PHYSICAL REVIEW D 103, 012008 (2021)

Neutron-antineutron oscillation search using a 0.37 megaton-years exposureof Super-Kamiokande
K. Abe,1,42 C. Bronner,1 Y. Hayato,1,42 M. Ikeda,1 S. Imaizumi,1 H. Ito,1 J. Kameda,1,42 Y. Kataoka,1 M. Miura,1,42
S. Moriyama,1,42 Y. Nagao,1 M. Nakahata,1,42 Y. Nakajima,1,42 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 Y. Suzuki,1 A. Takeda,1,42 Y. Takemoto,1 A. Takenaka,1
H. Tanaka,1 T. Yano,1 R. Akutsu,2 S. Han,2 T. Kajita,2,42 K. Okumura,2,42 T. Tashiro,2 R. Wang,2 J. Xia,2
D. Bravo-Berguño,3 L. Labarga,3 Ll. Marti,3 B. Zaldivar,3 F. d. M. Blaszczyk,4 E. Kearns,4,42 J. D. Gustafson,4 J. L. Raaf,4
J. L. Stone,4,42 L. Wan ,4,† T. Wester,4 J. Bian,5 N. J. Griskevich,5 W. R. Kropp,5 S. Locke,5 S. Mine,5 M. B. Smy,5,42
H. W. Sobel,5,42 V. Takhistov,5,‡ P. Weatherly,5 J. Hill,6 J. Y. Kim,7 I. T. Lim,7 R. G. Park,7,7 B. Bodur,8 K. Scholberg,8,42
C. W. Walter,8,42 A. Coffani,9 O. Drapier,9 S. El Hedri,9 A. Giampaolo,9 M. Gonin,9 Th. A. Mueller,9 P. Paganini,9B. Quilain,9 T. Ishizuka,10 T. Nakamura,11 J. S. Jang,12 J. G. Learned,13 L. H. V. Anthony,14 A. A. Sztuc,14 Y. Uchida,14
V. Berardi,15 M. G. Catanesi,15 E. Radicioni,15 N. F. Calabria,16 L. N. Machado,16 G. De Rosa,16 G. Collazuol,17 F. Iacob,17
M. Lamoureux,17 N. Ospina,17 L. Ludovici,18 Y. Nishimura,20 S. Cao,21 M. Friend,21 T. Hasegawa,21 T. Ishida,21T. Kobayashi,21 T. Matsubara,21 T. Nakadaira,21 M. Jakkapu,21 K. Nakamura,21,42 Y. Oyama,21 K. Sakashita,21T. Sekiguchi,21 T. Tsukamoto,21 Y. Nakano,22 T. Shiozawa,22 A. T. Suzuki,22 Y. Takeuchi,22,42 S. Yamamoto,22 A. Ali,23
Y. Ashida,23 J. Feng,23 S. Hirota,23 A. K. Ichikawa,23 T. Kikawa,23 M. Mori,23 T. Nakaya,23,42 R. A. Wendell,23,42
K. Yasutome,23 P. Fernandez,24 N. McCauley,24 P. Mehta,24 A. Pritchard,24 K. M. Tsui,24 Y. Fukuda,25 Y. Itow,26,27
H. Menjo,26 T. Niwa,26 K. Sato,26 M. Tsukada,26 P. Mijakowski,28 M. Posiadala-Zezula,51 C. K. Jung,29 C. Vilela,29
M. J. Wilking,29 C. Yanagisawa,29,§ M. Harada,30 K. Hagiwara,30 T. Horai,30 H. Ishino,30 S. Ito,30 Y. Koshio,30,42 W. Ma,30
N. Piplani,30 S. Sakai,30 Y. Kuno,31 G. Barr,32 D. Barrow,32 L. Cook,32,42 A. Goldsack,32 S. Samani,32 C. Simpson,32,42
D. Wark,32,37 F. Nova,33 T. Boschi,19 F. Di Lodovico,19 S. Molina Sedgwick,19,∥ M. Taani,19 S. Zsoldos,19 J. Y. Yang,34
S. J. Jenkins,35 J. M. McElwee,35 M. D. Thiesse,35 L. F. Thompson,35 M. Malek,35 O. Stone,35 H. Okazawa,36 S. B. Kim,38
I. Yu,38 K. Nishijima,39 M. Koshiba,40,* N. Ogawa,40 K. Iwamoto,41 M. Yokoyama,41,42 K. Martens,42 M. R. Vagins,42,5
M. Kuze,43 S. Izumiyama,43 M. Tanaka,43 T. Yoshida,43 M. Inomoto,44 M. Ishitsuka,44 R. Matsumoto,44 K. Ohta,44
M. Shinoki,44 J. F. Martin,45 H. A. Tanaka,45 T. Towstego,45 M. Hartz,46 A. Konaka,46 P. de Perio,46 N. W. Prouse,46
B. W. Pointon,52 S. Chen,47 B. D. Xu,47 B. Richards,48 B. Jamieson,49 J. Walker,49 A. Minamino,50 K. Okamoto,50
G. Pintaudi,50 and R. Sasaki50(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 California,
Irvine, Irvine, California 92697-4575, USA
6
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
7
Institute for Universe and Elementary Particles, Chonnam National University, Gwangju 61186, Korea
8
Department of Physics, Duke University, Durham North Carolina 27708, USA
9
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France
10
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
11
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
12
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
13
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
14
Department of Physics, Imperial College London, London, SW7 2AZ, United Kingdom
15
Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Università e Politecnico di Bari,
I-70125, Bari, Italy
16
Dipartimento di Fisica, INFN Sezione di Napoli and Università di Napoli, I-80126, Napoli, Italy
17
Dipartimento di Fisica, INFN Sezione di Padova and Università di Padova, I-35131, Padova, Italy
18
INFN Sezione di Roma and Università di Roma “La Sapienza,” I-00185, Roma, Italy
19
Department of Physics, King’s College London, London, WC2R 2LS, United Kingdom
20
Department of Physics, Keio University, Yokohama, Kanagawa, 223-8522, Japan

2470-0010=2021=103(1)=012008(12)012008-1

Published by the American Physical Society

K. ABE et al.

PHYS. REV. D 103, 012008 (2021)
21

High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
22
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
23
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
24
Department of Physics, University of Liverpool, Liverpool, L69 7ZE, United Kingdom
25
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
26
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
27
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,
Nagoya, Aichi 464-8602, Japan
28
National Centre For Nuclear Research, 02-093 Warsaw, Poland
29
Department of Physics and Astronomy, State University of New York at Stony Brook,
New York 11794-3800, USA
30
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
31
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
32
Department of Physics, Oxford University, Oxford, OX1 3PU, United Kingdom
33
Rutherford Appleton Laboratory, Harwell, Oxford, OX11 0QX, United Kingdom
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
Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom
49
Department of Physics, University of Winnipeg, Manitoba R3J 3L8, Canada
50
Department of Physics, Yokohama National University, Yokohama, Kanagawa, 240-8501, Japan
51
Faculty of Physics, University of Warsaw, Warsaw, 02-093, Poland
52
Department of Physics, British Columbia Institute of Technology,
Burnaby, British Columbia, V5G 3H2, Canada(Received 6 December 2020; accepted 24 December 2020; published 21 January 2021)
As a baryon number violating process with ΔB ¼ 2, neutron-antineutron oscillation (n → n̄) provides aunique test of baryon number conservation. We have performed a search for n → n̄ oscillation with boundneutrons in Super-Kamiokande, with the full dataset from its first four run periods, representing an
exposure of 0.37 Mton-years. The search used a multivariate analysis trained on simulated n → n̄ eventsand atmospheric neutrino backgrounds and resulted in 11 candidate events with an expected background of
9.3 events. In the absence of statistically significant excess, we derived a lower limit on n̄ appearance*

Deceased.
Corresponding author.
wanly@bu.edu‡
Also at Department of Physics and Astronomy, UCLA, California 90095-1547, USA.
§
Also at BMCC/CUNY, Science Department, New York, New York, 10007, USA.
∥
Present address: Queen Mary University of London, London, E1 4NS, United Kingdom.
†

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.

012008-2

NEUTRON-ANTINEUTRON OSCILLATION SEARCH USING A …

PHYS. REV. D 103, 012008 (2021)

lifetime in 16O nuclei of 3.6 × 1032 years and on the neutron-antineutron oscillation time ofτn→n̄ > 4.7 × 108 s at 90% C.L.
DOI: 10.1103/PhysRevD.103.012008

I. INTRODUCTION
The present baryon asymmetry of the universe provides
indirect evidence for baryon number violating (BNV)
processes [1], which cannot be sufficiently explained bymechanisms within the Standard Model (SM) [2]. Searches
for BNV processes probe physics beyond the reach of the
SM can be classified based on the baryon number violation(ΔB) involved. Processes with ΔB ¼ 1 are tightly constrained by null observations from proton decay searches,and processes with ΔB ¼ 3 are expected to conflict with
nucleosynthesis scenarios [3]. The Standard Model allows
for non-perturbative processes involving sphalerons thatwould wash out any baryon number asymmetry fromprocesses that conserve B − L, where L is lepton number,before the electroweak phase transition [4]. Therefore, as a
BNV process violating both B and B − L, neutron-antineutron oscillation provides a unique probe of baryon
number violation and essential insight into the baryon
asymmetry and baryogenesis.
Several models predicting n − n̄ oscillations have been
proposed since the 1970s, including those employing anSUð2ÞL × SUð2ÞR × SUð4Þc gauge group to generate abaryon asymmetry [5,6] and others that propagate SM
fields into extra space-time dimensions [7]. The predictedoscillation times vary from 109 s [7] to 5 × 1010 s [6] andcorrespond to energy scales of 102 –103 TeV, well above
the scale that can currently be probed by accelerators [8].
Recent developments from a lattice QCD calculation on thepostsphaleron baryogenesis model [9] and a left-rightsymmetric model with extra dimensions [10] indicate thatn − n̄ oscillation is more sensitive to baryon number
violation than previously expected, providing further motivation for experimental searches.
The probability of a free neutron oscillating to an
antineutron can be parametrized as a simple 2 × 2
Hamiltonian and can be written as
Pn→n̄ ðtÞ ¼

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 
δm2
2
sin
ΔE2 þ δm2 t ;ΔE2 þ δm2

ð1Þ

where ΔE is the energy difference between the neutron andantineutron and δm ¼ 1=τn−n̄ , where τ is the neutronantineutron oscillation time. In the case of degenerate
neutron and antineutron energies, Eq. (1) has a simplified
form,

2

Pn→n̄ ðtÞ ≈ ðδmtÞ ¼

t

τn−n̄

2

:

ð2Þ

For bound neutrons in nuclei, the probability can be written
as [11]
Pnuc ðn → n̄Þ ¼

1
1¼;
T nuc Rτ2n−n̄ð3Þwhere T nuc is the observed neutron lifetime in neutronantineutron oscillation, and R is the so-called nuclear
suppression factor that accounts for the suppression ofoscillations due to differences in the nuclear potentials ofneutrons and antineutrons. Theoretical calculations of R
using effective field theories vary [12,13], but, in thefollowing, we adopt R ¼ 0.517 × 1023 s−1 for 16O based
calculations by Friedman et al. [11].
Experimental searches for n − n̄ oscillation rely on
observing particles (mostly pions) produced when a neutron oscillates into an antineutron and annihilates with anearby nucleon. There have been a number of n − n̄
searches using either free neutrons [14] or bound neutrons[15–21], none of which have yielded a positive signal.
Accordingly, constraints on the n − n̄ oscillation time havebeen set at τn−n̄ > 0.86 × 108 s for free neutron oscillation[14] and at τn−n̄ > 2.7 × 108 s for bound neutrons [15].
In this paper, we present a search for n − n̄ oscillations
using the full dataset from the first four running periods ofSuper-Kamiokande and update the result presented inRef. [15], which used data from the first period. The
current analysis includes an updated dataset, an updated
hadron production model, final state interactions, andadopts a multivariate method to achieve better discrimination between the background and signal processes. This
paper is organized as follows. After a short description of
the Super-Kamiokande detector in Sec. II, we describe thesimulation of both the n − n̄ signal and atmospheric
neutrino background in Sec. III. The selection algorithm
and analysis cuts are explained in Sec. IV, followed bydiscussion of systematic uncertainties in Sec. V. Analysis
results and concluding remarks are presented in Secs. VI
and VII, respectively.
II. THE SUPER-KAMIOKANDE EXPERIMENTSuper-Kamiokande (SK) is a cylindrical 50 kiloton
water Cherenkov detector located in Kamioka, Japan, thatis shielded by a 2700 meter water-equivalent rock overburden [22]. The detector consists of an outer detector
instrumented with 1885 outward-facing 8-inch
Photomultiplier tubes (PMTs) mounted 2 m from thedetector’s outer wall on a structure that optically separates

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PHYS. REV. D 103, 012008 (2021)

it from the inner detector (ID). This structure also supports
the 11,129 inward-facing 20-inch PMTs that form the ID
and view its 32 kton target volume. The outer detector is
primarily used as a veto for charged particles entering fromoutside the detector or identifying particles that exit the ID,
and the ID itself is used reconstruct the energies, vertexes,
and particle types of most interest to the present work.
The experiment started data taking in 1996 and underwent four data-taking phases since then labeled as SK-I, II,
III, and IV. The SK-I period ran from 1996 until thedetector underwent maintenance in 2001. During that
period, an accident destroyed more than half of the SK
PMTs, reducing the photocathode coverage from ∼40% to∼19% for the SK-II period in 2002-2005. After replacing
the missing PMTs in 2005, the detector restarted operations
as SK-III in 2006–2008. Following upgrades of the frontend electronics and water purification system, the SK-IV
period ran from 2008 until May of 2018, when the datataking was paused and the detector tank was opened forfurther upgrades. The analysis in this work uses the full
dataset from the SK-I-IV periods. Details of the detector
and its calibration can be found in [23].
III. SIMULATION
Following the oscillation of a neutron into an antineutron, the subsequent annihilation of the antineutron with anucleon in the oxygen nucleus is expected to produce many
visible particles, most of which are pions. The simulation ofthis signal is broken into stages: oscillation, hadronization,
final state interactions of particles before exiting thenucleus, and finally propagation and subsequent reinteraction of those particles with detector media. During thefirst stage, the position of the oscillated neutron within the
nucleus is determined using the standard Woods-Saxon
distribution [11,24] with a Fermi momentum simulation
based on the spectral function measured in [25]. The effectof nuclear binding energy is taken into account by
subtracting it from the nucleon masses when calculating
the annihilation products, using 39.0 MeV for s-state and15.5 MeV for p-state nucleons, respectively. Thereafter theoscillated antineutron is assumed to have an equal probability of annihilating with any remaining nucleons.
Modeling of the n̄n or n̄p annihilation products is done
based on available accelerator data. Due to a lack ofantineutron scattering data, the hadronization simulation
uses results from antiproton scattering experiments instead.
Assuming isospin symmetry, we used data from the p̄pannihilation experiment Crystal Barrel [26,27] to simulate
the n̄n annihilation. For the n̄p channel, we used the p̄nannihilation branching ratio measurements from the
OBELIX experiment [28] and bubble chamber data
[29–31] and then flipped the signs of the charged pions
to match n̄p. Tables I and II show the branching ratios forn̄n and n̄p adopted in the simulation. The branching ratiosof kaonic channels are artificially constructed due to lack of

TABLE I. Branching ratios (BR ), relative uncertainties, andcorresponding efficiencies for n̄n annihilation products.
BR [%] Relative uncertainty Efficiency [%]
2π 0
3π 0
4π 0
5π 0
7π 0

0.1
0.7
0.3
1.0
0.1

5%
6%
6%
4%
8%

3.2
3.6
4.4
3.8
2.1

πþπ−
πþπ−π0π þ π − 2π 0π þ π − 3π 0π þ π − 4π 0π þ π − 5π 0

0.3
1.6
13.1
11.2
3.3
1.4

4%
15%
15%
15%
14%
15%

4.8
4.8
4.3
4.2
4.0
4.7

2π þ 2π −2π þ 2π − π 0
2π þ 2π − 2π 0
2π þ 2π − 3π 0

6.0
13.6
15.7
0.6

16%
15%
15%
33%

4.2
4.5
4.5
4.9

3π þ 3π −3π þ 3π − π 0

2.2
2.0

15%
15%

3.7
4.1

ρ0 π 0ρþ=− π −=þ
ωω
ρ0 ω
π0π0ω
πþπ−ω
ηω
πþπ−η
Kaonic channels

1.8
3.7
3.5
2.4
2.7
7.1
1.6
1.7
2.3

15%
15%
15%
15%
15%
15%
15%
15%
15%

4.8
4.5
4.5
4.0
3.8
4.5
4.6
3.8
4.5

experimental data, and the kaonic production for n̄p is lessthan 1=2 from n̄n, and thus is omitted. Corresponding
uncertainty calculations can be found in Sec. V, and theefficiency calculation is explained in Sec. IV.
Hadronization products are mostly pions. The pion
interaction probability within the oxygen nucleus is
TABLE II. Branching ratios (BR ), relative uncertainties, andcorresponding efficiencies for n̄p annihilation products.
BR [%]

Relative uncertainty

Efficiency [%]πþπ0
π þ 2π 0
π þ 3π 0
π þ 4π 0

0.1
0.7
14.8
1.4

32%
32%
32%
32%

3.4
3.2
3.5
2.6

2π þ π −2π þ π − π 0
2π þ π − 2π 0
2π þ π − 3π 0

2.0
17.0
10.8
30.1

10%
10%
10%
10%

3.6
3.5
3.4
3.8

3π þ 2π −3π þ 2π − π 0

5.5
3.2

10%
10%

3.2
3.2

πþπ0ω
2π þ π − ω

2.0
12.4

32%
32%

3.4
3.6

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NEUTRON-ANTINEUTRON OSCILLATION SEARCH USING A …
expected to be large, and these so-called final stateinteractions (FSI) include quasielastic scattering (e.g.,
π þ n → π þ n), absorption (π þ þ n → p, π − þ p → n),charge exchange (π þ þ n → p þ π 0 , π − þ p → n þ π 0 ),and pion production (π  þ n → π  þ n þ π 0 ) [32]. For
pions above 500 MeV=c, the surrounding nucleons aretreated as quasifree particles, while for lower momentum
pions the interaction probabilities are calculated according
to the model of Salcedo and Oset [33] in consideration of
the effect of Pauli blocking. More details can be foundin Ref. [32].
Atmospheric neutrino interactions in water are thedominant background to the search for n − n̄ oscillation
at SK. The theoretical calculation from the HKKM model[34,35] predicts the atmospheric neutrino flux at Kamiokain the energy region from sub-GeV up to several TeV after
oscillation. Using this flux prediction, we simulated atmospheric neutrino interactions, including the outgoing particles and their subsequent interactions with the nuclear
medium in water, with NEUT version 5.3.6 [36]. Final stateinteractions for both the signal and background are simulated with NEUT.
Particles escaping the nucleus are passed to a GEANT3based [37] detector simulation. The simulation tracks
particles through the detector medium, simulating theirinteractions in water as well as the production of secondary
particles and the response of the PMTs to Cherenkov
radiation. Detailed tuning and calibration has been performed to provide a tailored simulation of photon propagation in SK [38]. The interaction of hadrons with water issimulated using the GCALOR package [39], except for pions
below 500 MeV=c, which are simulated using a model
based on NEUT’s FSI simulation. The final background isreweighted to the result of the analysis in [40], adjusting its
central value to the best fit oscillation and systematic error
parameters favored by the SK data.
IV. EVENT RECONSTRUCTION AND SELECTION
The present analysis uses the full dataset from the SK-I
through SK-IV periods, corresponding to 6050.0 live-days.
Events are required to be fully contained (FC), meaning thenumber of PMTs in the highest charge cluster of outerdetector hits is less than 10 in SK-I and less than 16 in SKII-III-IV. Timing information in each event’s hit PMTs in
the ID is used to reconstruct an overall vertex from theevent, from which an iterative search based on the Houghtransform [41] is performed to identify Cherenkov rings.
Each Cherenkov ring is classified according to its hit
pattern and opening angle as either “showering” (e-like)for particles that create electromagnetic showers such as eand γ or as “nonshowering” (μ-like) for particles such as μand π  . The momentum of each ring is determined by theparticle type and the charge among all hit PMTs within a
70° cone around the ring with consideration of charge
shared between multiple rings. An additional search for

PHYS. REV. D 103, 012008 (2021)

delayed electrons from muon decays is performed from
1.2–20 μs after the primary event trigger.
This analysis starts with FC events more than 2.0 m fromthe ID wall, which defines a 22.5 kton fiducial volume.
The reduction efficiency is 92% for n → n̄ signal events in
fiducial volume. This sample is then processed in twostages, first applying simple analysis cuts before applying a
multivariate technique to extract the signal.
A. Analysis precuts
Based on the distinct features of n − n̄ and atmospheric
neutrino events, several preliminary cuts are applied toreduce background rates while maintaining high signal
efficiency. The n − n̄ oscillation signal is expected to havemultiple pions, while a large number of atmospheric
neutrino interactions are elastic scatters with only one
Cherenkov ring from the outgoing charged lepton.
Therefore, the number of reconstructed rings is required
to be >1. This cut removes ∼75% of the background while
keeping 89% of the signal. Unlike the wide range ofenergies covered by atmospheric neutrinos, the n − n̄ signal
is more kinetically constrained, and thus a set of kinematic
cuts are also applied. Here, the total reconstructed momentum is required to be within ½35; 875 MeV=c, the visibleenergy in [30, 1830] MeV, and the total reconstructedinvariant mass in ½80; 1910 MeV=c2 . After the cut on thenumber of rings, these kinematic cuts further remove ∼50%of the background with a relative signal efficiency of 98%.
B. Multivariate analysis
Event displays of a simulated n → n̄ signal event anda simulated background event are shown in Fig. 1. Dueto the high ring multiplicity, the performance of ringreconstruction for n → n̄ signal events is not as satisfactory
as typical sub-GeV neutrino events. To compensate for thelimitation of ring reconstruction and to include more
discriminant features, we applied a multivariate analysis(MVA) to events passing the precuts. Compared to aconventional box-cut analysis [15], this analysis significantly enhance the separation between n → n̄ signal andbackground. An estimation using the same Monte Carlo(MC) set shows that the sensitivity of the MVA method is
twice that of the box-cut method.
Compared to atmospheric neutrino backgrounds, n̄n orn̄p annihilation within oxygen are generally expected to be
more constrained kinematically and have more Cherenkov
rings isotropically distributed in the detector. To exploit
these features, we introduced 12 variables into the MVA,
among which three are conventional kinematic quantities,
including the visible energy, total momentum, and total
invariant mass.
The remaining nine input variables are as follows. Since
only a fraction of atmospheric neutrinos has sufficientenergy to produce multiple charged particles, signal events
are typically expected to have more visible Cherenkov

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PHYS. REV. D 103, 012008 (2021)

rings. The number of such rings is used as a variable.
However, the full reconstruction is limited to five rings, asin the case of Fig. 1. Therefore, an additional variable thatcounts ring fragments, or potential rings, is also introduced.
The total momentum of an n − n̄ event is limited by
the momenta of the interacting nucleons, while a background event can carry more momentum from the incident
neutrino and is expected to be more forward going at theenergies needed to produce multiple particles. Therefore,
this search employs four variables to quantify the isotropyof candidate events. The energy ring ratio is defined as

FIG. 1. The event display of a simulated n → n̄ oscillation
event (top) and a simulated background event (bottom). The top
figure shows the n̄p annihilation producing six pions. In total,
there are 13 rings of these pions and their decay products, among
which five were reconstructed (colored rings). The beige ring is a
successfully reconstructed π þ . The dashed small ring is a π −mistakenly reconstructed as a electron-like particle, and thedashed large ring is a similarly misreconstructed π þ . The twosolid cyan rings are 2γ s from the decay of a π 0 . The bottom
figure shows the deep inelastic scattering process of a νe . In thisevent, there are four rings reconstructed by the algorithm, all ofwhich are γs.

ðEtot − Emax Þ=½Etot · ðnring − 1Þ, where Emax is the energyof the ring with highest energy in an event, Etot is the totalenergy of the event, and nring is the number of rings. For then − n̄ signal, the annihilation energy is more uniformly
distributed among the outgoing pions and therefore, thedistribution of this variable is expected to have a sharperpeak than of backgrounds. Signal events are also expected tohave higher sphericity than backgrounds, so this analysis
adopts a sphericity variable [42]. Fox-Wolfram moments,
which are superpositions of spherical harmonics that measure correlations between particle momenta (see Ref. [43]for details) are also adopted to describe the correlation
between rings. This analysis employs the first and second
order Fox-Wolfram moments, since higher orders were
found to provide little extra discrimination ability.
Finally, three variables related to particle identification
are used: the number of e-like rings, the number of decay
electrons, and the maximum distance to any decay electronfrom the primary vertex. Due to the large number of signal
modes with one or more π 0 s in the final state, signal eventsare expected to have more e-like rings from their decays
into photons. Corresponding distributions for signal andbackground MC set after the precuts are shown in Fig. 2.
These 12 variables are used in the construction of amultilayer perceptron (MLP) [44], which is trained onn − n̄ signal and atmospheric neutrino background MC.
The MLP consists of a network of layers of nodes that are
weighted and interconnected in order to optimize thediscrimination between event types. Input variables form
the input layer nodes and are combined in the MVA into asingle node at the output layer, which is the estimator
describing how signal- or backgroundlike an event is.
Between these layers there can be so-called hidden layers,
whose structure and connectivity can be altered to optimize
performance. In this analysis, a trial-and-error optimization
for the hyperparameters of the MLP structure was performed and the final structure was determined to be
1 hidden layer with 18 hidden nodes.
The signal efficiency and background efficiency as afunction of the estimator value is shown in Fig. 3, where 0
corresponds to backgroundlike and 1 is signal-like. A
sensitivity analysis was performed assuming a 0.37 megaton-years exposure and realistic systematic errors(described below) using the Rolke method [45] to determine the optimal cut position in the output estimator. The
optimized cut was found to be 0.789, where the signal(background) efficiency from the MVA alone is 5.0%
(0.1%). Combined with the preselection efficiency, thetotal signal efficiency is 4.1% with an expected backgroundof 0.56 events per year, or 9.3 events over the entire data
period. Selection efficiencies for each of the signal channels can be found in the last column of Tables I and II.
Among the multiple types of neutrino interactions, thedominant background in this analysis is from deep inelastic scattering (DIS), with secondary contributions from012008-6

NEUTRON-ANTINEUTRON OSCILLATION SEARCH USING A …
(a)
800

300

Background

600

Data

500 1000 1500 2000
visible energy [MeV]

(e)

0

4000
3000
2000

500

1000
0

200 400 600 800 1000
total momentum [MeV]

0

0

(f)

1000

1500

0

500
1000 1500
invariant mass [MeV]

3000

(g)
1000

10
15
potential rings

20

(i)

0

0

2
4
1st F-W moment

6

(h)

1000

200
5

3
4
5
number of rings

1500
500

500

0

2

2000

600
400

0

1

2500

800

1000

(d)

5000

1000

100

200
0

6000

(c)

200

400

0

1500

400 (b)SignalPHYS. REV. D 103, 012008 (2021)

500
0

0.1 0.2 0.3 0.4
energy ring ratio

0.5

0

5000

(j)

4000

0

3000

0.2

0.4 0.6
sphericity

0.8

0

1

(k)

(l)

4000

3

10

3000
3000

2000
2000
1000

2000

1000

0

0

0

2
4
2nd F-W moment

102

1000
0

2
4
e-like rings

6

0

0

1
2
3
4
number of decay-e

50
500 1000 1500 2000
maximum decay-e distance [cm]FIG. 2. The 12 input variables to the multivariate analysis for signal (blue), background (red), and data (black), after precuts. Signal
and background simulations are normalized to data.

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

0.5

1

104

Number of events1

the remaining backgrounds in the final sample are shown in
Table III, with νμ þ ν̄μ contributing 5.8 events, and νe þ ν̄econtributing 3.5 events. The contribution from ντ þ ν̄τ isless than 0.1 event and is not shown in Table III.

τ [1032 year]

Efficiency

charged current pion production (CC 1π), neutral current
pion production (NC 1π), and charged current elastic
scattering (CC EL). Figure 4 shows the remaining backgrounds before the MVA cut. After applying the MVA cut,

NCDIS

CCDIS

CC1π

CCEL

NC1π

other

0.4

0.6

103
102

10
1

0

10−1

MVA estimator

0

0.2

0.8

1

MVA estimator

FIG. 3. Signal (blue) and background (red) efficiency as afunction of the MVA output estimator threshold. The expected
sensitivity at each value of the estimator threshold as estimatedusing the Rolke method is shown in the gray curve. The dashedline indicates the optimum cut point.

FIG. 4. Remaining neutrino interaction backgrounds as afunction of the MVA estimator after preselection and before
MVA cut, broken down into interaction channels, as shown in thelegend.

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K. ABE et al.

PHYS. REV. D 103, 012008 (2021)

TABLE III. Summary of remaining atmospheric neutrino
background events after the MVA selection and scaled to thefull SK-I-IV live time.
ChannelEventsνμ þ ν̄μνe þ ν̄e

NC DISCC DIS
CC 1π
CC EL
NC 1π
Other

3.7
3.6
1.1
0.3
0.1
0.3

…
2.0
0.7
0.1
…
…

…
1.6
0.4
0.2
…
…

Total

9.3

…

…

V. SYSTEMATIC ESTIMATIONIn this analysis systematic uncertainties are separated
into two categories, those that arise from uncertainty in thephysics modeling, such as the hadronization process andfinal state interaction, and those related to the detector
response and event reconstruction.
A. Modeling uncertainties
1. Signal
Uncertainty in the momentum of the oxygen nucleons is
expected to impact the resulting momentum of the n − n̄annihilation products. A systematic uncertainty is derived
from the difference between the default spectral function
model (described in Sec. III) and the Fermi gas model [46]used in the atmospheric neutrino simulation. It yields anuncertainty in the signal efficiency of 7%. Our model does
not account for the recent measurement of higher momentum distribution, as summarized in Ref. [47]. With thedominance of FSI systematic uncertainties, the influence isestimated to be small.
Measured uncertainties in the branching fraction of eachannihilation channel also introduce a systematic uncertainty in the hadronization process, resulting in uncertainties in the pion multiplicity of signal events. This
uncertainty is accounted for by assigning uncertainties
on the branching ratio of each channel listed in Table I
and Table II based on the statistical uncertainty in the
results from the Crystal Barrel [26,27] and the OBELIX
experiments [28]. They were then propagated to theanalysis by reweighting the various final states accordingly
and result in a 4% uncertainty on the signal efficiency.
Final state interaction modeling is the dominant systematic error on the signal efficiency. To estimate this uncertainty, we generated separate MC sets, each with different
FSI model parameters that control the strength of theinteraction cross sections and are allowed by fits topion-nucleon scattering data [20]. These MC samples were
processed through the same event selection, and the largest
change in the signal efficiency is taken as the uncertainty. In
this analysis, the largest deviation came from a variation

with enhanced quasielastic scattering and absorption, butwith decreased inelastic scattering, which produces fewer
hadrons and thus lower efficiency. The assigned uncertainty
is 31%.
2. Background
Uncertainties on the atmospheric neutrino backgroundwere calculated using the fit result from the SK atmospheric
neutrino analysis [40]. A set of weights was constructed foreach event, describing how it changes under a 1σ variationof each systematic error parameters used in that analysis.
Applying these weights to the MC set allows the uncertainty to be conservatively propagated to the background
prediction.
The overall atmospheric neutrino flux normalization has
an uncertainty of 15% [40] in the dominant backgroundenergy range between 1 and 10 GeV, resulting in a 7%
uncertainty in the background rate. In total, the uncertainty
introduced by modeling of the flux was estimated to be 8%.
Neutrino oscillation parameter uncertainties, particularly
from θ23 , also introduce a 3% uncertainty. Uncertainties
from the neutrino interaction modeling are the mostsignificant contribution to the error budget. The total
uncertainty from neutrino interaction was estimated at
24%, among which the main contribution was found to
originate from uncertainties in the deep inelastic scatteringmodel and its cross section.
B. Detector systematics
Uncertainties in the detector’s energy scale and thereconstruction’s ability to accurately identify the numberof and particle type of each ring introduce uncertainties inboth the signal efficiency and background rate. The energy
scale uncertainty is evaluated using calibration sources andcontrol samples, such as cosmic ray muons and their decay
electrons [40], and is 3.3% in SK-I, 2.8% in SK-II, 2.4% in
SK-III, and 2.1% in SK-IV. It results in a 5% and 11%
uncertainty on the signal efficiency and background rate,
respectively. Similarly, differences in the water quality inthe top and bottom regions of the SK tank introduces anasymmetry in the energy scale that introduces an additional
4% signal efficiency uncertainty and 6% background rate
uncertainty.
Ring counting introduces 2% uncertainty in signal
efficiency and 1% in background rate. This uncertainty
is estimated by comparing the ring counting likelihood
distribution of MC sets and a controlled sample ofdata [48].
For MVA variables besides ring counting, energy scale,and nonuniformity, we use an inclusive controlled sample(FC data after precuts, before MVA), and compare data andMC prediction, as shown in Fig. 2. The source uncertainties
are assigned from the deviation of data and MC sets. Thesesource uncertainties are then propagated to efficiency
uncertainties.

012008-8

NEUTRON-ANTINEUTRON OSCILLATION SEARCH USING A …
7

TABLE IV. Summary of systematic uncertainties on the signal
efficiency and backgrounds. The atmospheric neutrino row
represents the combined uncertainty from modeling of their fluxand interactions.
Background

7%
4%
31%
…

…
…
…
24%

Physics
Fermi motion
Hadronization
FSI
Atmospheric ν

5%
4%
2%
4%

11%
6%
2%
7%

Total

33%

28%

4
3
2
1
0.8

0.85

0.9

0.95

1

MVA estimator

FIG. 6. MVA output estimator after applying the cut at 0.789 inthis variable. The expected background is shown in red, the signalin blue, and the data points are shown in black.

Overall efficiency and systematic uncertainty.

SignalBackground50

Detector
Energy scale
Non-uniformity
Ring counting
Other MVA variables

TABLE V.

6

Number of events

Signal Efficiency

PHYS. REV. D 103, 012008 (2021)

Efficiency

Event rate

Systematics

4.1%
…

…
0.56 / year

33%
28%

variables to the MVA show a similar agreement (Fig. 2).
Accordingly, we find no evidence for neutron-antineutron
oscillations.
Figure 7 shows the 11 candidate events within thedetector. The spatial distribution is uniform as expected.
Figure 8 shows the distribution in time. The dependence of
15

The individual systematic sources and their uncertainties
are summarized in Table IV, while the total efficiency anduncertainty are presented in Table V.

10
y [m]

5

VI. RESULT

0−5This full SK-I-IV dataset corresponds to an exposureof 0.37 megaton-years. After applying the cuts above, 11
events are found in data, which is consistent with the
expected background of 9.3  2.7 events. Furthermore,data and MC sets are in good agreement both before(Fig. 5) and after (Fig. 6) the MVA cut. The input

−10
−15
−10

0

10

x [m]
15

104
10

z [m]

Number of events

10
3

102

5
0
−5

10

−10
−15

1

0
0

0.2

0.4

0.6

0.8

50

100

150

200

r2 [m2]

1

MVA estimator

FIG. 5. MVA output estimator after applying the analysis
precut. The expected background is shown in red, the signal(scaled to data) in blue, and the data points are shown in black.

FIG. 7. Spatial distribution of observed events after precuts(black), and after the MVA cut (red) in the plane perpendicular tothe detector axis (top) and in the radial and axial direction(bottom).

012008-9

K. ABE et al.

PHYS. REV. D 103, 012008 (2021)

Events per 2 months

100
80
60
40
20
0

2000

2005

2010

2015

Year

FIG. 8. Distribution of observed events in time after precuts(black) and after the MVA cut (red). For comparison the background expectation after the MVA cut scaled by a factor of 500 isshown in blue.

events after precut on time is due to the live time of SK.
Performing a K-S test on the distrbution yields a maximum
distance between data and MC sets at 0.33. To determine
the likelihood of this result, this procedure was repeated on
simulated datasets with the same size as the observation and
TABLE VI. Comparison of the expected atmospheric neutrino
background, signal efficiency, live time, and observation in eachrun period.

Efficiency
Background events
Live days
Candidates

SK-I

SK-II

SK-III

SK-IV

3.7%
1.98
1489.2
0

3.3%
1.03
798.6
1

3.7%
0.74
518.1
1

4.4%
5.50
3244.19TABLE VII. Expected and observed limits from the background-only hypothesis.

Expected
Observed

EventsT n−n̄ (1032 yrs)

τn→n̄ (108 s)

9.3
11

4.3
3.6

5.1
4.7

assuming a constant rate. Among these pseudoexperiments,
14% had a K-S distance larger than 0.33, indicating no
significant deviation from the assumed uniform distribution
and is consistent with the expectation from atmosphericbackgrounds.
A comparison of the expected atmospheric neutrino
background, signal efficiency and observed data in each
SK run period is shown in Table VI. Signal efficiencies andbackground rates are slightly different across these run
periods, and the majority of candidate events are found in
SK-IV, which has the longest live time. The Poisson
probability of observing nine or more events in SK-IV
with an expectation of 5.5 events (ignoring systematic
uncertainties) is 10.6%. This observation is similarly
consistent with the background expectation.
In the absence of a statistically significant excess in data,a lower limit is established. To account for both statisticaland systematic uncertainties, we used Rolke method in
confidence interval calculation. The observation limit on
neutron lifetime is set at 3.6 × 1032 years (90% C.L.).
Equation (3) and R ¼ 0.517 × 1023 s−1 [11] are used toderive the corresponding limit on the n − n̄ oscillation time,τn→n̄ > 4.7 × 108 s. A comparison between the expected
sensitivity and this result is shown in Table VII. Alternative
calculations of the nuclear suppression factor R can befound in Refs. [12,13].
Table VIII compares the present results with those fromother bound neutron experiments and free neutron oscillation experiments. Papers before the year 2000 typicallyreport τn→n̄ assuming R ¼ 1 × 1023 =s, and the previous SK
result considered uncertainty in the theoretical prediction of
R. For better pcomparison
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ and easier conversion, τn→n̄ ispresented as T n−n̄ =R with corresponding nuclear suppression factor R listed in Table VIII. The limit from freeneutron experiments is also listed for reference, but should
not be directly compared with the limits from boundneutron experiments due to the medium modifications of
the six-quark operator which is still a subject for theoreticalinterpretation [49]. Among the bound neutron experimental
searches so far, this analysis gives the most stringent limit
on n → n̄ oscillation.

TABLE VIII. Comparisonof n − n̄ oscillation searches from bound neutrons and free neutrons. All values of τn→n̄
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
results are presented as T n−n̄ =R, where R is the nuclear suppression factor used in each reference.
16O
16

O
O
2
H
56
Fe
56Fe
16
O
Free neutron
16

T n−n̄ ð1032 yearsÞ

R (1023 =s)τn→n̄ ð108 sÞ

3.6
1.9
0.4
0.1
0.7
0.7
0.2
…

0.517
0.517
0.517
0.25
1.4
1.4
0.517
…

4.7
3.4
1.6
1.4
1.3
1.2
1.2
0.9

SK-I-IV (this study)
SK-I [15] (2015)
Kamiokande [18] (1986)
SNO [16] (2017)
Soudan II [17] (2002)
Frejus [21] (1990)
IMB [19] (1984)
Grenoble [14] (1994)

012008-10

NEUTRON-ANTINEUTRON OSCILLATION SEARCH USING A …

PHYS. REV. D 103, 012008 (2021)

We gratefully acknowledge the cooperation of
the Kamioka Mining and Smelting Company. The

Super-Kamiokande 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 and the Ministry of
Education (Grants No. 2018R1D1A3B07050696 andNo. 2018R1D1A1B07049158), the Japan Society for the
Promotion of Science, the National Natural Science
Foundation of China under Grant No. 11620101004, theSpanish Ministry of Science, Universities and Innovation(Grant No. PGC2018-099388-B-I00), the Natural Sciencesand Engineering Research Council (NSERC) of Canada,
the Scinet and Westgrid consortia of Compute Canada, theNational Science Centre, Poland (2015/18/E/ST2/00758),
the Science and Technology Facilities Council (STFC) and
GridPPP, United Kingdom, the European Union’s Horizon
2020 Research and Innovation Programme under theMarie Skłodowska-Curie Grant Agreement No. 754496,
H2020-MSCA-RISE-2018 JENNIFER2 Grant Agreement
No. 822070, and H2020-MSCA-RISE-2019 SK2HK Grant
Agreement No. 872549.

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VII. CONCLUSION
We performed a n − n̄ oscillation search with SK-I-IV
data using a multivariate analysis. Compared to previous
results [15], the updated final state interaction model
predicts fewer pions and less separation between signal
and neutrino backgrounds. With the advanced MVA
method and the inclusion of multiple new variables, thesensitivity of this analysis is still greatly enhanced.
For the 0.37 megaton-year exposure at SK, we observed
11 events with an expected background of 9.3  2.7
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