement `t requirement
AllErec < 23.5 MeV dt > 0.001 sec -Erec < 23.5 MeV dt > 0.1 sec `t > 400 cm
Misfit 15.5 < Erec < 19.5 MeV dt > 1.5 sec -
Well-fitted single through-going15.5 < Erec < 17.5 MeV dt > 7 sec `t > 150 cm17.5 < Erec < 19.5 MeV dt > 7 sec `t > 100 cm
Stopping 15.5 < Erec < 19.5 MeV dt > 0.05 sec -All multiple 15.5 < Erec < 19.5 MeV dt > 0.05 sec -
Well-fitted multiple15.5 < Erec < 19.5 MeV dt > 0.1 sec -15.5 < Erec < 19.5 MeV dt > 1 sec `t > 400 cm
where Nbefore and Npost,after are the numbers of eventsin the post-sample before and after spallation cuts. Wevalidate this efficiency by evaluating the impact of spal-lation cuts on events from solar neutrino elastic interac-tions, using the opening angle θsun defined in Section IVas a discriminator.
To estimate the background rejection power of thespallation cuts, we use a sample of DSNB candidateevents verifying cos θsun < 0. In order to suppress re-maining radioactivity and atmospheric neutrino events,we also apply cuts on the effective distance to the walland the Cherenkov angle, that will be defined in Sec-tion V C, and require Erec < 15.5 MeV. The spallationremaining rate (εspall) is then estimated as the fraction ofevents remaining after spallation cuts, after the expectednumber of remaining atmospheric neutrino events fromMonte-Carlo simulation has been subtracted.
The procedure outlined above allows to accurately es-timate the spallation remaining rate for Erec < 15.5 MeV—where spallation largely dominates even after cuts, butnot to assess the impact of spallation cuts on individ-ual isotopes. Using the spallation-dominated sample de-scribed above, we therefore refine our approach as fol-lows. To compute the remaining fraction of a specificisotope, we attribute a random dt, drawn from the iso-tope decay time distribution, to each pair in the sample,leaving all other observables untouched. This is equiva-lent to renormalizing the spallation likelihood from Equa-tion 3 by the isotope’s exponential decay time distribu-
tion. Then, we apply the likelihood cuts described aboveto the pairs with the modified dt, and compute the frac-tion of remaining events, εpre,iso. For each event, thisfraction can be expressed as:
εpre,iso = ε(pair)iso,likeli × εrandom,iso (A2)
where ε(pair)iso,likeli is the probability for a pair formed by a
spallation event and its parent muon to pass the likeli-hood cuts. Conversely, εrandom,iso is the probability forall other (uncorrelated) pairs between the event and pre-ceding muons to pass these cuts. This probability canbe computed using a post-sample analogous to the onedescribed in Section V B 2 and, since we reassigned dt forall pairs in each event, will be artificially lower than thesignal efficiency εrandom. The probability for a given iso-tope decay to pass the likelihood cuts (εiso,likeli) is thusgiven by:
εiso,likeli = εpre,iso/εrandom,iso × εrandom. (A3)
The fraction of remaining events after both preselectionand likelihood cuts (εiso,spall) can then be estimated as:
εiso,spall = εpre,iso/εrandom,iso × εrandom × εpresel, (A4)
where εpresel =εspall
εlikeli. (A5)
37
|dt| [sec]2−10 1−10 1 10
pro
b.
0
0.02
0.04
0.06
0.08
0.1
Spallation PDFRandom PDF
[cm]tl0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
pro
b.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
[cm]ll5000− 4000− 3000− 2000− 1000− 0 1000 2000 3000 4000 5000
pro
b.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
[p.e.]µQ0 500 1000 1500 2000 2500
310×
pro
b.
4−10
3−10
2−10
1−10
[p.e.]resQ500− 0 500 1000 1500 2000 2500 3000 3500 4000 4500
310×
pro
b.
4−10
3−10
2−10
1−10
FIG. 32. Spallation and random PDFs for dt (top left), `t (top right), `l (middle left), Qµ (middle right), and Qres (bottom),for the pre (blue) and post (red) samples. Results from the single through-going muons for the dt region of 0−0.05 sec and the`t region of 0−300 cm are shown here.
Here, εspall is the spallation remaining rate for all isotopesafter spallation cuts and εlikeli is the rate after likelihoodcuts only. This ratio yields εpresel ∼ 70% while the pres-election cut alone removes about half of the background,highlighting the significant overlap between preselectionand likelihood cuts.
This procedure is used throughout this study to es-timate the remaining fractions of various isotopes. ForErec <15.5 MeV, we will notably use it to estimate theimpact of spallation cuts on the 9Li background. Above15.5 MeV, we will estimate the remaining fractions of 8Li
and 8B, two isotopes that are particularly difficult to re-move due to their long half-lives. This estimate will allowus to model the spallation background spectrum for thespectral analysis.
In order to estimate the remaining amounts of individ-ual isotopes without relying on a simulation we made twomajor assumptions. First, that the time difference be-tween spallation events and their parent muon is not cor-related with other spallation observables. Second, thatthe impact of spallation cuts above 15.5 MeV can be es-timated using a sample of lower energy events. Both
38
spallL-30 -20 -10 0 10 20 30
Eve
nts
210
310
410 Pre sample Post sample
underflow bin
overflow bin
FIG. 33. Spallation log-likelihood ratio of the single through-going muon for 7.5 < Erec < 9.5 MeV. The values smaller orlarger than −30 or 30 are filled in the underflow or overflowbins, respectively.
assumptions would be verified if the `t, `l, Qµ, and Qresspallation observables described in Section V B 2 weresimilarly distributed for all isotopes. This is howevernot the case as their values will depend on the isotopeproduction mode. To estimate the effect of this isotopedependence, we split the sample described above into four2-MeV bins from 7.5 to 15.5 MeV, that will have differentisotope compositions. For a given spallation cut, we thencompute the spallation remaining rates for the four sub-samples and take the largest deviation from the averagevalue as our systematic uncertainty. This uncertainty de-pends on the isotope considered but typically lies around50%.
Appendix B: 241Am/Be calibration study forneutron tagging
As described in Section V D 3, in order to validate theefficiency of the neutron tagging procedure on real data,we applied neutron tagging to data collected in the pres-ence an 241Am/Be source, which, surrounded by a BGOscintillator, produces a prompt signal and a delayed neu-tron capture signal as part of its radioactive decay chain.However, the data collected with the 241Am/Be sourceis not fully modeled by the simulation software; notably,no modeling of the BGO scintillator is available. TheMonte-Carlo simulation that we use to model 241Am/Beevents is hence similar to the IBD simulation. Becauseof this limitation, a direct comparison between the neu-tron tagging efficiency in simulation and calibration datawould be overly pessimistic, as scintillation in the BGOcan produce prompt events that are not accompanied by
the production of a neutron, thus artificially reducingthe observed preselection efficiency of the neutron candi-dates (see Section V D 1). To account for this, we treateduncertainty associated with the preselection separatelyfrom that of the BDT selection, following the proceduredescribed in Ref. [74].
The preselection efficiency is based on the number ofhits in a given time window and is hence particularlysensitive to the PMT photon detection efficiency (quan-tum efficiency, QE). Hence, we determine the associatedsystematic uncertainty by determining the value of QEfor which the predicted N10 distribution fits the observa-tions best. The N10 predicted and observed distributionsare shown in Fig. 34 for the best-fit QE, that is found tobe 2.1% larger than the QE used in the IBD simulationfrom Section III B. The preselection efficiency associatedto this best-fit QE is 3.0% larger than the efficiency pre-dicted by our simulation. Moreover, the 1σ uncertaintyon this best-fit value, found using a χ2 fit, leads to a2.1% uncertainty on the value of the preselection effi-ciency. The combined preselection uncertainty is henceof 3.7%.
After the uncertainty on the preselection efficiency εIS,we evaluate the uncertainty associated with the BDT se-lection cuts by computing the relative efficiencies εrel =εBDT+IS/εIS for the data and the Monte-Carlo simula-tion for different values of the BDT discriminant. Wedetermine these efficiencies by fitting the timing distri-butions of neutron candidates by an exponential plus aconstant. Results for different BDT cuts are shown inTable XIII for the different 241Am/Be datasets consid-ered here. The maximum discrepancy between data andMonte-Carlo lies around 12% irrespective of the BDTcut.
Combining the 12% BDT reduction uncertainty to the3.7% preselection uncertainty leads to an overall uncer-tainty of 12.5% on the neutron tagging efficiency. Thisuncertainty also include possible discrepancies in neutronkinetic energy distributions, like the ones between 9Li de-cays and IBD events.
Appendix C: Neutrons produced from atmosphericneutrino interactions
The neutron multiplicities predicted by the Monte-Carlo simulation for atmospheric neutrinos are shownin Fig. 35. Note that a significant number of atmo-spheric neutrino interactions produce one or more neu-trons. However, these neutrons are more energetic thanfor the IBDs of DSNB neutrinos and sometimes travelfurther away from their production vertex. Since thecurrent neutron tagging algorithm requires neutrons tobe close to their associated positron vertex, it can alsobe used to reduce neutron-producing atmospheric back-grounds. A detailed study of neutrons associated withatmospheric neutrino backgrounds has been performedin Ref. [74].
39
TABLE XIII. Observed (‘Data’) and predicted (‘MC’) rel-ative efficiencies (in %) for different BDT cuts and for the241Am/Be calibration runs considered in this study. Datawas taken in 2009 and 2016, at three different locations in thetank: in the center of the detector, near the barrel wall (Y12)and the top wall (Z15).
BDT cut Position Year Data MC (Data − MC)/Data
0.40
Center2009 69.4 76.2 −9.82016 80.0 72.3 9.5
Y122009 74.6 77.4 −3.72016 83.8 77.6 7.2
Z152009 87.6 77.1 12.02016 80.2 74.1 −7.7
0.90
Center2009 50.0 55.3 −10.62016 56.1 52.8 5.8
Y122009 56.4 59.6 −5.72016 60.8 59.2 2.6
Z152009 65.8 58.3 11.42016 57.0 55.4 2.8
0.99
Center2009 33.6 35.5 −5.82016 34.9 33.2 4.8
Y122009 36.9 37.8 −2.42016 38.2 37.1 2.8
Z152009 38.8 34.5 10.52016 31.9 32.2 −0.1
0
1000
2000
3000
4000
5000
6000
Neu
tron
can
dida
tes
afte
r pr
esel
ectio
n
MC neutronsData (Am/Be 2016), background subtracted
6 8 10 12 14 16 18 20 22N10
0.0
0.5
1.0
1.5
2.0
Dat
a / M
C
FIG. 34. N10 observed and expected distributions for neu-trons. The expected distribution corresponds to the PMTphoton detection efficiency for which the N10 fits the obser-vations best. The observed distribution has been obtainedby subtracting the N10 background distribution from the to-tal observed distribution. This background distribution hasbeen obtained from data, using random triggers. The lowerpredicted number of events for N10 = 6 is due to harshercontinuous dark noise reduction cuts, as mentioned in Sec-tion V D 1.
0 1 2 3 4 5 6 7 8 9 10tagged-n N
1−10
1
10
210
310 Eve
nts
CCQE-likeπCC1
CC otherNCQE
πNC1NC other
FIG. 35. Predicted neutron multiplicity for atmospheric neu-trino backgrounds. Here we use the atmospheric neutrinoMonte-Carlo simulation in the 7.5−79.5 MeV range, after thenoise reduction cuts.
Appendix D: Spectral fitting
1. Modeling of atmospheric neutrino backgrounds
The probability distribution functions of the atmo-spheric neutrino background spectra used in the spectralanalysis are displayed in Fig. 36. As mentioned in Sec-tion VII, we divide atmospheric neutrino backgroundsinto four categories: µ/π, νe CC, decay electrons, andNCQE interactions. The decay electron spectrum is ob-tained from data while the other spectra are obtainedfrom the atmospheric neutrino Monte-Carlo simulation.
In the extended maximum likelihood fit described inSection VII, atmospheric background fluxes are treatedas nuisance parameters. In Table XIV, we comparethe predicted numbers of events in the four atmosphericbackground categories to the best-fit values obtainedwhen considering the Horiuchi+09 model [16]. Since,as discussed in Section VII, atmospheric events frome.g. pion-producing NC interactions could be categorizedas either NCQE or µ/π, we quote ranges rather thannumbers for these two categories. For decay electrons andνe CC interactions, the predicted and observed numbersof events are within at most 23% of each other.
TABLE XIV. Predicted and best-fit numbers of atmosphericevents using the Horiuchi+09 model [16]. The predicted num-bers of events in the NCQE and µ/π categories are quoted asranges, since certain types of NC events could belong to eithercategory after reconstruction.
Decay-e νe CC NCQE µ/πPredicted 218.5 121.4 81.9−138.4 10.6−67.2Observed 169.5 109.9 88.2 27.9
40
20 < θC < 38 38 < θC < 50 78 < θC < 900
or>
1nta
gs
1nta
g20 < θC < 38 38 < θC < 50 78 < θC < 90
0or>
1nta
gs
1nta
g
20 < θC < 38 38 < θC < 50 78 < θC < 90
0or>
1nta
gs
1nta
g
20 < θC < 38 38 < θC < 50 78 < θC < 90
0or>
1nta
gs
1nta
g
FIG. 36. Probability distribution functions used for the fitting of atmospheric backgrounds in the unbinned spectral fit of thedata. As detailed in Section VII, the backgrounds are separated into four categories, and for each category a PDF is definedover three Cherenkov angle regions (two sidebands and one signal region) and two neutron tagging regions (corresponding to=1 or 6=1 tagged neutrons). Each PDF is normalized to 1 over all regions. The blue histograms show the background spectraobtained from Monte-Carlo simulation or directly from data for the decay electron, while the red lines are the fitted PDFs,obtained by fitting the binned spectra with a piecewise polynomial. Top left: electrons from µ or π decays. Top right: νe CCinteractions. Bottom left: NCQE interactions. Bottom right: µ/π-producing backgrounds.
2. Modeling of spallation backgrounds
To model the spallation background PDF we vary theisotope composition of the background as described inEquation 3 and take the nominal spectrum as the averagebetween the two extreme slopes. We parameterize thisaverage by the following function:
Sspall(Erec) = N exp
(− (Erec + 0.511 MeV)α
β
), (D1)
where N is a normalization factor and α, β are deter-mined by a fit and depend on the SK phase considered.Then, as described in Section VII C 2, we both vary theisotope composition of the spallation spectrum and dis-tort it to account for energy scale and resolution uncer-tainties. We then fit the resulting extreme spectra by the
function from Equation D1 times a third order polyno-mial:
S′spall(Erec) =N ′ exp
(− (Erec + 0.511 MeV)α
β
)× [1 + P3(Erec)] , (D2)
and thus parameterize the 1σ systematic error distor-sions. The nominal spectrum and its associated analyt-ical fit are shown in Fig. 37 for SK-IV with its 1σ un-certainty range. Note that, in order to account for thesteepness of the spallation spectrum while avoiding un-physical results, we impose S′spall(Erec) = 0 for energieslarger than the minimal Erec for which the distorted PDFis zero.
41
FIG. 37. Nominal spallation spectrum (solid red) and itsassociated analytical fit (dashed black) for SK-IV. The 1σsystematic uncertainty is shown as a red band.
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