PHYSICAL REVIEW D 91, 072006 (2015)

Search for n − n̄ oscillation in Super-Kamiokande
K. Abe,1 Y. Hayato,1 T. Iida,1 K. Ishihara,1 J. Kameda,1 Y. Koshio,1 A. Minamino,1 C. Mitsuda,1 M. Miura,1 S. Moriyama,1
M. Nakahata,1 Y. Obayashi,1 H. Ogawa,1 H. Sekiya,1 M. Shiozawa,1 Y. Suzuki,1 A. Takeda,1 Y. Takeuchi,1 K. Ueshima,1
H. Watanabe,1 I. Higuchi,2 C. Ishihara,2 M. Ishitsuka,2 T. Kajita,2 K. Kaneyuki,2,* G. Mitsuka,2 S. Nakayama,2 H. Nishino,2
K. Okumura,2 C. Saji,2 Y. Takenaga,2 S. Clark,3 S. Desai,3 F. Dufour,3 A. Herfurth,3 E. Kearns,3 S. Likhoded,3 M. Litos,3
J. L. Raaf,3 J. L. Stone,3 L. R. Sulak,3 W. Wang,3,† M. Goldhaber,4,* D. Casper,5 J. P. Cravens,5 J. Dunmore,5 J. Griskevich,5W. R. Kropp,5 D. W. Liu,5 S. Mine,5 C. Regis,5 M. B. Smy,5 H. W. Sobel,5 M. R. Vagins,5 K. S. Ganezer,6 B. Hartfiel,6
J. Hill,6 W. E. Keig,6 J. S. Jang,7 I. S. Jeoung,7 J. Y. Kim,7 I. T. Lim,7 K. Scholberg,8 N. Tanimoto,8 C. W. Walter,8
R. Wendell,8 R. W. Ellsworth,9 S. Tasaka,10 G. Guillian,11 J. G. Learned,11 S. Matsuno,11 M. D. Messier,12 A. K. Ichikawa,13
T. Ishida,13 T. Ishii,13 T. Iwashita,13 T. Kobayashi,13 T. Nakadaira,13 K. Nakamura,13 K. Nishikawa,13 K. Nitta,13 Y. Oyama,13
A. T. Suzuki,14 M. Hasegawa,15 H. Maesaka,15 T. Nakaya,15 T. Sasaki,15 H. Sato,15 H. Tanaka,15 S. Yamamoto,15
M. Yokoyama,15 T. J. Haines,16 S. Dazeley,17 S. Hatakeyama,17 R. Svoboda,17 G. W. Sullivan,18 R. Gran,19 A. Habig,19
Y. Fukuda,20 Y. Itow,21 T. Koike,21 C. K. Jung,22 T. Kato,22 K. Kobayashi,22 C. McGrew,22 A. Sarrat,22 R. Terri,22
C. Yanagisawa,22 N. Tamura,23 M. Ikeda,24 M. Sakuda,24 Y. Kuno,25 M. Yoshida,25 S. B. Kim,26 B. S. Yang,26 T. Ishizuka,27
H. Okazawa,28 Y. Choi,29 H. K. Seo,29 Y. Gando,30 T. Hasegawa,30 K. Inoue,30 H. Ishii,31 K. Nishijima,31 H. Ishino,32
Y. Watanabe,32 M. Koshiba,33 Y. Totsuka,33,* S. Chen,34 Z. Deng,34 Y. Liu,34 D. Kielczewska,35 H. G. Berns,36
K. K. Shiraishi,36 E. Thrane,36,‡ K. Washburn,36 and R. J. Wilkes36(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 Physics, Boston University, Boston, Massachusetts 02215, USA
4
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, 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
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
8
Department of Physics, Duke University, Durham, North Carolina 27708, USA
9
Department of Physics, George Mason University, Fairfax, Virginia 22030, USA
10
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
11
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
12
Department of Physics, Indiana University, Bloomington, Indiana 47405-7105, USA
13High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
14
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
15
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
16
Physics Division, P-23, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
17
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
18
Department of Physics, University of Maryland, College Park, Maryland 20742, USA
19
Department of Physics, University of Minnesota, Duluth, Minnesota 55812-2496, USA
20
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
21
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan
22
Department of Physics and Astronomy, State University of New York,
Stony Brook, New York 11794-3800, USA
23
Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japan
24
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
25
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
26
Department of Physics, Seoul National University, Seoul 151-742, Korea
27
Department of Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japan
28
Department of Informatics in Social Welfare, Shizuoka University of Welfare,
Yaizu, Shizuoka 425-8611, Japan
29
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
30
Research Center for Neutrino Science, Tohoku University, Sendai, Miyagi 980-8578, Japan
31
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
32
Department of Physics, Tokyo Institute for Technology, Meguro, Tokyo 152-8551, Japan
33
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan

1550-7998=2015=91(7)=072006(8)072006-1© 2015 American Physical Society

K. ABE et al.

PHYSICAL REVIEW D 91, 072006 (2015)34

Department of Engineering Physics, Tsinghua University, Beijing 100084, China
Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
36
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 20 September 2011; published 10 April 2015)35

A search for neutron-antineutron (n − n̄) oscillation was undertaken in Super-Kamiokande using the1489 live-day or 2.45 × 1034 neutron-year exposure data. This process violates both baryon and baryon
minus lepton numbers by an absolute value of two units and is predicted by a large class of hypotheticalmodels where the seesaw mechanism is incorporated to explain the observed tiny neutrino masses and thematter-antimatter asymmetry in the Universe. No evidence for n − n̄ oscillation was found; the lower limitof the lifetime for neutrons bound in 16 O, in an analysis that included all of the significant sources ofexperimental uncertainties, was determined to be 1.9 × 1032 years at the 90% confidence level. The
corresponding lower limit for the oscillation time of free neutrons was calculated to be 2.7 × 108 s using atheoretical value of the nuclear suppression factor of 0.517 × 1023 s−1 and its uncertainty.
DOI: 10.1103/PhysRevD.91.072006

PACS numbers: 11.30.Fs, 12.10.Dm, 14.20.Dh, 29.40.Ka

I. INTRODUCTION
Searches for baryon number (B) violating processes are
motivated by various grand unification theories (GUTs) andby the observation first put forward by A. Sakharov in 1967
that B, C, CP violation and nonequilibrium thermodynamics are needed to explain the observed matter-antimatter orbaryon number asymmetry of the Universe [1]. Howeverrecent experimental limits on p → eþ π 0 [2–4] andp → ν̄K þ [5] have already ruled out the simplest B − L
conserving GUTs, minimal SUð5Þ and the minimal supersymmetric version of SUð5Þ, where L stands for lepton
number. It has also been shown that any B − L conserving
baryon asymmetry generated in the early Universe(above 10 TeV scale) should be washed out until now
by the triangle anomalies involving electroweak bosons.
Therefore the search for B − L violating reactions has
become increasingly important as a potential explanation of
the observed baryon number asymmetry in the Universe.
Neutron-antineutron (n − n̄) oscillation, a process that
violates B and B − L by two units (jΔBj ¼ 2 andjΔðB − LÞj ¼ 2), was first discussed by V. Kuzmin in1970 [6]. The discovery of neutrino oscillations [7] hasrenewed interest in theories with Majorana spinors
which yield B and L symmetry breaking by allowingjΔðB − LÞj ¼ 2, with jΔLj ¼ 2 as in neutrinoless double
beta decay and jΔBj ¼ 2 for n − n̄ oscillation [8,9]. Thesemodels include a large class of supersymmetric andright-left symmetric SUð2ÞL ⊗ SUð2ÞR ⊗ SUð4ÞC theories
that include the seesaw mechanism to generate neutrino
masses [10]. Neutron-antineutron oscillation has also been

predicted by GUTs with large or small extra space-time
dimensions [11,12].
An important property of n − n̄ oscillation is its dependence on a six quark operator, with a mass scaling of M −5
instead of M−2 as in the charged X and Y bosons that mediate
nucleon decay in minimal SUð5Þ. Therefore, the observationof a significant n − n̄ oscillation signal at Super-Kamiokande
would imply new physics at a scale of approximately
100 TeV, a factor of 10 larger than the maximum energies
scheduled for study at the Large Hadron Collider.
The previous best 90% confidence level (C.L.) lifetime
limits for bound neutrons are from IMB with 1.7 and2.4 × 1031 year [13] in two different analyses, Kamiokandewith 4.3 × 1031 year in oxygen [14], Soudan 2 with
7.2 × 1031 year in iron [15], and Frejus with 6.5 ×1031 year in iron [16]. The current best limit on theoscillation time of unbound neutrons is given by ILL(Grenoble) as 0.86 × 108 seconds [17]. The lifetime limit
for bound neutrons can be converted to the n − n̄
oscillation time for free neutrons by the relationshipT n−n̄ ¼ R · τ2n−n̄ð1Þwhere τn−n̄ and T n−n̄ are the oscillation time of a freeneutron and the lifetime of a bound neutron, and R is thenuclear suppression factor, for which theoretical estimatesare given in the literature [18].
In this paper, we describe the results of our neutronantineutron oscillation search in Super-Kamiokande. No
positive signal was observed, but from our data we obtained
a lower limit on the lifetime of a neutron in oxygen of
1.9 × 1032 year (90% C.L.), which is about four times
larger than the previous highest experimental limits.

*

Deceased.
Present address: Department of Physics, University of
Wisconsin-Madison, 1150 University Avenue Madison,
WI 53706, USA.
‡
Present address: Department of Physics and Astronomy,
University of Minnesota, MN 55455, USA.
†

II. THE SUPER-KAMIOKANDE DETECTOR
Super-Kamiokande is a ring imaging water Cherenkov
detector containing 50 ktons of ultrapure water, located in
Kamioka-town in Gifu prefecture, Japan. The detector is

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PHYSICAL REVIEW D 91, 072006 (2015)

composed of the inner detector, which contains 22.5 kton
fiducial volume, and the outer detector for tagging cosmic
ray muons entering the detector. Descriptive overviews ofSuper-Kamiokande and technical details are given in theliterature [19]. The n − n̄ oscillation analysis described inthis paper uses the complete Super-Kamiokande-I data set,
which is equivalent to 2.45 × 1034 neutron-year exposuredata. This data set of 1489 live-days was taken fromMay 31, 1996 to July 15, 2001.
An antineutron is expected to annihilate quickly with
one of the surrounding nucleons and to produce multiple
secondary hadrons, mainly pions. The total momentumof the secondaries is nearly zero, except for the Fermi
momenta of the annihilating n̄ and nucleon, and the totalenergy is nearly equal to the total mass of the two nucleons.
Therefore in the case of no nuclear interactions it was expectedthat n − n̄ oscillation events in oxygen would produce mesons
with a total energy of about 2 GeV, distributed isotropically.
III. MONTE CARLO SIMULATIONA detailed Monte Carlo (MC) simulation was formulated
for this study. Since the literature on (n̄ þ nucleon) annihilation in nuclei is sparse, p̄p and p̄d data from hydrogenand deuterium bubble chambers [20–22] were used todetermine the branching ratios for the annihilation final
states. The branching ratios included in our simulations are
displayed in Table I. The values of kinematic quantities in
our MC were determined using relativistic phase-space
distributions that included the Fermi momentum of
the annihilating nucleons. Pions and omegas produced in
the n̄-nucleon annihilations were propagated through theresidual nucleus. This study used a program originallydeveloped for the IMB experiment to simulate mesonnucleon interactions [13]. The cross sections for the pionresidual nucleus interactions were based on an interpolationfrom measured pion-carbon and pion-aluminum crosssections to those for pion-16 O interactions. Excitation of
the Δð1232Þ resonance was the most important effect in the
nuclear propagation phase. It was assumed that the pionand omega cross sections scaled linearly with matter
TABLE I. The branching ratios for the n̄ þ nucleon annihilations in our simulations. These factors were derived from p̄p andp̄d bubble chamber data [20–22].
n̄ þ pπþπ0π þ 2π 0
π þ 3π 02π þ π − π 0
2π þ π − 2π 0
2π þ π − 2ω
3π þ 2π − π 0n̄ þ n
1%
8%
10%
22%
36%
16%
7%

πþ π−

2π 0
þ − 0
π π π
π þ π − 2π 0π þ π − 3π 0
2π þ 2π −2π þ 2π − π 0πþ π− ω2π þ 2π − 2π 0

2%
1.5%
6.5%
11%
28%
7%
24%
10%
10%

density, a quantity that decreases as the mesons moveaway from the annihilation point and exit from the nucleus.
The Fermi momentum of the interacting nucleon and thepossibility of Pauli blocking were also included in our
simulations. We found that 49% of the pions did notinteract, while 24% were absorbed and 3% interacted with anucleon to produce an additional pion or occasionally two
more pions, and the rest of the pion interactions involved
scattering. These interaction probabilities yielded total andcharged pion multiplicities of 3.5 and 2.2, respectively,
with an average charged pion momentum of 310 MeV=c
and a root mean square width of 190 MeV=c. There wasa probability of 0.56% that an event included an ω0 thatemerged from the nucleus without having decayed. The
final states of the nuclear fragments were calculated using
an algorithm based on a simulation from Oak Ridge
National Laboratory [23]. Fragments of the residual
nucleus that contained two or more nucleons were notsimulated in water, since most of the nucleons in thesefragments had momenta that were below the threshold for
inelastic hadron interactions. Therefore only free n and p
fragments were propagated through water.
Since the largest source of background events for n − n̄
oscillation is atmospheric neutrinos, we prepared a large
MC event sample that corresponded to an atmospheric
neutrino exposure of 500 years. A detailed description ofthis simulation is given in Ref. [24]. The propagation ofparticles and Cherenkov light in the detector was modeledby a program that is based on the GEANT-3 package [25].
The detector geometry, the generation and propagationof Cherenkov radiation from charged particles, and the
response of the photomultiplier tubes (PMTs) and dataacquisition electronics were also included in our simulations. Hadron interactions were simulated using the
CALOR package [26] for nucleons and charged pions withpπ > 500 MeV=c, and through a custom-made program[27] for charged pions of pπ < 500 MeV=c.
IV. DATA REDUCTION AND RECONSTRUCTION
The trigger threshold for our search corresponds to
5.7 MeV of electromagnetic energy; therefore signal eventswould trigger with 100% efficiency. The majority oftriggered events in the Super-Kamiokande data are background due to inherent radioactivity or to cosmic ray muons
passing in the detector. Most of the cosmic ray muon events
are rejected by a requirement that the number of hit PMTs
in the outer detector within 800 ns of the trigger be less than
25. We also require that the reconstructed visible energy begreater than 30 MeV to remove the remaining low energy
radioactivity. This constraint is also necessary to maintainthe effectiveness of the event reconstruction. The reduction
algorithms are identical to those used for the atmospheric
neutrino analyses and nucleon decay searches [24].
Events remaining after the reduction procedure areprocessed by the full reconstruction program, which yields

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PHYSICAL REVIEW D 91, 072006 (2015)

an overall event vertex, the number of Cherenkov rings, anda direction, particle identification determination, and a
momentum for each ring [24]. For n − n̄ oscillation events
the vertex resolution is 26 cm. Each Cherenkov ring is
identified as being either “showering” (e; γ) or “nonshowering” (μ; π; p) based upon its hit pattern and opening angle.
The momentum is subsequently determined using theassigned particle type and the number of collected photoelectrons inside a cone with an opening half-angle of
70 degrees after corrections for geometric effects and lightattenuation are made. Our choice of cone angle completely
covers the Cherenkov cone in water, which has an opening
half-angle of about 42 degrees. In multiple-Cherenkov ring
events, we estimate and separate a sample of photoelectrons
for each ring using an expected Cherenkov light distribution.
(a)V. ANALYSIS
To isolate n − n̄ candidates we apply additional criteria
to the fully contained (FC) event sample within the innerdetector; this sample is used for our atmospheric neutrino
analyses and nucleon decay searches [24]. In addition,
we require the following: (a) The number of Cherenkov
rings > 1, (b) 700 MeV < Visible energy < 1300 MeV,(c) 0 MeV=c < Total momentum < 450 MeV=c and(d) 750 MeV=c2 < Invariant mass < 1800 MeV=c2 . The
visible energy is defined as the energy of an electronthat would produce the same total amount of light inPthe detector. The total momentum is Ptot ¼ j all-rings
p~i j,iwhere p~i is the reconstructed momentum vector of
the ith ring. The invariant mass is defined to be(b) 120
Number of events (/1489 day)

Number of events (/1489 day)

10000

8000

6000

4000

2000

0

100

80

60

40

20

0
1

2

3

4

5

0

Number of rings

200 400 600 800 1000 1200 1400 1600 1800 2000

Visible energy (MeV)

(c)

(d)
50

Number of events (/1489 day)

Number of events (/1489 day)

12

40

30

20

10

10

8

6

4

2

0

0
0

200

400

600

800

1000

1200

1400

0

200 400 600 800 1000 1200 1400 1600 1800 2000

Invariant mass (MeV/c2)

Total momentum (MeV)

FIG. 1 (color online). The distributions of the kinematic variables subject to additional criteria at each of the reduction steps describedin the text including (a) number of rings, (b) visible energy, (c) total momentum, and (d) invariant mass. Circles indicate data points withstatistical error bars; solid blue lines and dashed red lines represent the atmospheric neutrino MC and the n − n̄ MC, respectively.
Light vertical lines with arrows indicate the event selection criteria.

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SEARCH FOR n − n̄ OSCILLATION IN SUPER- …

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Mtot ¼ E2tot −p
P2ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ, while the total energy is defined as
Pall-rings tot
Etot ¼ i
pi 2 þ mi 2 , where mi is the mass of the
ith ring assuming that showering and nonshowering rings
are from γ rays and charged pions, respectively. The
selection criteria
pﬃﬃﬃ given above were optimized to maximize
the ratio ϵ= b, where ϵ is the signal detection efficiency
and b is the number of background events.
Distributions of the four reconstructed kinematic variables are displayed in Fig. 1. Our atmospheric neutrino MC
includes the effects of νμ to ντ neutrino oscillations, withmixing parameters of ðsin2 2θ;Δm2 Þ¼ð1.0;2.1×10−3 eV2 Þobtained from our publication on this topic [24].
Figure 1(b) shows the visible energy distribution after
the event selection criterion (a) based on the number of
Cherenkov rings was imposed. The average visible energy
for n − n̄ MC oscillation events is about 700 MeV, much
lower than twice the nucleon mass. The reasons forobserving lower visible energy include the mass of charged
mesons, energy loss by mesons scattering off nucleons, andthe absorption of mesons in nuclear reactions. The visibleenergy would approach twice the nucleon mass only if
the annihilation resulted fully in electromagnetic showers(such as multiple π 0 that decayed before interaction).
Application of the event selection criteria (a)–(d) yielded
24 candidate events, a detection efficiency of 12.1% fromthe remaining n − n̄ MC events in the final sample, and24.1 background events as estimated for the 1489 days ofSuper-Kamiokande-I. Final event samples are displayed
as scattered dots inside of the box-shaped scatterplotsthat apply criteria (c)–(d) in Fig. 2. Of the remaining

PHYSICAL REVIEW D 91, 072006 (2015)

background, 57.8% comes from multihadron production by
deep inelastic scattering (DIS), 31.4% from single pion
production via resonances, and 5.5% from single η and K
meson production via resonances. The remaining 5.2% of
the background results from charged current (CC) quasielastic (QE) scattering and neutral current (NC) elastic
scattering accompanied by energetic knocked-out nucleonsin the water.
VI. SYSTEMATIC ERRORS
Uncertainties in the detection efficiency, exposure, andbackground rates are given in Table II. The major sourcesof errors in the detection efficiency are the results ofuncertainties in the models for propagation of pions andomega mesons through the residual nucleus. In particular,
the error due to uncertainties in the π-nucleon cross section
TABLE II. Systematic uncertainties in the signal efficiency,
exposure, and background rate.
Signal efficiency
Sources
Fermi momentum of nucleons
Branching ratio of n̄ þ nucleons
π propagation modeling
π-nucleon cross section in the nucleus
Energy scale
Asymmetry of detector gain
Cherenkov ring finding
Total
Sources(A)

1500

Uncertainty (%)

Fiducial volume
Detector live-days
Total

1000
500
Total Momentum (MeV/c)

6.2
4.6
6.1
20.0
1.7
0.4
2.2
22.9

Exposure

2000

3.0
< 0.1
3.0
Background rate

2000

(B)

1500

Sources

1000
500
2000

(C)

1500
1000
500
0

Uncertainty (%)

0

250

500

750

1000 1250 1500 1750 2000
2

Invariant Mass (MeV/c )FIG. 2. Total momentum vs the invariant mass after applying
the selection criteria (a)–(b) on the FC sample: (A) signal MC,(B) atmospheric neutrino MC, and (C) data. The boxed region ineach panel shows the criterion (c)–(d) for the n − n̄ oscillation signal.

ðνe þ ν̄e Þ=ðνμ þ ν̄μ Þ, ν=ν̄ ratio
Up/down, horizontal/vertical flux ratios
K=π ratio
Neutrino energy spectrum (< 1, > 1 GeV)
Neutrino cross sections
QE
1-π production
DIS
coherent π productions
CC/NC cross section ratio
Axial vector mass in QE and 1π prod.
Fermi momentum for QE
π propagation in 16 O
Energy scale
Asymmetry of detector gain
Cherenkov ring finding
Total

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Uncertainty (%)
0.1, 1.0≪1
3.1
6.1,3.6
5.8
2.4
14.1
≪1
5.0
0.6
≪1
4.1
4.8
0.5
14.1
23.7

K. ABE et al.

PHYSICAL REVIEW D 91, 072006 (2015)is 20.0%, as estimated from the π-16 O scattering data
shown in [13] and by comparing results from two independent nuclear interaction programs originally developed
by IMB [13] and by Kamiokande [14] (6.1%). The
uncertainty from the (n̄ þ nucleon) annihilation branchingratios is estimated to be 4.6% by comparing different MC
results based on variations in the assumed branching ratios[28,29]. The 0.6% asymmetry in the detector gain and the
2.0% difference in the energy scale between the data andthe MC would affect the momentum cut and contribute
1.7% and 0.4% uncertainties, respectively. By comparing
real data with MC events we estimate that the uncertainty
in the Cherenkov ring finding procedure is 2.2%. The
detection efficiency is estimated to have a total uncertainty
of 22.9% while the exposure uncertainty was found to be
3.0% through an estimate of the error in the calculation of
the effective fiducial volume.
The uncertainties in the atmospheric neutrino flux, theatmospheric neutrino energy spectrum, and the componentsof the atmospheric neutrino flux contribute 7.8% to thesystematic uncertainty of the background rate. The DIS
cross section uncertainty in the low q2 region yields a large
contribution to the uncertainty in the background rate,
which is estimated to be 14.1% by comparing the resultsfrom two different parametrizations of the parton distribution functions [30,31]. The uncertainty in the energy scale,the lack of perfect uniformity in the PMT gain, and theuncertainty in the Cherenkov ring finding contribute a totalof 14.9% to the systematic errors. The total systematic
uncertainty in the background rate is estimated to be 23.7%.
VII. RESULTS
No significant excess was found in our full 1489 day
Super-Kamiokande-I data set. The lower limit on the
lifetime of a neutron bound inside an oxygen nucleus
due to n − n̄ oscillation was calculated from the 24
observed candidate and 24.1 expected background events.
All of the systematic uncertainties were included in thelimit calculation by employing the Bayesian statisticalmethod [32] as follows:

ZZZPðΓjnobs Þ ¼ Ae−ðΓλϵþbÞ ðΓλϵ þ bÞnobs
nobs !

× PðΓÞPðλÞPðϵÞPðbÞdλdϵdb:

The above normalization constant A
R in Eq. (2) was
determined by imposing the constraint 0∞ PðΓjnobs ÞdΓ ¼ 1
where Γ, λ ¼ NT, and ϵ are the true values of the event rate,
exposure, and detection efficiency, respectively, for n − n̄
oscillation. N and T are the number of neutrons and the
live-days, nobs ¼ 24 is the number of observed candidates,and b is the true mean number of background events.
PðΓÞ; PðλÞ; PðϵÞ; PðbÞ in Eq. (2) are the prior probability
density functions, which we assume are Gaussian distributions for λ, ϵ, and b. PðΓÞ is a flat distribution for Γ ≥ 0
and 0 for negative Γ. Finally, the 90% C.L. limit of theneutron lifetime for n − n̄ oscillation in oxygen with theinclusion of systematic uncertainties is determined from
Eqs. (3)–(4) as follows:
T n−n̄ ¼ 1=Γlimit ;
Z Γ
limit
C:L: ¼PðΓjnÞdΓ

ð3Þ
ð4Þ

0

where C:L: ¼ 0.9. The calculated result is
T n−n̄ > 1.9 × 1032 years:

ð5ÞThis lifetime for oscillation of a bound neutron isconverted to the n − n̄ oscillation time of a free neutron
using Eq. (1). The result depends on the choice of thenuclear suppression factor, R. A straightforward application of Eq. (1), using our result in Eq. (5) and the older
suppression factor R ¼ 1.0 × 1023 s−1 yields a limit on
the free neutron oscillation time of > 2.4 × 108 seconds.
This may be directly compared with the deduced freeneutron limits from Kamiokande and IMB, as listed inTable III, which used the same nuclear suppression factor.
Since the time of those experiments, Friedman and Gal
have published an improved calculation of the nuclear
suppression factor [18]. Their calculation uses nuclear

TABLE III. A comparison of the Super-Kamiokande results with those of previous n − n̄ experiments using
bound neutrons [13–16]. The abbreviation SK, SD2, and KAM stands for Super-Kamiokande, Soudan 2, andKamiokande, respectively.
Experiment
Source of neutrons
Exposure (1032 neutron · yr)
Efficiency(%)
Candidates
Backgrounds
T n−n̄ (1032 yr)
Suppression factor (1023 sec−1 )τn−n̄ (108 sec)

ð2Þ

SK

SD2

FrejusKAM

IMB

Oxygen
245
12.1
24
24.1
1.9
0.517
2.7

Iron
21.9
18.0
5
4.5
0.72
1.4
1.3

Iron
5.0
30.0
0
2.5(2.1)
0.65
1.4
1.2

Oxygen
3.0
33.0
0
0.9
0.43
1.0
1.2

Oxygen
3.2
50.0
3
–
0.24
1.0
0.88

072006-6

SEARCH FOR n − n̄ OSCILLATION IN SUPER- …

PHYSICAL REVIEW D 91, 072006 (2015)

potentials based on recent data [33], resulting in a significantly lower value of
R ¼ 0.517 × 1023 s−1 ;ð6Þwith a theoretical uncertainty of 20%–30% [18]. We notethat the earlier value of R is well outside this theoreticaluncertainty, but simply take the latest estimate and its
uncertainty at face value for interpreting our result. The
application of Eqs. (1) and (5) with this value of R results
in a limit on the free neutron oscillation time of τn−n̄ >3.4 × 108 s at the 90% C.L. We take account of thetheoretical uncertainty of 30% in R by applying the same
Bayesian treatment using Eq. (2) to the normalization.
With this consideration, the free neutron lifetime is moreconservatively limited to beτn−n̄ > 2.7 × 108 s

ð7Þ

at the 90% C.L. This limit represents the best understandingthat may be derived from our search and can be comparedto the direct result on free neutron oscillation from the ILL/
Grenoble experiment [17], τn−n̄ > 0.86 × 108 seconds.

and the distribution of events agrees with the expectationfrom atmospheric neutrino interactions. The signal efficiency was 12.1  2.8%. We performed a limit calculationthat incorporates systematic uncertainties, arriving at abound lifetime limit of T n−n̄ > 1.9 × 1032 years. This is
more than four times greater than the best limit from a water
Cherenkov experiment, despite having nearly eighty times
the exposure because these searches are backgroundlimited. Using a recent calculation of the nuclear suppression factor, the negative results of our search for n − n̄
oscillation in 16 O is equivalent to a limit for free n − n̄
oscillation time of greater than 2.7 × 108 seconds. This
result is three times more restrictive than the ILL/Grenoble
reactor experiment. This places strict limitations on(ΔB ¼ 2, ΔL ¼ 0) processes in physics beyond the standard model.
ACKNOWLEDGMENTS

We have searched for neutron-antineutron oscillation
with 2.45 × 1034 neutron years of exposure of 16 O in the
Super-Kamiokande-I experiment. A small number of simple selection criteria were employed and the search window
in total momentum versus invariant mass was optimized forthis exposure. Twenty-four events pass the selection criteria, but the estimated background was 24.1  5.7 events,

We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment was built from, and has been
operated with, funding by the Japanese Ministry of
Education, Science, Sports and Culture, and the UnitedStates Department of Energy. We also express our gratitude
to the following agencies for their support of our research;
the U.S. National Science Foundation (including Grants
No. PHY 0401139 and No. PHY 0901048 to CSUDH),
the National Research Foundation of Korea (Grant
No. NRF-2009-353-C00046), and the National Natural
Science Foundation of China.

[1] A. D. Sakharov, Violation of CP invariance, C asymmetry,
and Baryon asymmetry of the Universe, Pis'ma Zh. E'ksp.
Teor. Fiz. 5, 32 (1967) [JETP Lett. 5, 24 (1967)].
[2] C. McGrew et al. (IMB-3 Collaboration), Search fornucleon decay using the IMB-3 detector, Phys. Rev. D
59, 052004 (1999).
[3] K. Hirata et al. (Kamiokande-II Collaboration), Experimental limits on nucleon lifetime for lepton þ meson decay
modes, Phys. Lett. B 220, 308 (1989).
[4] M. Shiozawa et al. (Super-Kamiokande Collaboration),
Search for Proton Decay via p → eþ π 0 in a Large Water
Cherenkov Detector, Phys. Rev. Lett. 81, 3319 (1998); H.
Nishino et al. (Super-Kamiokande Collaboration), Search fornucleon decay into charged antilepton plus meson in SuperKamiokande I and II, Phys. Rev. D 85, 112001 (2012).
[5] K. Kobayashi et al. (Super-Kamiokande Collaboration),
Search for nucleon decay via modes favored by supersymmetric grand unification models in Super-Kamiokande-I,
Phys. Rev. D 72, 052007 (2005).

[6] V. A. Kuzmin, CP violation and baryon asymmetry of theuniverse, Pis'ma Zh. E'ksp. Teor. Fiz. 12, 335 (1970) [JETP
Lett. 12, 228 (1970)].
[7] Y. Fukuda et al. (Super-Kamiokande Collaboration),
Evidence for Oscillation of Atmospheric Neutrinos, Phys.
Rev. Lett. 81, 1562 (1998).
[8] R. N. Mohapatra, Neutron − anti-neutron oscillation: theory
and phenomenology, J. Phys. G 36, 104006 (2009).
[9] D. G. Phillips, II, W. M. Snow, K. Babu, S. Banerjee, D. V.
Baxter, Z. Berezhiani, M. Bergevin, S. Bhattacharya et al.,Neutron-antineutron oscillations: theoretical status andexperimental prospects, arXiv:1410.1100 [Phys. Rep. (tobe published)].
[10] K. S. Babu and R. N. Mohapatra, Observable neutronantineutron oscillations in seesaw models of neutrino mass,
Phys. Lett. B 518, 269 (2001).
[11] S. Nussinov and R. Shrock, n − n̄ Oscillations in Models
with Large Extra Dimensions, Phys. Rev. Lett. 88, 171601(2002).

VIII. SUMMARY

072006-7

K. ABE et al.

PHYSICAL REVIEW D 91, 072006 (2015)[12] S. J. Huber and Q. Shafi, Neutrino oscillations and rare
processes in models with a small extra dimension, Phys.
Lett. B 512, 365 (2001).
[13] T. W. Jones et al. (IMB Collaboration), Search for n − n̄Oscillation in Oxygen, Phys. Rev. Lett. 52, 720 (1984).
[14] M. Takita et al. (Kamiokande Collaboration), Search forneutron-antineutron oscillation in 16 O nuclei, Phys. Rev. D
34, 902 (1986).
[15] J. Chung et al. (Soudan 2 Collaboration), Search forneutron-antineutron oscillations using multiprong events
in Soudan 2, Phys. Rev. D 66, 032004 (2002).
[16] C. Berger et al. (Frejus Collaboration), Search for Neutron Antineutron Oscillations in the Frejus Detector, Phys. Lett.
B 240, 237 (1990).
[17] M. Baldo-Ceolin et al., A new experimental limit on
neutron-antineutron oscillations, Z. Phys. C 63, 409 (1994).
[18] E. Friedman and A. Gal, Realistic calculations of nuclear
disappearance lifetimes induced by nn̄ oscillations, Phys.
Rev. D 78, 016002 (2008).
[19] Y. Fukuda et al. (Super-Kamiokande Collaboration), The
Super-Kamiokande detector, Nucl. Instrum. Methods Phys.
Res., Sect. A 501, 418 (2003).
[20] R. Armenteros and B. French, Antinucleon-nucleon interactions, High Energy Physics (Academic, New York, 1969),
Vol. 4, p. 237.
[21] P. Pavlopoulos et al., Possible evidence for narrow boundstates related to the pp̄ system, AIP Conf. Proc. 41, 340(1978).
[22] A. Backenstoss et al., Proton - anti-proton Annihilations at
rest into π 0 ω, π 0 η, π 0 γ, π 0 π 0 , and π 0 η0 , Nucl. Phys. B 228,424 (1983).
[23] Ye. S. Golubeva, A. S. Iljinov, and L. A. Kondratyuk,
Antineutron annihilation event generator for n − n̄ searchexperiment, ORNL-6910, in Proceedings of theInternational Workshop on Future Prospects of Baryon
Instability Search in p-Decay and n − n̄ Oscillation Experiments, Oak Ridge, Tennessee, 1996, p. 295, http://www.osti.gov/scitech/servlets/purl/461127.
[24] Y. Ashie et al. (Super-Kamiokande Collaboration), Measurement of atmospheric neutrino oscillation parameters by
Super-Kamiokande I, Phys. Rev. D 71, 112005 (2005).
[25] R. Brun and F. Carminati, GEANT detector description andsimulation tool, CERN Report No. W5013, 1993.
[26] T. A. Gabriel, J. E. Brau, and B. L. Bishop, The physics
of compensating calorimetry and the new Calor89 code
system, IEEE Trans. Nucl. Sci. 36, 14 (1989).
[27] M. Nakahata et al. (Kamiokande Collaboration), Atmospheric neutrino background and pion nuclear effect for
KAMIOKA nucleon decay experiment, J. Phys. Soc. Jpn.
55, 3786 (1986).
[28] C. Baltay, P. Franzini, G. Lütjens, J. C. Severiens, D. Tycko,
and D. Zanello, Annihilations of antiprotons at rest inhydrogen. V. multipion annihilations, Phys. Rev. 145,
1103 (1966).
[29] A. Bettini et al., Annihilation into pions of the p̄n systemfrom antiprotons at rest in deuterium, Nuovo Cimento 47,
642 (1967).
[30] M. Glück, E. Reya, and A. Vogt, Dynamical parton
distributions revisited, Eur. Phys. J. C 5, 461 (1998).
[31] A. Bodek and U. K. Yang, Modeling neutrino and electron
scattering inelastic cross sections, arXiv:hep-ex/0308007.
[32] R. M. Barnett et al. (The Particle Data Group), Review ofparticle physics, Phys. Rev. D 54, 165 (1996).
[33] E. Friedman, A. Gal, and J. Mares, Antiproton − nucleus
potentials from global fits to antiprotonic X-rays andradiochemical data, Nucl. Phys. A761, 283 (2005).

072006-8