PHYSICAL REVIEW D 99, 032005 (2019)

Measurement of the neutrino-oxygen neutral-current quasielastic crosssection using atmospheric neutrinos at Super-Kamiokande
L. Wan,47 K. Abe,1,42 C. Bronner,1 Y. Hayato,1,42 M. Ikeda,1 K. Iyogi,1 J. Kameda,1,42 Y. Kato,1 Y. Kishimoto,1,42 Ll. Marti,1
M. Miura,1,42 S. Moriyama,1,42 T. Mochizuki,1 M. Nakahata,1,42 Y. Nakajima,1,42 Y. Nakano,1 S. Nakayama,1,42 T. Okada,1
K. Okamoto,1 A. Orii,1 G. Pronost,1 H. Sekiya,1,42 M. Shiozawa,1,42 Y. Sonoda,1 A. Takeda,1,42 A. Takenaka,1 H. Tanaka,1
T. Yano,1 R. Akutsu,2 T. Kajita,2,42 Y. Nishimura,2 K. Okumura,2,42 R. Wang,2 J. Xia,2 L. Labarga,3 P. Fernandez,3F. d. M. Blaszczyk,4 C. Kachulis,4 E. Kearns,4,42 J. L. Raaf,4 J. L. Stone,4,42 S. Sussman,4 S. Berkman,5 J. Bian,6
N. J. Griskevich,6 W. R. Kropp,6 S. Locke,6 S. Mine,6 P. Weatherly,6 M. B. Smy,6,42 H. W. Sobel,6,42 V. Takhistov,6,*
K. S. Ganezer,7 J. Hill,7 J. Y. Kim,8 I. T. Lim,8 R. G. Park,8 B. Bodur,9 K. Scholberg,9,42 C. W. Walter,9,42 M. Gonin,10
J. Imber,10 Th. A. Mueller,10 T. Ishizuka,11 T. Nakamura,12 J. S. Jang,13 K. Choi,14 J. G. Learned,14 S. Matsuno,14
R. P. Litchfield,15 Y. Uchida,15 M. O. Wascko,15 N. F. Calabria,16 M. G. Catanesi,16 R. A. Intonti,16 E. Radicioni,16G. De Rosa,17 A. Ali,18 G. Collazuol,18 F. Iacob,18 L. Ludovici,19 S. Cao,20 M. Friend,20 T. Hasegawa,20 T. Ishida,20
T. Kobayashi,20 T. Nakadaira,20 K. Nakamura,20,42 Y. Oyama,20 K. Sakashita,20 T. Sekiguchi,20 T. Tsukamoto,20 KE. Abe,21
M. Hasegawa,21 Y. Isobe,21 H. Miyabe,21 T. Sugimoto,21 A. T. Suzuki,21 Y. Takeuchi,21,42 Y. Ashida,22 T. Hayashino,22
S. Hirota,22 M. Jiang,22 T. Kikawa,22 M. Mori,22 KE. Nakamura,22 T. Nakaya,22,42 R. A. Wendell,22,42 L. H. V. Anthony,23
N. McCauley,23 A. Pritchard,23 K. M. Tsui,23 Y. Fukuda,24 Y. Itow,25,26 M. Murrase,25 P. Mijakowski,27 K. Frankiewicz,27
C. K. Jung,28 X. Li,28 J. L. Palomino,28 G. Santucci,28 C. Vilela,28 M. J. Wilking,28 C. Yanagisawa,28,† D. Fukuda,29
K. Hagiwara,29 H. Ishino,29 S. Ito,29 Y. Koshio,29,42 M. Sakuda,29 Y. Takahira,29 C. Xu,29 Y. Kuno,30 C. Simpson,31,42
D. Wark,31,37 F. Di Lodovico,32 B. Richards,32 S. Molina Sedgwick,32 R. Tacik,33,46 S. B. Kim,34 M. Thiesse,35
L. Thompson,35 H. Okazawa,36 Y. Choi,38 K. Nishijima,39 M. Koshiba,40 M. Yokoyama,41,42 A. Goldsack,42,31
K. Martens,42 M. Murdoch,42 B. Quilain,42 Y. Suzuki,42 M. R. Vagins,42,6 M. Kuze,43 Y. Okajima,43 T. Yoshida,43
M. Ishitsuka,44 J. F. Martin,45 C. M. Nantais,45 H. A. Tanaka,45 T. Towstego,45 M. Hartz,46,42 A. Konaka,46 P. de Perio,46
S. Chen,47 and A. Minamino48(Super-Kamiokande Collaboration)
1

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,
Kamioka, Gifu 506-1205, Japan
2
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo,
Kashiwa, Chiba 277-8582, Japan3
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
4
Department of Physics, Boston University, Boston, Massachusetts 02215, USA
5
Department of Physics and Astronomy, University of British Columbia,
Vancouver, British Columbia, V6T1Z4, Canada
6
Department of Physics and Astronomy, University of California,
Irvine, Irvine, California 92697-4575, USA
7
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
8
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
9
Department of Physics, Duke University, Durham North Carolina 27708, USA
10
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France
11
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
12
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
13
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
14
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
15
Department of Physics, Imperial College London, London, SW7 2AZ, United Kingdom
16
Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Università e Politecnico di Bari,
I-70125, Bari, Italy
17
Dipartimento di Fisica, INFN Sezione di Napoli and Università di Napoli, I-80126, Napoli, Italy
18
Dipartimento di Fisica, INFN Sezione di Padova and Università di Padova, I-35131, Padova, Italy
19
INFN Sezione di Roma and Università di Roma “La Sapienza”, I-00185, Roma, Italy
20High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
21
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
22
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
23
Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom

2470-0010=2019=99(3)=032005(11)032005-1

Published by the American Physical Society

L. WAN et al.

PHYS. REV. D 99, 032005 (2019)24

Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
26
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,
Nagoya, Aichi 464-8602, Japan
27
National Centre For Nuclear Research, 00-681 Warsaw, Poland
28
Department of Physics and Astronomy, State University of New York at Stony Brook,
New York 11794-3800, USA
29
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan30
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
31
Department of Physics, Oxford University, Oxford, OX1 3PU, United Kingdom
32
School of Physics and Astronomy, Queen Mary University of London, London, E1 4NS, United Kingdom
33
Department of Physics, University of Regina, 3737 Wascana Parkway,
Regina, Saskatchewan, S4SOA2, Canada
34
Department of Physics, Seoul National University, Seoul 151-742, Korea
35
Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, United Kingdom
36
Department of Informatics in Social Welfare, Shizuoka University of Welfare,
Yaizu, Shizuoka, 425-8611, Japan
37
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory,
Warrington, OX11 0QX, United Kingdom
38
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
39
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
40
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
41
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
42
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes
for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8583, Japan
43
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
44
Department of Physics, Faculty of Science and Technology, Tokyo University of Science,
Noda, Chiba 278-8510, Japan
45
Department of Physics, University of Toronto, Ontario, M5S 1A7, Canada
46
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T2A3, Canada
47
Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
48
Faculty of Engineering, Yokohama National University, Yokohama, 240-8501, Japan
25(Received 16 January 2019; published 15 February 2019)
Neutral current (NC) interactions of atmospheric neutrinos on oxygen form one of the major
backgrounds in the search for supernova relic neutrinos with water-based Cherenkov detectors. The
NC channel is dominated by neutrino quasielastic (NCQE) scattering off nucleons inside 16O nuclei. In thispaper we report the first measurement of NCQE cross section using atmospheric neutrinos at SuperKamiokande (SK). The measurement used 2,778 live days of SK-IV data with a fiducial volume of
22.5 kiloton water. Within the visible energy window of 7.5–29.5 MeV, we observed 117 events comparedto the expected 71.9 NCQE signal and 53.1 background events. Weighted by the atmospheric neutrino
spectrum from 160 MeV to 10 GeV, the flux averaged NCQE cross section is measured to be−38 cm2 .
ð1.01  0.17ðstat:Þþ0.78−0.30 ðsys:ÞÞ × 10
DOI: 10.1103/PhysRevD.99.032005

I. INTRODUCTION*

Also at Department of Physics and Astronomy, UCLA,
California 90095-1547, USA.
†
Also at BMCC/CUNY, Science Department, New York,New York, USA.
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
and DOI. Funded by SCOAP3.

Neutral current quasielastic interaction (NCQE) of
atmospheric neutrinos with 16O is one of the majorinteraction channels in water based neutrino detectors forneutrinos with several hundred MeV energy [1]. Theinteraction processes can be written as

032005-2

ν þ 16O → ν þ 15O þ n þ γ;ν þ 16O → ν þ 15N þ p þ γ;

ð1ÞMEASUREMENT OF THE NEUTRINO-OXYGEN NEUTRAL- …
in which neutrinos knock out nucleons from oxygen andthe residual nuclei are likely to produce deexcitation γ’s.
The γ ray propagates in water and is detected by the
Cherenkov light of the electrons or positrons from compton
scattering and pair production. The emitted proton is below
Cherenkov threshold, while the emitted neutron will be
captured on hydrogen, releasing a 2.2 MeV γ-ray. We use
these γ-rays to tag the interaction.
Supernova relic neutrinos (SRN), also known as
diffused supernova neutrino background (DSNB), areneutrinos emitted from all past core-collapse supernovae[2]. The detection of SRNs via inverse beta decay (IBD,ν̄e þ p → n þ eþ ) is a goal of current and future large
neutrino detectors [3]. In water Cherenkov detectors suchas Super-Kamiokande (SK), where e=γ discrimination is
feasible but still challenging, NCQE interactions ofatmospheric neutrinos with oxygen form a significant
background to SRN searches as well as other rare signal
searches [4–7].
Theoretical calculations of the NCQE cross section on
oxygen exist for both low [8–10] and high [1] energies
and a measurement using the T2K beam [11] is in good
agreement with the predictions. However, no previous
measurement of this process has been performed using
the atmospheric neutrino flux, where NCQE interactions
are of relevance for SRN searches. In this paper, we report
the first measurement of the NCQE cross section on
oxygen using atmospheric neutrinos. This measurement
is particularly important for SRN searches in future water
Cherenkov experiments such as SK-Gd [12,13] and HyperKamiokande [14].
The paper is organized as follows: Sec. II introduces theSuper-Kamiokande experiment. Section III illustrates thesimulation of NCQE events, the Monte-Carlo (MC) setup,
and the corresponding features expected. The NCQE
sample is extracted from data and compared with MC in
Sec. IV. Section V presents the measurement of NCQE
cross section, and discusses applications and future
improvements. Section VI concludes the paper.
II. THE SUPER-KAMIOKANDE EXPERIMENTSuper-Kamiokande is a cylindrical 50-kiloton water
Cherenkov detector located in Kamioka, Japan, shieldedby 2,700 meter water equivalent overburden [15]. SK
consists of an outer detector (OD) instrumented with
1885 8-inch PMTs, optically separated from the innerdetector (ID), which is viewed by 11,129 20-inch PMTs.
SK started data taking in 1996, and since then has
undergone four data-taking phases: SK-I, II, III and IV.
This measurement uses data in SK-IV only, collected from
October 2008 to October 2017. SK-IV started in thesummer of 2008, when new front-end electronics and dataprocessing system were installed. The data acquisition time
window for a typical event above 7.5 MeV in SK-IV is½−5; 35 μs from the trigger timing [16]. If the kinetic

PHYS. REV. D 99, 032005 (2019)energy of an event is above 9.5 MeV (or 7.5 MeV after thesummer of 2011), and if the event is not a cosmic-ray
muon, a special high energy trigger (SHE) and a following
after-trigger with 500 μs time window are issued, allowing
for the detection of delayed-coincidence 2.2 MeV γ signals
from neutron captures on hydrogen within a 535 μs searchwindow.
The interaction vertex of a low-energy event is reconstructed with a time-of-flight (TOF) based algorithm [17],with a vertex resolution of 65 cm for a 7.5 MeV electron,
improving as the energy increases. The energy is reconstructed from the number of detected Cherenkov photons
corrected for water attenuation, photo-coverage, and PMT
response. A detailed description of reconstruction andcalibration for low-energy events can be found in Ref. [18].
III. SIMULATIONThe MC simulation of atmospheric neutrino events is
performed in two stages. First, an event generator models
the interactions of atmospheric neutrinos in water. Finalstate particles resulting from these interactions are thentracked through a simulation of the ID to model the detector
response. This analysis uses a MC sample equivalent to
500 years of live-time with the SK-IV setup.
A. Atmospheric neutrino flux
Super-Kamiokande performed a comprehensive study of
the atmospheric neutrino flux in the energy region from
sub-GeV up to several TeV at the Kamioka Observatory[19]. The measured observables, including event rate,energy spectrum, and directionality, are consistent withthe theoretical prediction from the HKKM model [20,21],
after accounting for neutrino oscillation. Uncertainties on
the flux are taken from the SK measurement and theneutrino/antineutrino ratio uncertainty is derived from thetheoretical prediction.
B. Neutrino interactions
Atmospheric neutrino interactions with constituentsof water molecules in SK are simulated by the NEUT
generator [22], with several modifications in the neutral
current model [23]. We describe here the simulation for
NCQE.
The NCQE cross section on oxygen in NEUT is
simulated by an oxygen spectral function model [24] with
the BBBA05 vector form factor [25] and the dipole
parametrization of the axial form factor [25], taking into
consideration the Pauli blocking effect at pF ¼ 225 MeV=c.
This cross section reproduces well the Ankowski model [1]while providing additional information on kinematics offinal state particles which cannot be directly extracted fromthe model. The cross section per nucleon as a function ofneutrino energy for neutrinos and antineutrinos is shownin Fig. 1.

032005-3

L. WAN et al.

PHYS. REV. D 99, 032005 (2019)

Cross section [10-38 cm2]

0.3

IV. EVENT RECONSTRUCTION
AND SELECTION

ν-p
ν-n
ν-p
ν-n

0.25
0.2

A. Data set

0.15
0.1
0.05
0

0

5
Energy [GeV]10

FIG. 1. NCQE cross section on oxygen per nucleon as afunction of neutrino energy. Solid lines show the neutrino crosssections with proton (black) and neutron (red), and dashedlines show antineutrinos cross section with proton (green) andneutron (blue).

The interacting nucleus is left with a hole in 1p1=2 , 1p3=2
or 1s1=2 state in the simple shell model. The deexcitation γenergy (and corresponding branching ratio) from the 1p3=2
state is 6.32 MeV (86.9%) or 9.93 MeV (4.9%) in the caseof a proton knock-out, and 6.18 MeV (86.9%) in the caseof a neutron knock-out. The spectroscopic factors follow
the summary in Ref. [11]. Other decay channels include
further nucleon emission. The branching ratios for the 1s1=2hole state, which decays through several channels withgamma and nucleon emission, are based on the measurements of the 16Oðp; 2pÞ15N experiment RCNP-E148 [26].
Continuum states with multinucleon knock-out are
assumed to have no gamma emission. This assumption
is taken into account in the estimation of systematic
uncertainty on primary gamma emission.

This analysis uses SK-IV data collected in a fiducial
volume 2 m away from the ID wall in all directions,containing 22.5 kton of water. Due to a lowered thresholdof SHE triggers since September 2011, the live-time isdifferent for the kinetic energy range [9.5, 29.5] MeV and[7.5, 9.5] MeV, with 2,778 days and 1,886 days respectively.
This relatively high trigger threshold of 7.5 or 9.5 MeV ischosen to avoid the overlap with the dominant cosmic-rayinduced spallation background [31]. An upper limit of
29.5 MeV in electron kinetic energy is imposed to reduce
backgrounds from atmospheric neutrino charged-current(CC) interactions, including Michel electrons [32] fromdecays of muons below the Cherenkov threshold.
Energy resolution and secondary gamma emission contribute to the reconstruction of NCQE events above therelatively high energy thresholds of 7.5 and 9.5 MeV.
B. Data reduction
One of the main motivations for the measurement of the
NCQE cross section using atmospheric neutrinos is todetermine the contamination of NC events in SRN
searches. Similar selection steps to those used in SRN
searches [33] are used to select NCQE events. These
criteria can be categorized into the first reduction, thespallation cut, the further reductions, and the Cherenkov
angle cut, the last of which distinguishes the data sample of
SRN and NCQE events. In addition, neutrons are tagged tofurther reduce the remaining backgrounds. Neutron tagging
is a technique to detect neutron capture on hydrogen, andwill be covered in the next subsection.
1. First reduction

C. Detector simulation
The SKDETSIM GEANT3 based [27] simulation package is used to model particle propagation in the water, as
well as the optical properties, photosensor and electronics
response in SK. This model has been tuned to match SK
calibration data.
In interactions of atmospheric neutrinos with oxygen
nuclei, hundreds of MeV are typically transferred to thestruck nucleons, often resulting in the emission of further
secondary nucleons and deexcitation gammas. These secondary processes are simulated with the GCALOR package
in GEANT3 [28]. In particular, the NMTC [29] model isused for protons of all energies and neutrons above
20 MeV, while MICAP [30] is used for neutrons below
20 MeV. The discontinuity between the two models
at 20 MeV is treated as a source of systematic uncertainty
in secondary gamma emission. There is no experimental
data on the production of secondary particles in NCQE
interactions in water.

The following reduction cuts are first applied to remove
spurious events and entering backgrounds [18,34]. First, a
trigger cut is applied to remove calibration events and events
that trigger the OD, which are most likely to be a cosmic-ray
muon. T2K beam events are also removed from the data
sample by a beam trigger. Then, a time difference cut isapplied to remove events within 50 μs to the precedingcosmic-ray muon, which are likely to be decay-electrons or
noise from energetic muons. Afterwards, remaining low
energy events are reconstructed with fitting goodness
information. If the fitting goodness is too low, the eventis also excluded. A fiducial volume cut is further applied toremove radioactivities from the PMTs. The first reduction
efficiency for the signal events is estimated to be >99%.
2. Spallation cut
The spallation products from energetic muons traversing
the detector form the main background in the 7.5–29.5 MeV

032005-4

MEASUREMENT OF THE NEUTRINO-OXYGEN NEUTRAL- …

3. Further reduction
External gamma rays from PMT surfaces and tankmaterial may enter the fiducial volume and can be reconstructed as inward-pointing tracks. We place a cut on the
distance between the PMT surface and event vertex in
the reconstructed direction of the candidate event [38]. The
efficiency for this cut is estimated to be 93%.
Other possible electronlike backgrounds include scattering of solar neutrinos off electrons and decay-electrons
from unobserved muons. Solar neutrinos form an importantbackground in the energy range below 17.5 MeV.
Therefore, a solar angle cut is applied to remove solar
neutrino events at 98% signal efficiency [18]. To accountfor the remaining background from atmospheric CC events,a pre-/post-activity cut which tags multiple peaks close intime, and a multi-ring cut which tags multiple Cherenkov
rings close in space are applied [33,38]. These cuts remove
misreconstructed muons and the leakage of decay electronfrom these muons at high signal efficiencies of 95%
and 99%. Muons and pions can also leak into the NC
sample due to resolution smearing and misreconstructed
Cherenkov angle [33]. These events are tagged by the hit/charge pattern and the sharpness of their Cherenkov rings.

a TOF-subtracted time window of 15 ns and the bin withmost entries is taken as the reconstructed Cherenkov angle
for the event.
The Cherenkov angle of an electron above thresholdpeaks at 42°, while for a pion or muon below energy upper
limit of 29.5 MeV, the opening angle is less than 42°. Single
γ rays with the energy above the analysis threshold of 7.5
or 9.5 MeV are likely to produce multielectrons during
propagation, thus producing a more isotropic Cherenkov
light distribution. The multi-γ’s from secondary processes
further smear the Cherenkov light direction. Therefore, theCherenkov angle of NCQE events is usually reconstructedwith high Cherenkov angles. The angle distribution after
neutron tagging is shown in Fig. 2. Events with Cherenkov
angles greater than 50° are accepted as the signal at an
efficiency of 86%, as summarized in Table I.
C. Neutron tagging
NCQE events from atmospheric neutrinos are highly
likely to knock out a nucleon from the oxygen nucleus.
Knocked-out neutrons will propagate in water and thermalize. The thermalized neutron is then captured by a hydrogen nucleus and emits a single γ at 2.2 MeV, which can beused to tag this event.
1. Tagging algorithm
The identification of neutrons emitted in IBD processes
via captures on hydrogen in water Cherenkov detectors
was initially developed for SRN searches [33]. First, we
calculate the hits within a sliding 10 ns TOF-subtracted
time window and apply a precut. A hit cluster is selected asa candidate for neutron tagging only when the number ofhits within this 10 ns time window exceeds 7. Given thepoor vertex resolution for 2.2 MeV gammas, the vertex of
40
Data
Non-NC
NC non-QE
NCQE

35
30
25
Entriesenergy range at SK [35,36]. This background increases
rapidly at lower energy.
To remove spallation background while keeping signal
efficiency, the time and track of a muon close to a low
energy event are used. A spallation-rich sample shortly
after muon events and a random sample before muon eventsare used to construct a spallation likelihood function. Thisfunction is the product of four parts depending on thetransverse distance between the low energy vertex and themuon track, the longitudinal difference between the low
energy vertex and the peak energy deposit of the muon, theamount of energy deposited near this peak, and the timedifference between muon and candidate, respectively. The
maximum kinetic energy of spallation events is 20.6 MeV[37]. Considering energy resolution effects, spallation cuts
are applied to all events with reconstructed energy up to
23.5 MeV. If an event is highly likely to be a spallation
event, it is removed from the data sample. Spallation cuts
are dependent on energy, with looser cuts for higher energy
events. Signal efficiency for these spallation cuts is estimated to be 90% for the high energy bins above 17.5 MeV
and 51% for the energy bin at 7.5 MeV [37].

PHYS. REV. D 99, 032005 (2019)

20
15
10
5

4. Cherenkov angle cut
For low energy analyses at SK, particle identification(PID) is performed using the opening angle of theCherenkov ring in an event. The Cherenkov angle isreconstructed using 3-hit combinations. Given a reconstructed vertex, each set of 3-PMT hits uniquely defines acone and its opening angle. For each event, a histogram isfilled with the opening angles for all 3-hit combinations in

0

20

40

θC

60

80

FIG. 2. Cherenkov angle distribution in data (black points) andMC expectation (colored histograms) after all other cuts and withneutron tagging. The green histogram shows the non-NC backgrounds, blue shows the NC non-QE components, and red shows
the NCQE components.

032005-5

L. WAN et al.

PHYS. REV. D 99, 032005 (2019)

TABLE I. Reduction efficiency and remaining sample size foreach data reduction step without neutron tagging. Cuts areapplied sequentially.

TABLE II. Neutron tagging efficiency for different physics
processes with primary events at 14.5 MeV. Background here
refers to accidental coincidence events.

Reduction step

Signal eff.

Remaining events

Process

Pre-cut

Pre-cut þ MLP

First reduction
Spallation cut
Incoming cut
Solar cutPre-/post-activity
Multi-ring
Cherenkov angle

>99%
77%
93%
98%
95%
99%
86%

∼1; 600; 000∼170; 000
73,34864,03756,65056,156
27,577SRN
NC
Bkg. per event

35.4%
29.8%
1.6

25.2%
19.1%
5.4 × 10−4

Total

54%

27,577the prompt event is used in the TOF calculation. Second,
for every neutron candidate, a multilayer perceptron (MLP)
is applied using derived parameters characterizing hit time,
hit pattern, and PMT charge. A cut on the output of the
MLP is used to select neutron events, and its efficiency is
obtained using a sample where random trigger data is used
to model the noise and the simulated signal events aresuperimposed [37].
For this work, a recently upgraded neutron-tagging
algorithm takes into consideration the reconstruction ofneutron capture vertex using both the TOF-based algorithm
and a brute-force fitter [39]. It greatly enhances thediscrimination power between neutron capture signals
and accidental coincidence backgrounds. The MLP cut
value is optimized for every reconstructed prompt energy
bin with the expected background and signal MC, imposing
a more stringent cut for lower energy events, for which thebackground rate is higher. This neutron-tagging technique
has been validated with a calibration Am/Be source in
SK-IV [40].

neutron tagged. The neutron capture time for the NC
sample after all reductions and with only one neutron isshown in Fig. 3. The accidental event rate can be estimatedby using the same neutron-tagging criteria on a random
trigger sample, and is calculated to be 13.7 events in thisNC sample. Fitting to an exponential signal and a fixedbackground at the accidental background level, the total
number of events with neutrons is 75.3  9.4 and the lifetime is given as 219.5  47.2 μs, consistent with the
expectation of 204.7 μs [40]. Using a fixed τ at 204.7 μs
fitting as a cross-check, the total number of events withneutrons is calculated to be 68.5  12.1, consistent with
fixed background fitting. The neutron multiplicity comparison between data and MC is shown in Fig. 4. The
distributions are consistent within the uncertainties.
In this analysis, we select events with at least one neutron
tagged. The reduction efficiency including neutron tagging
as a function of reconstructed prompt energy for NCQE
gamma events within [7.5, 29.5] MeV is shown in Fig. 5.
This efficiency is relative to the NCQE events with neutron
production and deexcitation γ emission in the selectedenergy range. The main efficiency sacrifice for events
above the threshold comes from the spallation cut and18
2. Tagging NC neutrons

16
14
Entries / 25μs

Since the TOF-subtracted time is corrected with regards
to the primary vertex, the distance between primary vertex
and neutron capture vertex affects the neutron-tagging
efficiency. For IBD neutrons from SRN neutrinos, theneutron energy is sub-MeV and the neutron drifts typicallyless than 5 cm away from the primary vertex. However, forneutrons from NC events, their energy can reach several
hundreds of MeVs and the neutrons can drift meters away;
hence the neutron-tagging efficiency is dependent on
neutron drift distance. The difference in neutron-tagging
efficiencies for different physics processes are shown in
Table II. The average neutron-tagging efficiency for asingle NCQE neutron in this analysis is 10.4%. The
difference between SKDETSIM and another neutron
propagation simulation in GEANT4 [41] is taken as asource of systematic uncertainty.
There are 117 events with tagged neutrons remaining in
the data sample, among which 89 events have only one

12
10
8
6
4
2
0

100

200
300
Δ T(μs)

400

500

FIG. 3. Neutron tagging time distribution for events with only
one neutron tagged. The black points show the data distribution
and the blue line shows the fitted exponential distribution. The
red histogram indicates the accidental background.

032005-6

MEASUREMENT OF THE NEUTRINO-OXYGEN NEUTRAL- …

1

PHYS. REV. D 99, 032005 (2019)

0.07

Efficiency

Fraction

0.06
0.05
0.04
0.03

0.5

0.02
2

0

8

10

FIG. 6. Detection efficiency as a function of the incident
neutrino energy. The error bars represent the reduction efficiency
uncertainty and the neutron tagging uncertainty.

2
4
6
Number of tagged neutrons per event

FIG. 4. Neutron multiplicity in data (black points) and MC (redhistogram). The uncertainties assigned to data are statistical while
those assigned to MC are the 10% intrinsic neutron-tagging
uncertainty.

0.3

V. CROSS SECTION EXTRACTION
The 117 events in the final data sample include NCQE,
NC non-QE channels, neutron backgrounds including
leakage from reactor neutrinos and spallation, and accidental backgrounds. To evaluate the contribution from nonNC and NC non-QE events, and to derive the NCQE crosssection, further analysis is performed using MC anddifferent data samples.
A. Observed events

0.25
Efficiency

4
6
Neutrino energy [GeV]

The vertex distribution of the final NC sample is shown in
Fig. 7. The vertices are uniformly distributed and consistent
with the expectations of the NC signal. The energy distribution is shown Fig. 8. Note that the energy dependent
efficiency shown in Fig. 5 is not corrected in this figure.
Besides accidental background, non-NC backgrounds inthe data sample include leakage from spallations, reactor
neutrinos, as well as atmospheric neutrino CC interactions.
The spallation background is estimated using a spallation

0.2
0.15
0.1
0.05
10

15
20
25
Reconstructed prompt energy [MeV]

FIG. 5. Reduction efficiency as a function of the reconstructed
prompt energy. The energy dependence mainly comes fromspallation cut (50% to 100%) and the neutron-tagging cut (4%to 22%). The error bars represent the reduction efficiency
uncertainty and the neutron tagging uncertainty, as listed inTable. IV.

20
15
10
Z [m]

5
0
-5

neutron tagging. These cuts are tuned per MeV energy bin
towards a best significance on MC, putting an energy
dependence on the final efficiency. The overall detection
efficiency relative to the number of true NCQE events in thefiducial volume with de-excitation γ’s is also calculated.
Figure 6 shows the overall detection efficiency as a functionof the incident neutrino energy. The higher detection
efficiency for higher energy neutrinos originates from theirhigher neutron multiplicity.

-10
-15
-20

0

100

R2 [m2]200

300

FIG. 7. Vertex distributions of the NC sample. The solid
rectangle shows the inner detector of SK, and the dotted rectangle
shows the fiducial volume region.

032005-7

L. WAN et al.

PHYS. REV. D 99, 032005 (2019)
B. Measured cross section

18
Data
NCQE
Single pion
Multi pion
Non-NC
Accidental

16
Events/1 MeV

14
12The NCQE cross section is measured by comparing data
and MC expectation. The theoretical prediction of fluxaveraged NCQE cross section on oxygen, hσ theory
NCQE i, can be
expressed as:10

R 10 GeV P
theoryi¼ν;ν̄ ϕi ðEν Þ × σ i ðEν ÞNCQE dEν
160 MeVtheoryRPhσ NCQE i ¼
10 GeVi¼ν;ν̄ ϕi ðEν ÞdEν
160 MeV−382

86¼ 1.14 × 10

4
2
0

10
15
20
25
Reconstructed prompt energy [MeV]

FIG. 8. Energy distribution of the NC data sample (black
points) against MC expectations (colored histograms). The redhistogram shows NCQE signal, green shows single-pion channels, blue shows multipion channels, black shows non-NC
backgrounds, and yellow shows the accidental backgroundwithout any true neutron. Summing up the green and the blue
histogram gives the NC non-QE backgrounds.

TABLE III. Predictions of components in the final data sample
and the comparison with signal MC.
Components

EventsNC single π
NC multi-π’sDISν̄e CCν̄μ CC
Accidental
Spallation
Reactor

33.4
4.2
0.0
0.4
0.8
13.7
0.5
0.1

Total background
Observed data

53.1
117

Background subtracted data

63.9

NEUT NCQE prediction

71.9

ð2Þ

where ϕi ðEν Þ is the atmospheric neutrino flux at neutrinoenergy Eν, σ i ðEν Þ is the corresponding theoretical crosssection, and i sums for neutrino and antineutrino species.
The energy integral is performed between 160 MeV and
10 GeV, above which the atmospheric neutrino flux isdecreasing rapidly, and below which the NCQE crosssection is very small. The uncertainty introduced by thecutoff is evaluated and included as a systematic error. The
measured cross section is therefore expressed as:hσ observed
NCQE i ¼

data sample derived by the local proximity to a muon inboth time and space [37]. The same cuts as in the NC event
selection are then applied to this data sample, and thenumber of spallation background is estimated to be 0.5,
mainly contributed by 9Li. Reactor neutrinos produce IBD
positrons, for which the event rate is predicted by asimulation based on the IAEA data [42]. Their leakage
into the NC sample through Cherenkov angle resolution isestimated to be 0.1 event. Atmospheric neutrino CC
backgrounds include νe CC and νμ CC. This backgroundis estimated from MC to be 0.4 events for νe CC and 0.8
events for νμ CC. These non-NC backgrounds are summarized in Table III and compared with the MC predictionsin NCQE and other NC channels.

cm ;

exp
exp
exp
N obs
tot − N acc − N others − N NCothers
× hσ theory
NCQE iN exp
NCQE¼ ð1.01  0.17stat: Þ × 10−38 cm2 ;ð3Þwhere N obs
tot refers to the observed number of events in the
final reduction sample, N exp
acc refers to the accidental background without a true neutron, which is evaluated fromrandom trigger data, and N exp
others refers to the non-NC
backgrounds including spallation products, reactor antineutrinos, and atmospheric neutrino CC interactions. The
term N exp
NCothers refers to the expected number of NC non-QE
backgrounds, and N exp
NCQE refers to the expected number of
NCQE events.
C. Systematic uncertainties
Atmospheric neutrino flux uncertainty varies for different energy bins, as given in Ref. [19]. In this paper, aconservative estimation at 18% in [160 MeV, 10 GeV] istaken. Atmospheric ν=ν̄ ratio has 5% uncertainty [20]. The
cross sections for NC processes other than NCQE have
18% uncertainty [11]. The spectroscopic factors and the
gamma emission branching ratios determines the uncertainty from primary simulation [43]. The uncertainty fromsecondary gamma emission is estimated by varying theneutron energy profile and neutron multiplicity from thesimulation [43].
Since this analysis requires at least one neutron to be
detected via neutron tagging on hydrogen, an additional
systematic uncertainty arises from the uncertainty ofneutron multiplicity in neutral-current interactions. There
are no data available to estimate neutron multiplicity in
NCQE process for oxygen, so this uncertainty is evaluated032005-8

MEASUREMENT OF THE NEUTRINO-OXYGEN NEUTRAL- …

TABLE IV.

Uncertainties in NCQE measurement.
NCQE

νatm flux
ν=ν̄ ratio
Cross-section
Primary γ’s
Secondary γ’s
Neutron multiplicity
Neutron energy
Neutron transportation
Data reduction
Neutron tagging
OthersNC non-QE
18%
5%
18%
3%
13%
16%
14%
þ4%

15%
13%
21%
18%
þ7%
3%
10%
0.7%

3

Cross section [10-38 cm2]

by comparing different simulations. We compared themultiplicity and spectra of primary neutrons predicted by
NEUT and GENIE [44], and the secondary neutron
production as well as neutron thermalization and capture
predicted by SKDETSIM and GEANT4 for different
energy spectra of the primary neutrons. Taking the result
from NEUT and SKDETSIM as the central value, thedifference in neutron multiplicity predictions after applying
the tagging efficiency is 12% for NCQE events. For aconservative estimation, we take the difference in neutron
multiplicity prediction at 100% detection effciency, 21%,as the systematic uncertainty. The neutron energy spectrafrom GENIE introduces 18% deviation the NEUT spectra
for NCQE events and 14% for NC non-QE events. The
GEANT4 simulation of neutron transportation introduces
þ7% deviation from SKDETSIM for NCQE events, andþ4% for NC non-QE events. We assign asymmetric
uncertainty to the neutron transportation simulation term,
and leave the neutron multiplicity and energy spectra
uncertainty to be symmetric.
Data reduction besides neutron tagging imposes
a 3% systematic uncertainty. Neutron tagging efficiency
has 10% intrinsic uncertainty from calibration (Am/Be)
and MC for low-energy neutrons. The cutoff at 10 GeV
imposes a 0.1% uncertainty using simulation with themeasured high energy atmospheric neutrino flux [19].
The cutoff at 160 MeV imposes <0.7% uncertainty, whichis estimated by simulation with the theoretical predictionof low energy atmospheric neutrino flux [45]. The evaluation of non-NC (reactor, 9Li, CC, etc) leakage into NC
sample imposes 21% uncertainties to N exp
others , but due to thesmall ratio of events from non-NC background, thisuncertainty propagates to only 0.2% on the final crosssection result.
All the uncertainties are listed in Table IV. To accountfor the correlations including the flux uncertainty andthe reduction uncertainty between the NCQE sample
and other samples, A toy-MC is used to derive theuncertainty envelope for the NCQE cross section. The

PHYS. REV. D 99, 032005 (2019)

2.5
Prediction

2

Prediction (flux averaged)

1.5

Data
Atmospheric neutrino spectrum

1
0.5
0

0

5
Energy [GeV]10

FIG. 9. The gray histogram shows the atmospheric neutrino
spectrum predicted by HKKM model, the black curve shows the
cross section from Ankowski model, the red line shows thepredicted flux-averaged cross section, and the black point shows
the measured cross section.

68% confidence level region is finally calculated as½0.69; 1.83 × 10−38 cm2 , and the cross section is measured−38
to be ð1.01 0.17ðstat:Þþ0.78
cm2 , as shown−0.30 ðsys:ÞÞ×10
in Fig. 9.
D. Discussion on future improvement
The uncertainty in this measurement is dominated bysystematic uncertainties including the atmosphericflux, cross section of other NC processes, primary andsecondary process simulation, neutron simulation, as well
as neutron-tagging efficiency. The flux measurement will
improve with future Cherenkov detectors such as HyperKamiokande [14]. The cross section for other NC processes
can be improved by the T2K off-axis near detector
ND280 [46,47] and other experiments such as
MiniBooNE [48] and MINERvA [49]. Hadron production
experiments such as EMPHATIC [50] will also contributeto reducing flux uncertainties. For the simulation ofprimary and secondary processes, the gamma ray emission
experiment at RCNP is likely to reduce the uncertainty
soon [51,52].
The statistics in this analysis is limited by the neutrontagging efficiency and the energy threshold. The
present efficiency for NCQE neutrons in pure water isrelatively poor at 4–22%. When SK updates to SK-Gd[12,13], the efficiency would increase to about 80% due tothe higher total energy of the γ cascades. A measurementof neutron multiplicity will also provide constraints on thesimulation of neutron production. Besides, at SK-Gd,
the neutron capture signal can trigger the detector
directly, and thus the lower energy threshold of thisanalysis for prompt γ’s will not be limited by the SHE
trigger threshold. Lowering the analysis threshold to
3.5 MeV will double the detection efficiency of NCQE
γ events.

032005-9

L. WAN et al.

PHYS. REV. D 99, 032005 (2019)
VI. CONCLUSIONACKNOWLEDGMENTS

The first measurement of the NCQE cross section withatmospheric neutrinos on oxygen is reported. NCQE events
are selected by the nuclear deexcitation gamma and neutron
capture signal on hydrogen. The neutron-tagging technique
is employed to enhance the signal-background separation.
We obtained 117 events after data reduction, in agreementwith the expectation of 125.0, including 71.9 estimated fromNCQE channel, 37.6 from non-QE NC channels, and 15.5
from non-NC background. The NCQE cross section averaged over the atmospheric neutrino flux at SK is measured to−38 cm2 , consistentbe ð1.01  0.17ðstat:Þþ0.78−0.30 ðsys:ÞÞ × 10
with the theoretical prediction of 1.14 × 10−38 cm2 .
This result improves the estimation of NCQE component
in low energy rare signal detection in water Cherenkov
detectors, especially in the search of SRNs. It will also
benefit future water Cherenkov experiments, such as
SK-Gd and Hyper-K.

We gratefully acknowledge the cooperation of
the Kamioka Mining and Smelting Company. The
SuperKamiokande experiment has been built and operated
from funding by the Japanese Ministry of Education,
Culture, Sports, Science and Technology, the U.S.
Department of Energy, and the U.S. National Science
Foundation. Some of us have been supported by funds
from the National Research Foundation of Korea
NRF20090083526 (KNRC) funded by the Ministry of
Science, ICT, and Future Planning, the European Union
H2020 RISEGA641540SKPLUS, the Japan Society for
the Promotion of Science, the National Natural Science
Foundation of China under Grants No. 11620101004, theNational Science and Engineering Research Council(NSERC) of Canada, the Scinet and Westgrid consortia
of Compute Canada, and the National Science Centre,
Poland (2015/17/N/ST2/04064, 2015/18/E/ST2/00758).

[1] A. M. Ankowski, O. Benhar, T. Mori, R. Yamaguchi, and
M. Sakuda, Phys. Rev. Lett. 108, 052505 (2012).
[2] S. Ando and K. Sato, New J. Phys. 6, 170 (2004).
[3] S. Horiuchi, J. F. Beacom, and E. Dwek, Phys. Rev. D 79,
083013 (2009).
[4] G. E. Kocharov, G. A. Kovaltsov, and I. G. Usoskin, Nuovo
Cimento Soc. Ital. Fis. 14C, 417 (1991).
[5] Y. Hayato et al. (Super-Kamiokande Collaboration),
Astrophys. J. 857, L4 (2018).
[6] K. Abe et al. (Super-Kamiokande Collaboration), Astrophys. J. 830, L11 (2016).
[7] Y. Cui, M. Pospelov, and J. Pradler, Phys. Rev. D 97,
103004 (2018).
[8] K. Langanke, P. Vogel, and E. Kolbe, Phys. Rev. Lett. 76,
2629 (1996).
[9] J. F. Beacom and P. Vogel, Phys. Rev. D 58, 053010 (1998).
[10] E. Kolbe, K. Langanke, and P. Vogel, Phys. Rev. D 66,
013007 (2002).
[11] K. Abe et al. (T2K Collaboration), Phys. Rev. D 90, 072012(2014).
[12] J. F. Beacom and M. R. Vagins, Phys. Rev. Lett. 93, 171101(2004).
[13] H. Sekiya, J. Phys. Conf. Ser. 888, 012041 (2017).
[14] K. Abe et al., arXiv:1109.3262.
[15] Y. Fukuda et al. (Super-Kamiokande Collaboration), Nucl.
Instrum. Methods Phys. Res., Sect. A 501, 418 (2003).
[16] S. Yamada et al., IEEE Trans. Nucl. Sci. 57, 428 (2010).
[17] M. Smy (SUPERKAMIOKANDE Collaboration), in Proceedings, 30th International Cosmic Ray Conference (ICRC
2007): Merida, Yucatan, Mexico, 2007 (Yucatan Autonoma
University, Merida, Mexico, 2007), Vol. 5, pp. 1279–1282.
[18] K. Abe et al. (Super-Kamiokande Collaboration), Phys.
Rev. D 94, 052010 (2016).

[19] E. Richard et al. (Super-Kamiokande Collaboration), Phys.
Rev. D 94, 052001 (2016).
[20] M. Honda, T. Kajita, K. Kasahara, S. Midorikawa, and T.
Sanuki, Phys. Rev. D 75, 043006 (2007).
[21] M. Honda, T. Kajita, K. Kasahara, and S. Midorikawa, Phys.
Rev. D 83, 123001 (2011).
[22] Y. Hayato, Acta Phys. Pol. B 40, 2477 (2009).
[23] K. Ueno, Study of neutral-current de-excitation gamma-rays
with the T2K neutrino beam, Ph.D. thesis, The University ofTokyo, 2012.
[24] O. Benhar, N. Farina, H. Nakamura, M. Sakuda, and R.
Seki, Phys. Rev. D 72, 053005 (2005).
[25] R. Bradford, A. Bodek, H. S. Budd, and J. Arrington, Nucl.
Phys. B, Proc. Suppl. 159, 127 (2006).
[26] K. Kobayashi et al., arXiv:nucl-ex/0604006.
[27] R. Brun, F. Bruyant, M. Maire, A. C. McPherson,
and P. Zanarini, CERN, Report No. CERN-DD-EE-84-1,
1987.
[28] C. Zeitnitz and T. A. Gabriel, Nucl. Instrum. Methods Phys.
Res., Sect. A 349, 106 (1994).
[29] H. W. Bertini, Phys. Rev. 188, 1711 (1969).
[30] J. Johnson and T. Gabriel, A user’s guide to MICAP: A
Monte Carlo Ionization Chamber Analysis Package, 1988,
DOI: 10.2172/5567506.
[31] S. W. Li and J. F. Beacom, Phys. Rev. D 91, 105005(2015).
[32] C. Bouchiat and L. Michel, Phys. Rev. 106, 170 (1957);[33] H. Zhang et al. (Super-Kamiokande Collaboration), Astropart. Phys. 60, 41 (2015).
[34] K. Abe et al. (Super-Kamiokande Collaboration), Astrophys. J. 850, 166 (2017).
[35] S. W. Li and J. F. Beacom, Phys. Rev. C 89, 045801(2014).

032005-10

MEASUREMENT OF THE NEUTRINO-OXYGEN NEUTRAL- …
[36] S. W. Li and J. F. Beacom, Phys. Rev. D 92, 105033(2015).
[37] Y. Zhang et al. (Super-Kamiokande Collaboration), Phys.
Rev. D 93, 012004 (2016).
[38] K. Bays et al. (Super-Kamiokande Collaboration), Phys.
Rev. D 85, 052007 (2012).
[39] T. J. Irvine, Development of neutron-tagging techniques
and application to atmospheric neutrino oscillation analysis
in Super-Kamiokande, Ph.D. thesis, University of Tokyo,
Tokyo, 2014.
[40] H. Watanabe et al. (Super-Kamiokande Collaboration),
Astropart. Phys. 31, 320 (2009).
[41] S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 506, 250 (2003).
[42] I. A. E. Agency (2017), http://www.iaea.org/.
[43] K. Huang, Measurement of the neutrino-oxygen neutral
current quasi-elastic interaction cross-section by observing
nuclear de-excitation γ-rays in the T2K experiment,
Ph.D. thesis, Kyoto University, 2016.

PHYS. REV. D 99, 032005 (2019)[44] C. Andreopoulos et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 614, 87 (2010).
[45] G. Battistoni, A. Ferrari, T. Montaruli, and P. R. Sala,
Astropart. Phys. 23, 526 (2005).
[46] K. Abe et al. (T2K Collaboration), Phys. Rev. D 87, 092003(2013).
[47] K. Abe et al. (T2K Collaboration), Phys. Rev. D 95, 012010(2017).
[48] A. A. Aguilar-Arevalo et al. (MiniBooNE Collaboration),
Phys. Rev. D 83, 052007 (2011).
[49] C. L. McGivern et al. (MINERvA Collaboration), Phys.
Rev. D 94, 052005 (2016).
[50] K. Gameil, Hadron production measurements of the
EMPATHIC group, Ph.D. thesis, University of British
Columbia, 2018.
[51] Y. Ashida (RCNP-E487 Collaboration), Proc. Sci., NuFact2017 (2018) 077.
[52] I. Ou et al., J. Phys. Soc. Jpn. Conf. Proc. 12, 010048(2016).

032005-11