PHYSICAL REVIEW D 86, 012006 (2012)

Search for proton decay via p ! þ K0 in Super-Kamiokande I, II, and III
C. Regis,6 K. Abe,1 Y. Hayato,1,28 K. Iyogi,1 J. Kameda,1 Y. Koshio,1 Ll. Marti,1 M. Miura,1 S. Moriyama,1,28
M. Nakahata,1,28 S. Nakayama,1 Y. Obayashi,1 H. Sekiya,1 M. Shiozawa,1,28 Y. Suzuki,1,28 A. Takeda,1 Y. Takenaga,1
K. Ueno,1 T. Yokozawa,1 H. Kaji,2 T. Kajita,2,28 K. Kaneyuki,2,28,* K. P. Lee,2 K. Okumura,2 T. McLachlan,2 L. Labarga,3
E. Kearns,4,28 J. L. Raaf,4 J. L. Stone,4,28 L. R. Sulak,4 M. Goldhaber,5,* K. Bays,6 G. Carminati,6 W. R. Kropp,6 S. Mine,6
A. Renshaw,6 M. B. Smy,6,28 H. W. Sobel,6,28 K. S. Ganezer,7 J. Hill,7 W. E. Keig,7 J. S. Jang,8,† J. Y. Kim,8 I. T. Lim,8J. B. Albert,9 K. Scholberg,9,28 C. W. Walter,9,28 R. A. Wendell,9 T. Wongjirad,9 T. Ishizuka,10 S. Tasaka,11 J. G. Learned,12
S. Matsuno,12 S. N. Smith,12 T. Hasegawa,13 T. Ishida,13 T. Ishii,13 T. Kobayashi,13 T. Nakadaira,13 K. Nakamura,13,28
K. Nishikawa,13 Y. Oyama,13 K. Sakashita,13 T. Sekiguchi,13 T. Tsukamoto,13 A. T. Suzuki,14 Y. Takeuchi,14,28 K. Ieki,15
M. Ikeda,15 H. Kubo,15 A. Minamino,15 A. Murakami,15 T. Nakaya,15,28 Y. Fukuda,16 K. Choi,17 Y. Itow,17,18 G. Mitsuka,17
M. Miyake,17 P. Mijakowski,19 J. Hignight,20 J. Imber,20 C. K. Jung,20 I. Taylor,20 C. Yanagisawa,20 H. Ishino,21
A. Kibayashi,21 T. Mori,21 M. Sakuda,21 J. Takeuchi,21 Y. Kuno,22 S. B. Kim,23 H. Okazawa,24 Y. Choi,25 K. Nishijima,26
M. Koshiba,27 Y. Totsuka,27,* M. Yokoyama,27,28 K. Martens,28 M. R. Vagins,28,6 S. Chen,29 H. Sui,29 Z. Yang,29
H. Zhang,29 K. Connolly,30 M. Dziomba,30 and R. J. Wilkes30(The Super-Kamiokande Collaboration)
1

2

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan
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
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
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
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
11
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
12
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, 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
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
17
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan
18
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, Aichi 464-8602, Japan
19
National Centre for Nuclear Research, 00-681 Warsaw, Poland
20
Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794-3800, USA
21
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
22
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
23
Department of Physics, Seoul National University, Seoul 151-742, Korea
24
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan
25
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
26
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
27
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
28
Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba 277-8583, Japan
29
Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
30
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 30 May 2012; published 23 July 2012)
We have searched for proton decay via p ! þ K 0 using data from a 91:7 kiloton  year
exposure of Super-Kamiokande- I, a 49:2 kiloton  year exposure of Super-Kamiokande II, and a
31:9 kiloton  year exposure of Super-Kamiokande III. The number of candidate events in the data

*Deceased.
†
Present address: GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea.

1550-7998= 2012=86(1)=012006(14)012006-1

Ó 2012 American Physical Society

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PHYSICAL REVIEW D 86, 012006 (2012)

was consistent with the atmospheric neutrino background expectation and no evidence for proton
decay in this mode was found. We set a partial lifetime lower limit of 1:6  1033 years at the 90%
confidence level.
DOI: 10.1103/PhysRevD.86.012006

PACS numbers: 13.30.Ce, 11.30.Fs, 14.20.Dh, 29.40.Ka

II. SUPER-KAMIOKANDE DETECTOR

I. INTRODUCTION
The experimental observation of proton decay would
provide strong evidence for grand unified theories(GUTs) [1] which unify the strong, electromagnetic, andweak forces. Supersymmetry (SUSY) GUTs predict theunification of coupling constants consistent with thenonobservation of p ! eþ 0 [2] via gauge boson
exchange. In some SUSY GUT models [3] p ! K
 þ isthen favored by dimension five operators. However, inother models [4] p ! þ K0 may dominate. So far there
has been no experimental observation of either of these
decays and in this paper we focus on the latter, whose
most stringent partial lifetime lower limit comes fromSuper-Kamiokande (SK), =Bp!þ K0 > 1:3  1033 years(90% CL) [5]. The partial lifetime of p ! þ K0 is predicted to be just above this limit [4].
The K0 is a composite state of the KS0 (50%) and0KL (50%). The analysis presented in [5] searched only
for proton decay into þ KS0 using data from the first run
period of SK (91:7 kton  years). In this paper we present a
combined search for proton decay into both KS0 and KL0
with an updated data set (172:8 kton  years).
A p ! þ K0 signal would appear in SK as one
muonlike (-like) ring with monochromatic momentumof about 327 MeV=c and secondary ring(s) from thedecay of the K 0 . The total momenta of all such rings
should be consistent with the decay of a proton, as wellas an invariant mass close to the proton mass. The
dominant decay modes of the KS0 are þ  (69.2%),and 0 0 (30.7%). The KL0 decays predominantly into e e (40.6%),    (27.0%), 30 (19.5%), andþ  0 (12.5%). Since the KL0 has a relatively long decay
length (c  8:4 m, where  is the mean life), proton
decay events into this channel are characterized by two
vertices separated in time and space: a primary vertex fromwhich the þ emerges and a secondary vertex for the
decay products of the KL0 . We developed new event reconstruction for events with two vertices.
The outline of this paper is as follows. A review of
the SK detector is presented in Sec. II. In Sec. III thep ! þ K0 Monte Carlo (MC) simulation as well as
the atmospheric neutrino MC simulation used to calculate
the signal efficiency and expected background rate arepresented. Sections IV and V describe the data reduction
and the event reconstruction, respectively. The resultsof the data analysis are summarized in Sec. VI and acomparison with the previous result [5] is described insubsection VI C. Finally, Sec. VII concludes this study.

The Super-Kamiokande detector [6] is located in
Gifu Prefecture, Japan, at a depth of 2700 m waterequivalent within the Kamioka mine at Mt. Ikenoyama.
The detector is a 50 kton right cylinder that is opticallyseparated into two concentric regions, an inner (ID) andan outer detector (OD). Inward-facing 20 inch diameter
Hamamatsu photomultiplier tubes (PMTs) [7] are mounted
uniformly on the walls of the ID. During the SK-I (SK-III)
run period from April 1996 (October 2006) to July 2001
(September 2008) approximately 11 100 PMTs lined the
ID walls. There were about 5200 PMTs in the ID during
the SK-II run period from October 2002 to October 2005.
The photocathode coverage during the run was about 40%(20%) in SK-I and -III (SK-II). A black sheet spans theregion between PMTs to absorb light and optically separate
ID and OD. Starting with SK-II, each ID PMT is encasedin an acrylic cover to reduce the effect of implosion onneighboring PMTs. The transparency of this cover is morethan 96% for >350 nm photons with normal incidence. A
22.5 kton fiducial volume used in the data analysis presented below is defined by the cylindrical volume taken
2 m from the ID walls.
The OD is a 2 m thick cylindrical shell enclosing the ID
that is instrumented with 1885 outward-facing 8 inch diameter Hamamatsu PMTs. To improve the light collection
efficiency, a 60 cm  60 cm wavelength shifting plate is
attached to each PMT and the OD walls are covered withreflective material called ‘‘Tyvek sheet’’. The main purposeof the OD is to tag incoming cosmic ray muons and muons
induced by atmospheric neutrinos that escape the ID. The
OD region also serves as a passive shield against radioactivity from outside the detector wall. The SK-I detector andits calibration are described in detail elsewhere [6].
III. SIMULATION
The p ! þ K0 MC and the SK atmospheric neutrino
MC are used to estimate signal efficiencies and the
expected background rates. Using these MCs the event
selections described in Sec. VI A are optimized to maximize the analysis’s sensitivity prior to examining the data.
A. Proton decayþThe p !  K MC used here is the same as that usedin [5] with the exception that p ! þ KL0 events are additionally simulated in this analysis. In this analysis the
decays of both free proton and protons bound on the oxygen nucleus are considered. For the decay of free protons

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PHYSICAL REVIEW D 86, 012006 (2012)0

the directions of the  and K are exactly back-to-back,and each has a momentum of 326:5 MeV=c. In the case of
proton decay within the oxygen nucleus, the effects of
Fermi momentum, correlation with other nucleons, thenuclear binding energy, kaon-nucleon interactions, andKL0 ! KS0 regeneration are all taken into account. The
Fermi momentum distribution measured by electron-12 C
scattering [8] is used in the simulation. The nuclear binding
energy effect is taken into account by modification of the
proton’s mass. The modified proton mass, m0p , is calculated
by m0p ¼ mp  Eb where mp is the proton rest mass and Eb
is the nuclear binding energy. The value of Eb for eachsimulated event was randomly selected from a Gaussian
probability density function with ð;Þ¼ð39:0;10:2Þ MeV
for the S state and ð; Þ ¼ ð15:5; 3:82Þ MeV for the P
state. The correlation of the decaying proton’s wave function with other nucleons reduces the invariant mass of the
decay products since some of the system’s momentum iscarried by these nucleons. This effect is present in about
10% of proton decays [9] and produces a broad invariant
mass spectrum down to about 600 MeV=c2 . The locationof protons within the 16 O nucleus is calculated according to
the Woods-Saxon nuclear density model [10]. The kaonnucleon interactions within the 16 O nucleus that are considered include elastic scattering and inelastic scattering
via charge exchange. The K þ N scattering amplitudes werefitted by a partial wave analysis using many data samples
by Hyslop et al. [11]. The Kþ n ! K0 p charge exchange
cross section was measured by Glasser et al. [12]. The
detail of the Kþ N interaction is described in [5]. Fromisospin symmetry, the K0 N reactions have essentially thesame magnitude as the Kþ N reactions. If an interaction
occurs, the effect of Pauli blocking is introduced byrequiring the nucleon momentum after interaction belarger than the Fermi surface momentum, given by
pF ðrÞ ¼ ð32 2 ðrÞÞð1=3Þ , where ðrÞ is the nuclear density
distribution and r is the distance from the center of thenucleus. The KL0 ! KS0 regeneration effect is implemented
as a decay mode of the KL0 in this analysis. The regeneration
probability in water is based on the results of a kaon
scattering experiment using a carbon target [13]. Regeneration within the 16 O nucleus is also considered andis assumed to be proportional to its density relative to water.
The fraction with regeneration is about 0.1% of the total
generated p ! þ KL0 MC events.
We simulate propagation of particles and Cherenkov
light production in water by custom software based on
GEANT [14]. The propagation of charged pions in water
is simulated using custom code based on [15] for pion
momenta less than 500 MeV=c and using CALOR [16]otherwise.

nucleon decay. For the p ! þ K 0 mode, the decay products of the KL0 and KS0 often include pions which can becreated in atmospheric neutrino interactions. Notably,charged current multiple pion production and deep inelastic scattering processes, again with multiple pions in the
final state, are backgrounds to the search presented here.
Accordingly, the accurate simulation of atmospheric neutrino events in SK is essential to properly estimate theproton decay background. In this paper, the atmospheric
neutrino MC is the same as used in other SK analyses[2,17]. The primary flux is taken from the Honda model[18] and atmospheric neutrino interactions are generated
within the detector using the NEUT simulator [19,20].
Kaon regeneration is not considered in the atmospheric
neutrino MC because the fraction of K0 production inthese events is negligibly small. For each of the SK run
periods presented here, independently about 200 year MC
samples were used to compute the background rates for thepresent search. Two-flavor neutrino oscillation effects withsin2 223 ¼ 1:0 and m2 ¼ 2:5  103 eV2 are includedin the background prediction. A more detailed explanationof the atmospheric neutrino MC is presented in [2,17].
IV. DATA SET AND REDUCTION
The current data set corresponds to a 91:7 kton  years(1489.2 days) exposure from SK-I, a 49:2 kton  years(798.6 days) exposure during SK-II, and a 31:9 kton years (518.1 days) exposure from SK-III. The data acquisition trigger threshold used in this data analysis during
these periods corresponds to the energy deposited by a
6 MeV electron during SK-I and SK-III and 8 MeVelectron
during SK-II. Most events above this threshold are cosmic
ray muons or low energy backgrounds from radioactivity indetector materials. To remove these backgrounds the data
are passed through several reduction stages before detailed
reconstruction processes (described in Sec. V) are applied.
To summarize, the starting point of the data analysis is the
fully contained (FC) fiducial volume (FV) data sample,
which contains events passing the following cuts:(i) The number of hit PMTs in the highest charge clusterof PMTs in the OD is less than 10.
(ii) The total visible energy in the ID is greater than
30 MeV.
(iii) The reconstructed vertex’s distance to the ID wall isgreater than 2 m.
After these cuts the FCFV event rate is about eight events
per day. Nonatmospheric neutrino backgrounds are estimated to represent less than 1% of this sample. Details of
the data reduction can be found in [17].

B. Atmospheric neutrinos

V. EVENT RECONSTRUCTION

The interactions of atmospheric neutrinos within SK
pose the dominant source of background to searches for

Event reconstruction programs are applied to the FCFV
sample described in the previous section. For the KS0012006-3

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PHYSICAL REVIEW D 86, 012006 (2012)searches, the standard event reconstruction [17,21] used in
the SK atmospheric neutrino oscillation analyses and proton decay searches is used. However, relative to the previous version of this analysis [5], several improvements to
the reconstruction algorithms have been made. The search
for KL0 events makes use of new event reconstruction
methods, which are explained in detail below.
The event reconstruction for the KS0 searches is(i) Vertex reconstruction.
The event vertex is initially determined by using thetime of flight-subtracted timing distribution of hit ID
PMTs assuming all light originated from a single
point (point fit). An initial direction for the event isthen estimated as the sum of vectors drawn from thisvertex to each hit PMT and weighted by its observed
charge. Defining this direction as the particle’s trajectory, the distribution of observed charge as afunction of the opening angle to this axis is used todetermine the edge of the brightest Cherenkov ringin the event. With the ring edge in hand, the vertex
position and particle direction are refined using thetiming residual distribution, but assuming that PMTs
within the ring are illuminated by photons generated
along the particle track and other PMTs receive light
generated at the event vertex.
(ii) Ring counting.
Based on the reconstructed vertex, additional ringcandidates in the event are searched for using atechnique based on the Hough transform [22].
Possible ring candidates returned by the Hough
mapping are tested using a likelihood method todetermine if the existence of a second ring better
describes the observed PMT hit pattern than a single
ring alone. If a second ring is found, the procedure isiterated up to a total of five rings. At each step the
likelihood is based on a comparison of the observed
charge in the event against the expectation from thenumber of proposed rings. With respect to the previous analysis there have been improvements to theprobability density function for the expected chargethat are used in the present analysis. More details
are presented below.
(iii) PID (e= separation).
After the number of rings has been determined eachring’s particle type (PID) is estimated taking into
account the effects of light scattering in the waterand reflection off PMT surfaces. Two likelihood
functions are used to separate electromagnetic
shower type (e-like) rings from muon type (-like)rings. The first is a pattern matching algorithm
that exploits topological differences in the PMT hit
pattern that arise from the scattering and pair production processes an electron experiences, but thatthe primarily unperturbed muon does not. A second
method makes use of the difference in the observed

Cherenkov angle between the two particles as a resultof their largely different masses. For the final estimation of a ring’s PID, the two methods are combined.
(iv) Decay electron search.
Electrons produced from the decay of muons in thedetector can occur in the same trigger timing gatewith the primary event or delayed. The search fordecay electrons extends to both cases.
(v) Momentum reconstruction.
The momentum of each ring is determined using
the sum of its assigned charges after correcting forthe attenuation of Cherenkov light in water and theincident angle dependence of the PMT acceptance.
Depending upon the result of the PID estimation, themomentum is then assigned based on the amount ofcorrected charge expected for the fitted particle
type. A pionic momentum (-like) that relies on
the expected Cherenkov angle as well as the total
corrected charge is also used in this analysis. The
time variation of the light attenuation length and the
PMT gain, as measured with cosmic rays traversing
the detector, is incorporated into the momentum
reconstruction.
Improvements made to the single photoelectron response functions used to predict the expected charge ineach PMT have led to improvements in the ring counting,
PID, and momentum estimations for this analysis.
The uncertainty in the detector’s energy calibration (theenergy scale) is one of the most important for the proton
decay searches. It is estimated by systematic studies of thedifferences between the absolute momenta of data and MC
in several control samples. At SK these control samples arechosen to probe a variety of energies where neutrino
interactions and nucleon decay searches are relevant,among which are cosmic ray muons that stop in the detector, their associated decay electrons (Fig. 1), and 0 ’s
produced in neutral current atmospheric neutrino interactions (Fig. 2). The uncertainty of the absolute energy scaleis estimated to be less than 0.74%, 1.60%, and 2.08% for
SK-I, SK-II, and SK-III, respectively. The time variation of
the reconstructed momenta of these muon and electron
samples during each of the SK run periods (Fig. 3) isalso taken into account. Overall, the uncertainty on theenergy scale is 1.1%, 1.7%, and 2.7% in SK-I, SK-II, and
SK-III, respectively. Further, the directional dependence of
decay electron momenta is used to estimate the asymmetryof the energy scale. During SK-I, SK-II, and SK-III, theasymmetry was estimated to be 0.6%, 0.6%, and 1.3%,
respectively. These errors on the SK energy scale areincorporated into the proton decay analysis as discussed
in Sec. VI B 2.
KL0 event reconstruction
The KL0 event reconstruction needs two vertices, one forthe þ candidate from the proton decay and another for

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250
200
150
100
50
0

SK-I

400

SK-II

200
0
600

SK-III

400
200
0

0

10

20

30

40

50

60

70

80

reconstructed momentum (MeV/c)

FIG. 1 (color online). The momentum distribution of decay
electrons of the data (dot) and MC (solid line) for SK-I, SK-II,and SK-III from top to bottom, respectively. MC events arenormalized by the number of observed data events. The meanvalues of the data distributions agree with those of the MC within
0.6%, 1.6%, and 0.8% for SK-I, SK-II, and SK-III, respectively.

particles produced in the delayed KL0 decay. The difference
between the two vertices is used to distinguish the KL0

number of events

decay signal from the atmospheric neutrino background.
However, the standard reconstruction described cannot byitself reconstruct two vertices. For instance, the standard
ring counting algorithm uses a cut on the PMT hit timing
after correcting for the time of flight taken from the initialvertex to help isolate genuine Cherenkov rings. Since thelight from the particles emerging from the KL0 is both
SK-I

100
50
0
60

SK-II

40
20
0
60

SK-III

40
20
0

0

50

100

150

200

250

300
2

invariant mass (MeV/c )FIG. 2 (color online). Invariant mass distribution of neutrinoinduced 0 events of the observed data (dot) and the atmospheric
neutrino MC events (solid line) for SK-I, SK-II, and SK-III from
top to bottom, respectively. MC events are normalized by the live
time of the observed data. The peak positions of the data
distributions agree with those from the MC within 0.7%, 1.3%,
and 0.3% for SK-I, SK-II, and SK-III, respectively.

FIG. 3. The time variation of the reconstructed momentum/
range of stopping muons and the reconstructed momentum of
decay electrons as a function of elapsed days with respect to themean value for SK-I, SK-II, and SK-III from top to bottom,
respectively. The largest variation (root mean square) among
these two calibration sources during SK-I, SK-II, and SK-III was
0.88%, 0.55%, and 1.79%, respectively. The time variation was
relatively larger in SK-III due to its poorer water quality.

delayed in time and spatially separated from this initialvertex, the inclusion of this PMT timing cut degrades theperformance of the ring counting algorithm on these
events. Therefore, we developed a specialized reconstruction. In the first step of the KL0 reconstruction, the standard
reconstruction algorithm is applied without making any cuton the PMT hit timing during the ring counting stage. It
outputs an initial vertex, the number of candidate rings, anda direction for each ring in much the same way as thestandard reconstruction.
In the second step of the reconstruction [23], an event’s
hit PMTs are divided into two groups for each ring foundby the first step. The first, called the inner domain, is acollection of hit PMTs that fall within a cone that is 10
larger than the ring’s reconstructed Cherenkov angle. The
second group, called the outer domain, is the remaining
collection of hit PMTs that are not part of the inner domain.
The charge and time information of PMTs in the outerdomain are zeroed and part of the standard reconstruction
is reapplied using only information from PMTs in the innerdomain. At this stage the vertex reconstruction, PID, andmomentum reconstruction are repeated, and the result isstored. A precise vertex fit, which adjusts the initial candidate vertex along the ring’s reconstructed momentum
using the expected charge distribution for a particle with

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the ring’s new PID, is applied. The vertex resolution isabout 0.3 m [17]. Finally, an algorithm designed to distinguish protons from muons [24] is applied to provide an
additional PID handle. Once the þ candidate from theoriginal proton’s decay is identified, this precision vertex
will be identified as that of the initial decay. The secondary
vertex from the KL0 decay is estimated by zeroing thecharge and time information of the inner domain PMTs
and applying the point fit algorithm to the outer domain.
Since  from the KL0 decay may be just above Cherenkov
threshold, these pions may not appear in the detector as
clear Cherenkov rings. Using the outer domain to performthe secondary vertex fit in this way incorporates light fromeven these particles to provide a better estimate of the point
where the KL0 decays. These reconstructions in the second
step are repeated for each ring found by the first step.
For each event, the ring with -like momentum closest
to 326:5 MeV=c is chosen as the þ candidate. A vertex
separation parameter is defined as the distance between
the þ (primary) candidate vertex and the KL0 (secondary)vertex along the þ candidate’s momentum vector. Thisparameter is used to define a cut to help reduce atmospheric
neutrino backgrounds and is described below. Figure 4 shows
the typical correlation between the true vertex separation,
extracted using MC information, and the reconstructedvertex separation for p ! þ KL0 decay MC events. A clear
correlation between the two can be seen. A typical event
display from one MC event showing both the primary andsecondary fitted vertices appears in Fig. 5. In this case thereconstruction has correctly identified the þ (thick cyanring) and the primary and secondary vertex are represented
by the blue triangle and solid green circle, respectively.

FIG. 4 (color online). Correlation between true and reconstructed vertex separations for the p ! þ KL0 decay MC events
in SK-I after the event selections (D1–D5) described inSec. VI A.

FIG. 5 (color online). Typical event display of p ! þ KL0 ,KL0 !  e  MC event in SK-I. The upper (lower) visible ringare from true þ (e). The thick cyan circle shows the þcandidate ring. The blue triangle and solid green circle show
the reconstructed vertex position horizontally and verticallyprojected on the detector wall for the þ and remaining particle
candidates, respectively. For this event, reconstructed and true
vertex separations are 6.58 m and 6.33 m, respectively.

The difference between the reconstructed and true vertex
separation is shown in Fig. 6 for proton decay events in eachof the SK run periods. A slight bias in this distribution,
represented by the shift of the peak away from zero, is used
to estimate the uncertainty coming from the vertex separation
cut discussed in Sec. VI B 2. This shift is typically Oð10Þ cm
for both proton decay and atmospheric neutrino MC events.

FIG. 6. Reconstructed  true vertex separation for thep ! þ KL0 decay MC events in SK-I, SK-II, and SK-III (fromtop to bottom), respectively, after the event selections (D1–D5)
described in Sec. VI A.

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The vertex separation resolutions for these two MC sets areabout 0.8 m and 1.1 m, respectively. Because of the cleaner
back-to-back event topology of the KL0 decay events, theseparation resolution for the proton decay events is slightly
better than that for the atmospheric neutrino events. Most of
this resolution comes from the application of the point fit
algorithm in determining the secondary vertex.
VI. DATA ANALYSIS
A. Event selection
The search for p ! þ K 0 decay is performed bysearching for decays into þ KS0 and þ KL0 separately.
The FCFV events (Sec. IV) are first passed through theKS0 selection and failing events at the KS0 selection are thenadditionally subjected to the KL0 search. The KS0 search
criteria are not changed with respect to the previous analysis [5], but are reviewed here for completeness.
To maximize the analysis’s sensitivity to the KS0 mode,
three distinct selections designed to extract events corresponding to each of the KS0 decay’s final states are used. It
should be noted that by construction there is no kinematic
overlap among the methods. For KS0 ! 0 0 decays(30.7% branching fraction), the proton decay selection
criteria are as follows:(A1) Three to five rings, corresponding to the initial þand the gammas emerging from the 0 decays.
(A2) One -like ring, to be identified as the þ candidate, and the other rings in the event are e-like.
(A3) One Michel electron, from the decay of the þ .
(A4) 150 MeV=c < p < 400 MeV=c.
(A5) 400 MeV=c2 < mK0 < 600 MeV=c2 .
(A6) pp < 300 MeV=c.
(A7) 750 MeV=c2 < mp < 1000 MeV=c2 .
Here p refers to the þ candidate momentum, mK0 is
the reconstructed K 0 invariant mass using only the e-likerings, and pp ðmp Þ is the total momentum (invariant mass)using all rings in the event. Figure 7 shows the mp and pp
distributions after applying these criteria (A1–A5). Under
the hypothesis of proton decay, initial proton momenta of
up to 300 MeV=c are considered in the search because theFermi momentum of protons in 16 O nuclei may reach about
200 MeV=c. This, in addition to the possibility of missing
gammas from the 0 decay, is similarly the reason for thesmall lower bound on the mp cut.
After this event selection the remaining background consists primarily of events from e or  charged current (CC)multiple pion production interactions, and neutral current
deep inelastic scattering processes, from the atmospheric

FIG. 7 (color online). Total invariant mass and momentum for events that satisfy criteria (A1–A5) in SK-I, SK-II, and SK-III from
top to bottom. The box shows criteria (A6, A7). From left to right, data (1489 days, 799 days, 518 days), atmospheric neutrino MC(200 years, 172 years, 194 years), and p ! þ K 0 MC are shown.

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PHYSICAL REVIEW D 86, 012006 (2012)

FIG. 8 (color online). þ momentum and total momentum for events that satisfy criteria (B1–B3) in SK-I, SK-II, and SK-III from
top to bottom. The box shows criteria (B4, B5). From left to right, data (1489 days, 799 days, 518 days), atmospheric neutrino MC(200 years, 172 years, 194 years), and p ! þ K 0 MC are shown.

neutrino MC. These backgrounds often have a single -likering back-to-back with several e-like rings and are consistent with the expected event signature of the signal.
To search for proton decays in which the KS0 decays intoþ   (69.2% branching fraction) two different methods
are used. The first method (Method 1) is designed to searchfor events where one of the outgoing pions does not produce
a clear Cherenkov ring, for instance when its momentum isbelow the Cherenkov production threshold, or when it captures on a 16 O nucleus. The search criteria are(B1) Two rings.
(B2) Both rings are -like, one from the þ and anotherfrom one of the charged pions.
(B3) Two Michel electrons, from the decays of the
primary þ and that from the charged pion.
(B4) 250 MeV=c < p < 400 MeV=c.
(B5) pp < 300 MeV=c.
In this method the most energetic -like ring is taken to be
the þ emerging from the initial proton decay and isassigned a -like momentum. On the other hand, thesecond energetic ring is assumed to be the charged pionand is assigned a -like momentum. Figure 8 shows the p
and pp distributions after applying these criteria (B1–B3).
The second method (Method 2) searches for proton decays

with KS0 ! þ  in which all of the emerging charged
particles produce Cherenkov radiation in the detector. In
this case the selection cuts become(C1) Three rings.
(C2) One or two Michel electrons.
(C3) 450 MeV=c2 < mK0 < 550 MeV=c2 .
(C4) pp < 300 MeV=c.
(C5) 750 MeV=c2 < mp < 1000 MeV=c2 .
Figure 9 shows the mp and pp distributions that result fromapplying the criteria (C1–C3). The primary background to
this search arises from  CC interactions with single ormultiple pions produced in the final state.
To search for proton decays with a KL0 decay the following criteria are applied:(D1) 500(100) pe < total charge < 8000ð3000Þpe in
SK-I,III(SK-II).
(D2) The number of rings without the PMT hit timing
cut > 1.
(D3) At least one -like ring that is neither e-like nor
protonlike.
(D4) The number of Michel electrons > 0.
(D5) 260 MeV=c < p < 410 MeV=c.
(D6) Vertex separation between þ candidate and KL0
decay is greater than 2.3 m.

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ν

→µ

ν

→µ

ν

→µ

FIG. 9 (color online). Total invariant mass and total momentum for events that satisfy criteria (C1–C3) in SK-I, SK-II, and SK-III
from top to bottom. The box shows criteria (C4, C5). From left to right, data (1489 days, 799 days, 518 days), atmospheric neutrino
MC (200 years, 172 years, 194 years), and p ! þ K 0 MC are shown.

The þ candidate is taken to be the -like ring with
momentum closest to 326:5 MeV=c. At the third cut (D3),the following criteria are required to increase purity of the
-like rings. In addition to requiring a -like classificationby the standard PID, the result of the proton ID algorithm
must also be -like. Further, the Cherenkov opening angle
is required to be greater than 30 , The cut value at (D6) has
been chosen to maximize this analysis’s sensitivity to theproton partial lifetime based on studies of the proton decay
and atmospheric neutrino MC. Figure 10 shows the vertex
separation distribution after applying criteria (D1–D5). The
net decay length of the p ! þ KL0 MC is about 2 m
because roughly 70% of the KL0 undergo hadronic interactions in the water before decaying. There is good agreement
between the data and the atmospheric neutrino MC.
The dominant background sources after the event
selection are primarily  CC quasielastic and singlepion production interactions. In these backgrounds therecoiling proton from the neutrino interaction is above
Cherenkov threshold and is selected as the þ candidate.
For this reason the primary vertex can be pulled along
the direction of the þ candidate momentum, increasing the separation between the two reconstructed vertices. Figure 11 shows a typical event display of these

FIG. 10 (color online). Vertex separation distributions forevents that satisfy criteria (D1–D5) in SK-I, SK-II, and SK-III
from top to bottom. Positive values of the vertex separation
indicate that the point fit vertex is separated from the þ vertex
in the direction opposite of the þ . Data (black dot), atmospheric neutrino MC (blue thinner histogram), and p ! þ K 0
MC (red thicker histogram) are shown. The MC samples arenormalized to data by entries. The cut value corresponding to(D6) is shown as a broken line.

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PHYSICAL REVIEW D 86, 012006 (2012)

FIG. 11 (color online). Typical event display of the remaining
atmospheric neutrino background MC event in the KL0 search in
SK-I. This is from  charged current quasielastic interaction.
The right (left) visible rings are from true proton (muon). The
thick cyan ring shows the þ candidate reconstructed ring. The
blue triangle and solid green circle show the reconstructed vertex
position horizontally and vertically projected on the detector
wall for the þ and remaining particle candidates, respectively.

backgrounds. In this particular event the reconstructedvertex separation is 3.9 m.
B. Result
The signal detection efficiency, the expected atmospheric neutrino background rate, and the number ofcandidate events for each of the search methods are summarized in Table I.
The detection efficiencies in SK-II are lower than in SKI and SK-III and their differences are at most 20% as shownin Table I. The estimated background rates of SK-I, SK-II,and SK-III are on the order of a few events and thedominant source of uncertainty is the MC statistical error
as described in Sec. VI B 2. For instance, the statisticalerror on the background in the KS0 ! þ  Method 2
search is 20%–40%.
The number of data and the expected background andsignal efficiencies at each step of the event selection arecompared for all four searches. For example, Fig. 12 shows
the KL0 search. After each event selection, the number ofremaining events in the data is consistent with the background expectation in each of the SK run periods. The
Poisson probability to observe the number of candidates
after all event selections for each search was calculated.
For example, the only probability smaller than 5% is seenin the SK-II Ks0 ! 0 0 search (2%). However, the number of candidates is smaller than the expected backgrounds
in SK-I and SK-III for this search. The sums of the expected backgrounds and the number of candidates from all
SK run periods for the KS0 and KL0 searches are 13.2 and 13,
respectively. They are consistent and therefore we conclude that there is no evidence for proton decay found in
this analysis.
All the candidate events in Table I were inspectedby hand. By checking event display with the reconstructed
information, all the events show sub-GeV (visible energy
is less than 1330 MeV) back-to-back rings and no obvious
misreconstruction. For example, Fig. 13 shows a typical real
data candidate event in the KL0 search. This event looks
consistent with the  background where the visible proton
is identified as the þ candidate ring (see Fig. 11).

TABLE I. Summary of the p ! þ K 0 search. Systematic errors are shown in the signal efficiencies and background rates(see Table II for more detail). The numbers in the parentheses of the background columns show the expected background rates inmegaton  years1 .
Detector (exposure)
SK-I (91:7 kton  years)

SK-II (49:2 kton  years)

SK-III (31:9 kton  years)

SK-I+SK-II+SK-III (172:8 kton  years)

Search method

Efficiency(%)

BackgroundKS0 ! 0 0
0
KS ! þ  Method 1
KS0 ! þ  Method 2
KL00
KS ! 0 0
0
KS ! þ  Method 1
KS0 ! þ  Method 2
KL00
KS !  0  0
0
KS ! þ  Method 1
KS0 ! þ  Method 2
KL0

7:0  0:5
10:6  1:0
2:5  0:2
3:8  0:7
6:2  0:7
10:3  1:2
2:4  0:2
3:3  0:6
6:7  0:7
10:3  1:8
3:0  0:2
3:8  0:7

0:37  0:05 (4:0  0:5)
3:0  0:5 (33  5)
0:12  0:08 (1:3  0:9)
3:5  1:1 (38  12)
0:20  0:05 (4:1  1:0)
1:6  0:4 (33  8)
0:23  0:08 (4:7  1:6)
1:4  0:5 (29  10)
0:19  0:04 (6:0  1:3)
1:2  0:2 (38  6)
0:09  0:02 (2:8  0:6)
1:3  0:6 (41  19)

Combined

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Lower limit
Candidate ( 1033 years)
0
6
0
2
2
0
1
0
0
1
0
1

0.92
0.42
0.32
0.30
0.19
0.71
0.11
0.21
0.30
0.32
0.14
0.11
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FIG. 12 (color online). The KL0 search: (upper plot) the signal
efficiencies along event selections are shown in SK-I, SK-II, and
SK-III from left to right, respectively [‘‘FV’’ stands for thenumber of p ! þ K 0 MC events generated in true fiducial
volume (22.5 kton). The events selected by the KS0 searches
are excluded]; (lower plot) the number of data candidates (black
circle) and the expected atmospheric neutrino background rate
(blue histogram) along event selections are shown in SK-I,
SK-II, and SK-III from left to right, respectively (‘‘FC’’ stands
for the FCFV events described in Sec. IV). Only statistical errors
are shown. There are no events remaining in the SK-II data after
selection (D6).

1. Lifetime limit
In the absence of significant excess of observed data
above the background expectation we calculate a lower
limit on the proton partial lifetime using a Bayesian
method [25]. The calculation used here follows the one
from the previous analysis [5].
The decay of the proton is assumed to follow a Poisson
probability, Pðjni Þ, and is expressed asPðjni Þ ¼

ZZZ eð i i þbi Þ ð i i þ bi Þni
ni !
 PðÞPð i ÞPð"i ÞPðbi Þd i d"i dbi ;where ni is the number of candidate events in the ith
proton decay search (i = 1, 2, 3, and 4 for KS0 ! 0 0 ,KS0 ! þ  Method 1, KS0 ! þ  Method 2, and KL0
searches, respectively, in SK-I, i ¼ 5–8 in SK-II, andi ¼ 9–12 in SK-III in Table I),  is the total decay rate,

FIG. 13 (color online). Typical event display of the real data
candidate event in the KL0 search in SK-I. The thick cyan ringshows the reconstructed ring edge of the þ candidate ring. The
blue triangle and solid green circle show the reconstructed vertex
position horizontally and vertically projected on the detector
wall for the þ and remaining particle candidates, respectively.
The reconstructed vertex separation for this event is 4.6 m. The
reconstructed Cherenkov angle is 30.6 while the expectationfrom the -like momentum (291 MeV=c) is 37.6.
i is the detector exposure, "i is the detection efficiency
including the meson branching ratio, and bi is the numberof expected background events. The probability density
function, PðÞ, describing the prior expectation of decayrate is taken to be PðÞ ¼ 1 for  > 0 and zero otherwise.
Introduction of systematic error effects is done throughprior probabilities for the detector exposure Pð i Þ, efficiency Pð"i Þ, and background expectation Pðbi Þ. They
are all assumed to be truncated Gaussian distributionsof the form8>
< exp  ðxi x20;i Þ2ðxi > 0Þ2xiPðxi Þ /ðxi ¼ i ; "i ; bi Þ;>:0ðxi  0Þ

where 0;i ( i ), "0;i ("i ), and b0;i (bi ) are the estimates(systematic errors) of the exposure, the detection efficiency, and the background, respectively. Here "0;i andb0;i correspond to the ith searches’ efficiency and background contamination, respectively. These values are summarized in Table I. The parameters "i and bi correspondto the total systematic error on the signal and backgroundcomposition for the ith search. Systematic error estimations are discussed in the next section and Table II summarizes the errors for each run period and search mode.
Finally, 0;i represents the detector exposure, taken to be
product of the number of target protons in the detector and012006-11

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TABLE II. Summary of systematic errors. The total systematic errors on the efficiency and background are shown in the third andfourth columns, respectively. The ‘‘physics’’ and ‘‘detector’’ in the parentheses represent the systematic errors from uncertainty of thephysics simulations and the SK detector, respectively.
Search method

Detector

Efficiency (%) total (physics, detector)

Background (%) total (physics, detector)

KS0 ! 0 0

SK-I
SK-II
SK-III
SK-I
SK-II
SK-III
SK-I
SK-II
SK-III
SK-I
SK-II
SK-III

7.5 (6.8, 3.2)
10.8 (6.8, 8.4)
10.0 (6.8, 7.4)
9.8 (8.8, 4.2)
11.6 (8.8, 7.6)
17.7 (8.9, 15.3)
7.5 (6.9, 2.8)
7.1 (6.9, 1.8)
7.9 (7.2, 3.4)
17.2 (9.6, 14.3)
19.2 (9.7, 16.6)
18.4 (9.4, 15.8)

14.2 (11.0, 9.2)
23.4 (11.5, 20.4)
19.1 (9.5, 16.5)
15.8 (15.2, 4.3)
22.8 (16.5, 15.8)
20.6 (16.2, 12.7)
63.7 (19.8, 60.5)
34.4 (12.7, 32.0)
24.6 (11.6, 21.7)
31.9 (9.9, 30.3)
38.9 (9.9, 37.6)
48.4 (9.4, 47.5)

KS0 ! þ  Method 1
KS0 ! þ  Method 2
KL0

the live time of each SK run. The corresponding uncertainty on the exposure,  i , is assumed to be 1%.
We calculate the lower limit of the nucleon decay rate,limit , using a 90% confidence level (CL) as
Rlimit QN
i¼1 Pðjni ÞdCL ¼ R¼0;
1 QN
i¼1 Pðjni Þd¼0
where Nð¼ 12Þ is the number of searches. The lower lifetime limit1
=Bp!þ K0 ¼
limitis set to be 1:6  1033 years at 90% CL. The result of thelimit calculation for each search method and data taking
period is shown in Table I.
2. Systematic error
Table II summarizes the systematic errors on the
KS0 ! 0 0 , KS0 ! þ  Method 1, KS0 ! þ 
Method 2, and KL0 searches, respectively.
As for the physics simulation, the following uncertainties are taken into account. In the signal efficiency, differences in the Fermi momentum modeling [8,19] anduncertainties in the correlated decay probability [5], theKL0 ! KS0 regeneration probability, as well as the charged
pion-nucleon cross section in water [5] are considered. The
dominant systematic error sources are correlated decay andthe pion-nucleon cross section. For the KL0 ! KS0 regeneration, the signal efficiencies for the default probability(about 0.1%) and about 0.2% or 0% (corresponding to100% error on the default probability) are comparedand difference of the efficiencies is used as the systematic
error (less than 1% for all the searches). Total physics
simulation errors are several percent in all four searches
in SK-I, SK-II, and SK-III. In the background rate, major
systematic error sources used in the SK atmospheric

neutrino data analyses [17], neutrino flux, neutrino
cross sections, and pion-nucleon interaction in oxygen,are taken into account and the total simulation errors areabout 10%–20%.
As for the SK detector, uncertainty of the event selection
cut value at each event selection step is considered as wellas the energy scale uncertainty. Any detector uncertainty
such as light attenuation and scattering in water is taken
into account in the systematic error estimations which
compare the cut efficiencies between control sample data
and MC. In the signal efficiency, the total detector errors
are several percent in the KS0 searches. In the KS0 ! 0 0
and KS0 ! þ  Method 1 searches, the errors in SK-III
are larger than those of SK-I by a factor of 2  3. The
larger errors in SK-III are due to its poorer water quality
which resulted in larger energy scale and ring counting
systematics. The total detector error in the KL0 search (a few
10%) is mostly due to the vertex separation. The vertex
separation error is estimated by changing the cut value
corresponding to the difference between true and reconstruction described in Sec. V. In the background rates, thedominant error (about 20%–60%) comes from statistics ofthe atmospheric neutrino events after all the event selections in the KS0 ! þ  Method 2 search. The otherdominant error (about 20%–40%) is from the vertex separation in the KL0 search.
C. Comparison with previous result
In this section we describe the differences between thepresent analysis and the previous result [5]. For the estimation of the signal efficiency the previous analysis only
considered the p ! þ KS0 channel while the present work
accounts for the entire p ! þ K0 channel including theKL0 contribution. This contribution coupled with improvements to the event reconstruction has resulted in an
efficiency increase from 5.4% to 7.0% in the KS0 ! 0 0012006-12

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PHYSICAL REVIEW D 86, 012006 (2012)

KS0 ! þ 

search and from 7.0% to 10.6% in the
Method 1 search. Signal efficiencies and the backgroundrates for the other searches are consistent within the systematic errors of the two analyses.
Similar systematic error sources are incorporated in bothanalyses. For instance, the error on the signal efficiencies isabout 10% in both. However, the systematic error on the
background rate in this analysis, ranging from 20% to 60%
across the searches, is improved over the previous work’s,
which ranged from 40% to 80%. Most of this improvement
is derived from the smaller statistical error on the atmospheric neutrino MC sample used in the present analysis.
If the KL0 search is excluded from the lifetime limit
computation and the data set restricted to the SK-I period,
the result is slightly worse than the previous analysis,
1:1  1033 years compared to 1:3  1033 years. Despite
the higher signal efficiencies and reduced systematic uncertainty on the expected background rates in this analysis, theincrease in the number of observed candidate events in the
KS0 ! þ  Method 1 search degrades the lifetime limit.
The three candidates found in the former analysis are also
found here, but three additional events that were previously
just outside of the signal region have now migrated in.
Under the older reconstruction, their momenta fell slightly
below the cut value of 250 MeV=c and thus failed to meet
condition (B4) from Sec. VI A. The improved reconstruction has increased their estimated momenta beyond thisthreshold. The þ candidate momentum reconstruction
has been checked using the atmospheric neutrino MC, andthe shift in the reconstructed momentum relative to the true
momentum and the momentum resolution are both smallerin the present work. The new result represents an improvement to the analysis.

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VII. CONCLUSIONThe SK p ! þ K 0 decay search presented in [5] hasbeen updated to include improved event reconstruction
algorithms and an additional 81:1 kton  years of data. A
search for proton decay into KL0 has also been added. Thereis no significant excess of proton decay candidates foundand the data remain consistent with the expected atmospheric neutrino background rates for both the p ! þ KS0
and p ! þ KL0 searches. Therefore a partial lifetime
lower limit is set at =Bp!þ K0 > 1:6  1033 years at the
90% confidence level using 172:8 kton  years of data.
The lifetime limits obtained by the KS0 and KL0 searches
alone are 1:37  1033 years and 0:55  1033 years, respectively. This result gives further constraints on relevant
SUSY GUT models.
ACKNOWLEDGMENTS
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 UnitedStates Department of Energy, and the U.S. National
Science Foundation. Some of us have been supported
by funds from the Korean Research Foundation (BK21),
the National Research Foundation of Korea (NRF20110024009), the State Committee for Scientific
Research in Poland (Grant No. 1757/B/H03/2008/35),
the Japan Society for the Promotion of Science, and the
National Natural Science Foundation of China under Grant
No. 10575056.

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