Astroparticle Physics 36 (2012) 131–136

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Astroparticle Physics
journal homepage: www.elsevier.com/locate/astropart

Search for GUT monopoles at Super–Kamiokande
K. Ueno a,⇑, K. Abe a,b, Y. Hayato a,b, T. Iida a, K. Iyogi a, J. Kameda a,b, Y. Koshio a,b, Y. Kozuma a, M. Miura a,b,
S. Moriyama a,b, M. Nakahata a,b, S. Nakayama a,b, Y. Obayashi a,b, H. Sekiya a,b, M. Shiozawa a,b,
Y. Suzuki a,b, A. Takeda a,b, Y. Takenaga a, K. Ueshima a, S. Yamada a,b, T. Yokozawa a, K. Martens b,
J. Schuemann b, M. Vagins b,e, C. Ishihara c, H. Kaji c, T. Kajita c, K. Kaneyuki c, T. McLachlan c, K. Okumura c,Y. Shimizu c, N. Tanimoto c, E. Kearns d,b, M. Litos d, J.L. Raaf d, J.L. Stone d,b, L.R. Sulak d, K. Bays e,
W.R. Kropp e, S. Mine e, C. Regis e, A. Renshaw e, M.B. Smy e,b, H.W. Sobel e, K.S. Ganezer f, J. Hill f,
W.E. Keig f, J.S. Jang g, J.Y. Kim g, I.T. Lim g, J.B. Albert h, K. Scholberg h,b, C.W. Walter h,b, R. Wendell h,T. Wongjirad h, T. Ishizuka i, S. Tasaka j, J.G. Learned k, S. Matsuno k, T. Hasegawa l, T. Ishida l, T. Ishii l,T. Kobayashi l, T. Nakadaira l, K. Nakamura l, K. Nishikawa l, Y. Oyama l, K. Sakashita l, T. Sekiguchi l,
T. Tsukamoto l, A.T. Suzuki m, Y. Takeuchi m,b, M. Ikeda n, A. Minamino n, T. Nakaya n, L. Labarga o,
Ll. Marti o, Y. Fukuda p, Y. Itow q, G. Mitsuka q, T. Tanaka q, C.K. Jung r, G. Lopez r, I. Taylor r,
C. Yanagisawa r, H. Ishino s, A. Kibayashi s, S. Mino s, T. Mori s, M. Sakuda s, H. Toyota s, Y. Kuno t,
M. Yoshida t, S.B. Kim u, B.S. Yang u, H. Okazawa v, Y. Choi w, K. Nishijima x, M. Koshiba y, Y. Totsuka y,
M. Yokoyama y,b, S. Chen z, Y. Heng z, Z. Yang z, H. Zhang z, D. Kielczewska aa, P. Mijakowski aa,
K. Connolly ab, M. Dziomba ab, E. Thrane ab, R.J. Wilkes ab, The Super-Kamiokande CollaborationaKamioka Observatory, Institute for Cosmic Ray Research, The University of Tokyo, Kamioka, Gifu 506-1205, Japan
Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo, Kashiwa, Chiba 277-8583, Japanc
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa, Chiba 277-8582, Japand
Department of Physics, Boston University, Boston, MA 02215, USAe
Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USAf
Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USAg
Department of Physics, Chonnam National University, Kwangju 500-757, Republic of KoreahDepartment of Physics, Duke University, Durham, NC 27708, USAi
Junior College, Fukuoka Institute of Technology, Fukuoka 811-0214, Japanj
Department of Physics, Gifu University, Gifu 501-1193, Japank
Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USAlHigh Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japanm
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japann
Department of Physics, Kyoto University, Kyoto 606-8502, Japano
Department of Theoretical Physics, University Autonoma Madrid, Madrid 28049, Spainp
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japanq
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japanr
Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794-3800, USAs
Department of Physics, Okayama University, Okayama 700-8530, Japant
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japanu
Department of Physics, Seoul National University, Seoul 151-742, Republic of Korea
v
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka 425-8611, Japanw
Department of Physics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
x
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japany
The University of Tokyo, Tokyo 113-0033, Japanz
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
aa
Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Polandab
Department of Physics, University of Washington, Seattle, WA 98195-1560, USAb⇑ Corresponding author.
E-mail address: ueno@suketto.icrr.u-tokyo.ac.jp (K. Ueno).
0927-6505/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.astropartphys.2012.05.008

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K. Ueno et al. / Astroparticle Physics 36 (2012) 131–136

a r t i c l e

i n f oa b s t r a c t

Article history:
Received 8 March 2012
Received in revised form 10 May 2012
Accepted 24 May 2012
Available online 2 June 2012

GUT monopoles captured by the Sun’s gravitation are expected to catalyze proton decays via the Callan–
Rubakov process. In this scenario, protons, which initially decay into pions, will ultimately produce me ; mll . After undergoing neutrino oscillation, all neutrino species appear when they arrive at the Earth,and mand can be detected by a 50,000 metric ton Water Cherenkov detector, Super–Kamiokande (SK). A search
for low energy neutrinos in the electron total energy range from 19 to 55 MeV was carried out with SK
and gives a monopole ﬂux limit of FM ðr0 =1 mbÞ < 6:3  1024 ðbM =103 Þ2 cm2 s1 sr1 at 90% C.L., wherebM is the monopole velocity in units of the speed of light and r0 is the catalysis cross section at bM ¼ 1.
The obtained limit is several orders of magnitude more stringent than the current best cosmic-ray supermassive monopole ﬂux limit for bM < 102 and also two orders of magnitude lower than the result of the
Kamiokande experiment, which used a similar detection method.
Ó 2012 Elsevier B.V. All rights reserved.

Keywords:
GUT monopole
Neutrino
Water Cherenkov detector

1. Introduction
Grand Uniﬁed Theories (GUTs) predict superheavy magnetic
monopoles (GUT monopoles) produced in the very early universe[1,2]. GUT monopoles are predicted to have appeared as topologicaldefects at the phase transition of vacuum, where the GUT gauge
group spontaneously broke to leave the U(1) of electromagnetism.
If we take as an example the temperature of the phase transition atwhich the monopoles were formed to equal 1015 GeV and assume
the average production rate of about one monopole per horizon
at that time [3], the density of the monopoles today would exceed
the critical density of the universe by more than 14 orders of magnitude. Even if we circumvent this problem by resorting to inﬂationary universe scenarios [4,5], we cannot avoid a large
uncertainty on the monopole ﬂux in the universe since the ﬂux depends on such parameters as monopole mass and the reheating
temperature. In fact, due to the wide variety of elementary particle
models, several models are compatible with the level of the Parker
bound ( 1015 cm2 s1 sr1 ) [6–9], and a ﬂux in that range can be
relatively easily detected by underground experiments. Arafune
and Fukugita et al. [10] pointed out that copious low energy neutrinos might be emitted when monopoles accumulating inside theSun catalyze proton decays,
0

þ

þ

þ

p ! ðq ; x; g; K ; . . .Þ þ e ðor l Þ

ð1Þ

along their paths with cross sections typical of strong interactions
via the Callan–Rubakov process [11,12]. When decay mesons produced by the above process subsequently decay into positive pions,l are produced1 by the(ðq0 ; x; g; K þ ; . . .Þ ! pþ ), me ; ml and mreactions,pþ ! lþ þ ml
lþ ! eþ þ me þ ml :

ð2Þ
ð3Þ

After undergoing neutrino oscillation, all neutrino species arepresent when they arrive at the Earth (Fig. 1), and such neutrinos
can be detected by a Water Cherenkov detector. Throughout thispaper, the neutrinos and antineutrinos are assumed to oscillate22with the same parameters of sin h12 ¼ 0:31; sin h13 ¼ 0:02 and5
2
2
Dm21 ¼ 7:6  10 eV [13]. The uncertainties of the mixing angles
are taken into account in the systematic errors.
2. Detector and expected signal
We searched for monopole-induced neutrinos using Super–
Kamiokande (SK) [14], a large Water Cherenkov detector located in1
Under the assumption that monopoles are accumulated in the center of the Sun,
pions decaying in ﬂight are negligible due to the high density of hydrogen in the Sun.

side Japan’s Kamioka mine. SK is a high-performance neutrino
detector consisting of 50,000 metric tons of pure water. Since there
are c-ray backgrounds near the wall, the ﬁducial volume for thissearch, which amounts to 22,500 metric tons, is deﬁned to be morethan two meters from the walls of the inner detector (ID).
Monopole-induced neutrinos include all six types, and so for themonopole-induced neutrino search both electron elastic scattering,mx ðmx Þ þ e ! mx ðmx Þ þ e , and inverse beta decay, me þ p ! eþ þ n,were assumed to contribute. Fig. 2 shows the expected spectra ofelastic scattering recoil electrons and inverse beta decay positronsin SK. The Mikheyev–Smirnov–Wolfenstein (MSW) effects [15] on
oscillation in both the Sun and the Earth were also taken into account. We adopted a simple approximate analytic formula presented in Ref. [16] for the calculation of the MSW effects andassumed the adiabaticity condition is fulﬁlled, i.e., the densitychanges so slowly inside the Sun and the Earth that the neutrinomass eigenstates propagate independently. The density proﬁles of
the Sun and the Earth were taken from Refs. [17,18], respectively.

3. Data reduction
In this analysis, we used 2853 live days of data consisting of SK-I
(Apr. 1996 - Jul. 2001: 1497.4 days), SK-II (Oct. 2002 - Oct. 2005:
793.7 days) and SK-III (Jul. 2006 - Aug. 2008: 562.0 days). In SK-II
the energy resolution was worse because the number of photomultiplier tubes (PMTs) was about half as many as those in the otherphases. This difference in detector geometry was taken into accountin the calculation of the expected spectra. However, as previously
demonstrated by the SK solar neutrino analysis [19], the broad energy spectra typical of monopole-induced neutrinos are hardly affected by the resolution.
The background events of the monopole-induced neutrino
events are mainly caused by the atmospheric neutrinos, the solar
neutrinos and muon-induced spallation products. To reduce thespallation products and the solar neutrino events, we set the lower
energy thresholds to 19 MeV for SK-I and III, and 20 MeV for SK-II inthis analysis.2 The upper energy threshold was set to 55 MeV, which
was determined by the end-point of the recoil electron (or positron)
spectrum (Fig. 2).
Besides setting the ﬁducial volume and energy criteria, some
additional background cuts were applied to the data. After the
event selection that removes cosmic ray muons and detector noise
events, the data sample is subjected to a spallation cut. Cosmic-ray
2
In the SK solar neutrino analysis, we reconstruct the event energy assuming all
Cherenkov photons in an event come from a single electron, and we deﬁne ‘‘energy’’ as
the total energy (not the kinetic energy) of the electron. Throughout this paper, we use
this deﬁnition.

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K. Ueno et al. / Astroparticle Physics 36 (2012) 131–136

Arbitrary Unit

10

2

10
–

νh
νh

1

10

νe

–

νe

-1

10

20

30

40

50

60

tern. Events having two or more Cherenkov rings were also
removed.
The remaining backgrounds include low energy muons produced by atmospheric ml charged current (CC) interactions andtheir decay electrons. Those events are removed using time andspatial correlations; any event pairs having a time difference anda spatial distance less than 50 ls and 500 cm, respectively, were removed. In case the candidate event is the second one in a pair, weremoved event pairs with the ﬁrst events having total photo-electrons (p.e.) more than 1000 p.e. for SK-I and III, and 500 p.e. for
SK-II, which correspond to 90  100 MeV electron equivalent energy. Although this selection (decay electron cut) removes somefraction of the atmospheric neutrino events, there still remain decay electrons which are not accompanied by nuclear de-excitation
c-rays, and whose parent muons are invisible because their energies are below Cherenkov threshold. Those background events are
distinguished from the signal events using angular correlation with
the Sun direction, which will be described later.

Neutrino energy (MeV)
4. Analysis and results
Fig. 1. Expected neutrino spectra at the SK detector. These are an analyticalevaluation, which includes neutrino oscillation effects. l; s components are collectively denoted as h since these two ﬂavors of neutrinos have identical cross sections
for electron scattering. The spikes at 29.79 MeV originate from ml produced by thetwo-body decay of pþ in Eq. (2), which also oscillates into me .

muons can spall oxygen and create unstable nuclei called spallation
products (l þ 16 O ! l þ X). This is one of the most abundant backgrounds in the K 20 MeV region, and as mentioned above, the ability to remove the background events mostly determines the lower
threshold for the monopole-induced neutrino search. The spallation
background events are further reduced by a likelihood method thatuses timing, position and photo-electron information of the muonspreceding the candidate events.
Then, we applied the Cherenkov opening angle cut to theremaining data sample. The opening angle is estimated by histogramming all the angles uniquely determined by the reconstructedvertex and the possible combinations of three hit PMTs. The histogram is divided into 100 angle bins and the peak is located by ﬁnding the successive seven bins with the largest number of entries.
The angle corresponding to the midpoint of the seven bins is regarded as the Cherenkov angle of the event. Most of the remaining
visible atmospheric (anti-)muon neutrino events are removed bythis cut. Electrons with E > 18 MeV have a Cherenkov angle hC of
about 42 , while visible muons remaining in the signal energy
range have momenta less than  250 MeV/c, which corresponds
to the maximum hC value of 36 . Thus, taking into account the ﬁnite
resolution of the Cherenkov angle measurements, events withhC < 38 were removed. Also we removed events with hC > 50 .
Those events do not have a clear Cherenkov ring pattern and originate from multiple c-rays emitted by excited nuclei created inneutral current (NC) interactions of atmospheric neutrinos.
Some events originating from the outside of the ﬁducial volume
are reconstructed within the ﬁducial volume of SK. These events are
c-rays from the materials of the detector structure and the surrounding rock. To remove such events, we cut on the event’s distance to the ID wall projected backwards from its vertex position
along its reconstructed direction. Events with this distance lessthan 300 cm were removed (c-ray cut [19]).3
We removed charged p background events based on the sharpness of the Cherenkov ring pattern. As a charged p interacts with oris absorbed by a nucleus and is less inﬂuenced by multiple Coulomb
scattering than electrons, it generates a sharp Cherenkov ring pat-3

Additionally, energy-dependent cut criteria were also applied.

The numbers of events remaining after each selection step aresummarized in Table 1. We found 317 candidate events in the ﬁnal
data sample. Three types of background events are considered.
The ﬁrst dominant source of background events are decay electrons from invisible muons induced by the atmospheric (anti-)
muon neutrinos. The second such source are electrons generated
by the atmospheric (anti-)electron neutrinos, while the third are
the multiple nuclear de-excitation c-rays produced by NC interactions of the atmospheric neutrinos.
The remaining spallation events are estimated to be 4:7  4:3
events in SK-I/III and 0:2  1:7 events in SK-II using the likelihood
distribution.
The number of remaining solar neutrino events is estimated to
be one from a separate MC simulation.
To extract the signal events, an angular distribution with respect
to the Sun direction is used. Fig. 3 shows the cos hSun distribution of
the 317 candidates, where hSun is the angle of the candidate event
direction with respect to the expected neutrino direction calculated
from the position of the Sun at the event time. To ﬁt the distribution, we use a v2 deﬁned in Eq. (4):v2 ðI0 ; aÞ 

20
X
fNobs;i  Nme;i ðI0 Þ  N mp;i ðI0 Þ  aNbkg;i g2
i¼1

r2stat;i þ r2sys;i;

ð4Þwhere we use Nobs;i as the observed number of events in the ith
angular bin. N me;i ðI0 Þ and N mp;i ðI0 Þ are the expected signal events fromelectron scattering and inverse beta decay in the ith bin, where I0 is
the total ﬂux of all ﬂavors of monopole-induced neutrinos in units ofcm2 s1 (Fig. 4). The theoretical calculation of the angular distribution of the inverse beta decay is from Ref. [20]. The systematic errors
used in the v2 function (rsys;i ¼ const:) are summarized in Table 2.
N bkg;i is the area-normalized background events for the ith bin.
We determine the N bkg;i values using the ﬁnal data sample byapplying an iterative procedure (described in Appendix) to remove
a possible bias caused by the solar-correlated events. The factor arepresenting the background normalization is determined so thatthe v2 value is minimized for each I0 value. In the ﬁt, we restricta P 0. As a result of the ﬁt, we obtain I0 ¼ 102  64 cm2 s1 , corresponding to a 1.6 r excess.
We determine the 90% C.L. upper limit ﬂux I90 by using the following equation:



R I90
exp v2 ðI0 Þ=2 dI0
R01¼ 0:9:
exp ðv2 ðI0 Þ=2ÞdI0
0

ð5Þ

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K. Ueno et al. / Astroparticle Physics 36 (2012) 131–136

5

-

νe+e

Events / MeV / year / 22.5 kton

Events / MeV / year / 22.5 kton

0.16
0.14
0.12
0.1
0.08

νh+e

0.06
–

νh+e

0.04
0.02
0

–

-

-

-

νe+e
0

10

20

30

40

50

4

3
–

νe + p
2

1

0

60

0

10

Electron total energy (MeV)

20

30

40

50

60

Positron total energy (MeV)

Fig. 2. Expected energy spectra of elastic scattering recoil electron (left) and inverse beta decay positron (right) in SK assuming neutrino ﬂux of 3:0  102 cm2 s1 without
energy resolution included. The discontinuity of some spectra at 29.79 MeV is caused by the spikes shown in the expected neutrino energy spectra in Fig. 1. h represents l ands components.

Table 1
Summary of the number of remaining events and the cut signal efﬁciency for electron
scattering and inverse beta decay after each selection.

Energy range cut,
Fiducial volume cut,
Noise event rejection
Spallation event cut
Cherenkov opening angle cut
c-ray cutPion-like event cut
Multi-ring cut
Decay electron cut



Data

Detection eff.
(m + e)Detection eff.
e + p)
(m

2108

0.99

0.99

1774
759
738
705
686
317

0.91
0.86
0.83
0.81
0.81
0.81

0.98
0.93
0.90
0.88
0.87
0.87


Fig. 5 shows the exp v ðI0 Þ=2 distribution as a function of I0 ,where the normalization is scaled so that the maximum value becomes one. We obtain I90 ¼ 166:6 cm2 s1 . Fig. 3 shows thecos hSun distribution superimposed with curves representing
I0 ¼ I90 and I0 = 0. We obtain a v2 ðI0 ¼ 0Þ value of 20.02 compared
to 19 degrees of freedom, which corresponds to a probability of
39.3% and is therefore consistent with a hypothesis of null signal
in the ﬁnal data sample.
The monopole-catalyzed proton decay rate fp in the Sun is given
by,

fp ¼

Z

Events / bin / 2853 days / 22.5 kton

Cut

35

2

SK-I/II/III 2853 days

30
25
20
15
10
SK-I/II/III data
background shape
90% CL limit

50-1 -0.8 -0.6 -0.4 -0.2 0

0.2 0.4 0.6 0.8

1

cos θSun
Fig. 3. Angular distributions with respect to the expected neutrino direction fromthe Sun. The points with error bars show the data events. The solid histogram
represents the ﬁtting result when the monopole-induced neutrino ﬂux is equatedwith the 90% C.L. upper limit obtained in this analysis, and the dashed one the result
when only background is used for the ﬁtting.
2

3

nM v rel rqp NA d x decays=s;ð6Þ

where nM is the monopole number density, v rel ¼ brel c the relative
velocity between the monopole and the proton, r ¼ r0 =b2rel (r0 
1 mb) the catalysis cross section [11,12,22], qp the proton mass density, and NA Avogadro’s number (6:0  1023 ). The space integral is taken over the interior of the Sun. Helium gives a negligible
contribution [22]. If we assume the monopoles are accumulated in
the center of the Sun where qp ¼ 50 g=cm3 and brel ¼ 1:7  103 ,4
we obtain fp ¼ 1:7  106 ðr0 =1 mbÞNM , where NM is the integrated
number of monopoles in the region. The rate fp is given by4
We take v rel as the thermal velocity of proton in the center of the Sun,brel c ¼ ð2kB T c =mp Þ1=2 ’ 1:7  103 m/s, where kB is the Boltzmann constant,T c ¼ 1:5  107 K is the temperature at the center of the Sun, and mp ¼ 0:938 GeV isthe proton mass.

fp ¼ 4pd I0 =3=fme , where d ¼ 1:5  1013 cm is the distance between
the Sun and the Earth. The factor three takes into account the factthat three neutrinos are emitted per proton decay. fme ¼ fpþ ð1  apþ Þis the fraction of me produced in a proton decay, where fpþ is thebranching fraction of a proton decay into pþ þ anything, and is about
0.5 for some GUT models. The factor apþ ¼ 0:2 is the absorption probability of pþ at the center of the Sun [10]. Using the I90 value, we obtain an upper limit on NM at the 90% C.L.:

NM

 r

0

 f þ 

1 mb

p

0:5

< 7:1  1017 ð90%C:L:Þ:ð7Þ

The monopole ﬂux is calculated from the following equation by
assuming monopole-antimonopole annihilation is negligible:

NM ¼ pR2 1 þ


2 !
besc
ðMM ; bM Þ4pF M t ;
bM

ð8Þ

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K. Ueno et al. / Astroparticle Physics 36 (2012) 131–136

MC for SK-I/II/III

Events / bin / 2853 days / 22.5 kton

Events / bin / 2853 days / 22.5 kton

80
14
12
10
8
6
4
2
0

-1 -0.8 -0.6 -0.4 -0.20

0.2 0.4 0.6 0.8

MC for SK-I/II/III
70
60
50
40
30
20
10
0

1

-1 -0.8 -0.6 -0.4 -0.2

cos θSun0

0.2 0.4 0.6 0.8

1

cos θSun

Fig. 4. Expected angular distributions of elastic scattering recoil electrons (left) and inverse beta decay positrons (right) assuming a monopole-induced neutrino ﬂux of
3:0  102 cm2 s1 and the detection efﬁciency of the cuts.

Table 2
Systematic errors (%) used in the v2 function. The systematic error on the crosssection of inverse beta decay is from Ref. [21].
Error source

SK-I (%)

Cross section
Neutrino propagation
Reduction efﬁciency
Fiducial volume
Livetime
Total

SK-II (%)

0.4
5.0
2.3
1.3
0.1
5.7

0.4
5.0
3.8
1.1
0.1
6.4

SK-III (%)
0.4
5.0
2.1
1.0
0.1
5.6

1.2

0.8

2

∝ exp(-χ (I0)/2)

1

0.6

0.4

0.2

I90
0

0

25

50

on the monopole mass MM and velocity bM . We estimate ðMM ; bM Þ
based on the calculation of the energy loss of a monopole inside theSun from Refs. [23,24]. From (7) and (8), we obtain for bM < 103FM

 r  f þ 
0
p
< 6:3
1mb 0:5 1024



bM

103

2

cm2 s1 sr1 ð90% C:L:Þ:ð9Þ

This limit is only valid for MM K 1017 GeV since ðMM ; bM Þ decreases
as the monopole mass increases and becomes signiﬁcantly less than
1 for higher monopole masses.
Our result is presented in Fig. 6. Also shown are monopole ﬂux
limits obtained by various recent direct detection experiments:[25–28], Kamioka track etch [29], Mica [30] and the MACRO ﬁnal
result [31], as well as ones from indirect detection experiments:
the Parker bound [6], limits from neutron star observations [32],and the Kamiokande experimental results [33,34]. As seen in theﬁgure, our new limit is many orders of magnitude more stringent
than those of the direct experiments and is also two orders ofmagnitude lower than the result of the Kamiokande experiment[33,34], which used a similar detection method. This is mainly because SK is a larger detector and the background events are subtracted effectively using angular distributions. The present limit islower than the one obtained from the X-ray excess of old neutronstars,

FM

 r 
0

1mb

< 3r  1023 cm2 s1 sr1 ;ð10Þ

75 100 125 150 175 200 225-2-1

I0 (cm s )Fig. 5. Likelihood function as a function of monopole-induced neutrino ﬂux (I0 ),which is deﬁned as proportional to exp v2 ðI0 Þ=2 . The dashed line represents the
90% C.L. limit on I0 . The deviation from the Gaussian shape beyond
I0 ¼ 183:4 cm2 s1 is due to the restriction of a P 0.

where besc ¼ 2  103 and bM are the escape velocity and the monopole velocity in units of the speed of light, respectively, R is the solar radius (7:0  1010 cm) and t  the elapsed time after the birth of
the Sun (4:6  109 yr). ðMM ; bM Þ is the efﬁciency with which the
Sun captures monopoles that strike its surface, which is dependent

where bM is 103 and r is the ratio of the total luminosity to the photon luminosity of old neutron stars. The value of r varies from 1 to
104 , where r  1 corresponds to the conventional neutron star equations of state while large values of r correspond to the possibility of apion condensate5 or quark matter core [32]. brel in old neutron stars
is of order of 0:1  0:3. Therefore, our limit is better than the neutronstar limit even in the most stringent case. Finally, we emphasize that
this result also provides constraints on the parameter space of inﬂation models as suggested in Refs. [7–9].
5
If there is a pion condensate in a neutron star, its total luminosity is dominated by‘ andneutrinos generated in the following reactions: p þ n ! n þ ‘ þ mn þ ‘ ! n þ p þ m‘ , where ‘ ¼ e or l.

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K. Ueno et al. / Astroparticle Physics 36 (2012) 131–136

We thank F. Vissani for providing to us the angular distribution of
the inverse beta decay positrons.

-12

10
-13

10

Appendix A. Estimation of {N bkg;i }UCSD II-14

10
Soudan-2-15Parker Bound

10

Kolar
BaksanKamioka (Track Etch)
MACRO (2002)

-17

10
Mica

-2

-18

10
-19

10
Ka Ka
Ne
Ne
mi mi
u
utr
ok ok
r-K tron
on
an an
am
St
St
d
d
ar
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iok ar (
(pi
co
II (
(27
an
on
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31
de
4
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e
9
co
d
-I/I
nti
da ays
nd
I/II
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ys
)
en
al
I (2
)
sa
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85
te)
3 d uati
on
ay
so
s)
fs
tat
e)

-1

-1

Flux upper limit (90% C.L.) (cm s sr )

-16

10

-20

10
-21

10
-22

10
-23

10
-24

10
-25

10

References

Su

pe

-26

10
-27

10
-5

10

-4

10

-3

10

βM

Although the background shape in the angular distribution withrespect to the direction of the Sun is expected to be almost isotropic, we tried rejecting directional biases including those caused bysolar-correlated events remaining in the ﬁnal data sample, which
will distort the cos hSun distribution.
We deﬁne Nﬁn as the number of the ﬁnal candidates in each SK
phase and prepare event direction vectors, di , and solar direction
vectors, sj for the ﬁnal sample (i; j ¼ 1; . . . ; Nfin ). Then, the angle
with respect to the direction of the Sun of the ith event is expressed
as cos hSun;i ¼ di si .
First we ﬁll the Nfin ðNfin  1Þ=2 possible combinations ofdi sj (i – j) into a histogram h1 , and ﬁt h1 with a polynomial
f1 ðxÞ; x 2 ½1; 1 . Also, we ﬁt the actual true cos hSun distribution
with another polynomial cðxÞ.
Then we ﬁll the Nfin ðNfin  1Þ=2 combinations of di sj (i – j) intoanother histogram h2 with weights of w1 ðdi sj Þ  f1 ðdi si Þ=cðdi si Þ.
Again we ﬁt h2 with another polynomial f2 ðxÞ.
Usually, fi ðxÞ; wi and hi sufﬁciently converge after several iterations of the above procedure. In this way, we eliminate the bias
from solar-correlated events in the limit that fi ðxÞ describes the histogramed distribution.

-2

10

-1

10

1

Fig. 6. 90% C.L. upper limits on the monopole ﬂux as a function of monopole velocity,bM . Each ﬂux limit is referenced in the text. Catalysis cross section (r0 =1 mb) andmonopole mass (MM ¼ 1016 GeV) are assumed for indirect searches.

5. Conclusion
A search for monopole-induced neutrinos from the Sun in theelectron total energy range from 19 to 55 MeV was carried out using
a data sample of 2853 days’ livetime and 22,500 metric tons ﬁducial
volume. We found no signal events and set the 90% conﬁdence level
limit on the monopole ﬂux: FM ðr0 =1mbÞ < 6:3  1024 ðbM =103 Þ2
cm2 s1 sr1 . Our result provides the world’s most stringent upper
limit for bM < 102 .

Acknowledgments
We gratefully acknowledge the cooperation of Kamioka Mining
and Smelting Company. The Super–Kamiokande experiment was
built and has been operated with funding from the Japanese Ministry of Education, Culture, Sports, Science and Technology, the United States Department of Energy, the U.S. National Science
Foundation, and the National Natural Science Foundation of China.
This work was supported by a Grant-in-Aid for Scientiﬁc Research.

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