PHYSICAL REVIEW D 102, 072002 (2020)

Indirect search for dark matter from the Galactic Center and halowith the Super-Kamiokande detector
K. Abe,1,44 C. Bronner,1 Y. Haga,1 Y. Hayato,1,44 M. Ikeda,1 S. Imaizumi,1 H. Ito,1 K. Iyogi,1 J. Kameda,1,44 Y. Kataoka,1
Y. Kato,1 Y. Kishimoto,1,44 Ll. Marti,1 M. Miura,1,44 S. Moriyama,1,44 T. Mochizuki,1 Y. Nagao,1 M. Nakahata,1,44
Y. Nakajima,1,44 T. Nakajima,1,44 S. Nakayama,1,44 T. Okada,1 K. Okamoto,1 A. Orii,1 G. Pronost,1 H. Sekiya,1,44
M. Shiozawa,1,44 Y. Sonoda,1 A. Takeda,1,44 A. Takenaka,1 H. Tanaka,1 S. Tasaka,1 T. Tomura,1,44 K. Ueno,1 T. Yano,1
T. Yokozawa,1 R. Akutsu,2 S. Han,2 T. Irvine,2 T. Kajita,2,44 I. Kametani,2 K. P. Lee,2 T. McLachlan,2 K. Okumura,2,44
E. Richard,2 T. Tashiro,2 R. Wang,2 J. Xia,2 D. Bravo-Berguño,3 L. Labarga,3 P. Fernandez,3 F. d. M. Blaszczyk,4J. Gustafson,4 C. Kachulis,4 E. Kearns,4,44 J. L. Raaf,4 J. L. Stone,4,44 L. R. Sulak,4 S. Sussman,4 L. Wan,4 T. Wester,4S. Berkman,5 S. Tobayama,5 J. Bian,6 G. Carminati,6 M. Elnimr,6 N. J. Griskevich,6 W. R. Kropp,6 S. Locke,6 S. Mine,6
A. Renshaw,6 M. B. Smy,6,44 H. W. Sobel,6,44 V. Takhistov,6,* P. Weatherly,6 B. L. Hartfiel,7 J. Hill,7 W. E. Keig,7 N. Hong,8
J. Y. Kim,8 I. T. Lim,8 R. G. Park,8 T. Akiri,9 B. Bodur,9 A. Himmel,9 Z. Li,9 E. O’Sullivan,9 K. Scholberg,9,44
C. W. Walter,9,44 T. Wongjirad,9 A. Coffani,10 O. Drapier,10 S. El Hedri,10 A. Giampaolo,10 M. Gonin,10 J. Imber,10
Th. A. Mueller,10 P. Paganini,10 B. Quilain,10 T. Ishizuka,11 T. Nakamura,12 J. S. Jang,13 K. Choi,14 J. G. Learned,14
S. Matsuno,14 S. N. Smith,14 J. Amey,15 L. H. V. Anthony,15 R. P. Litchfield,15 W. Y. Ma,15 A. A. Sztuc,15 Y. Uchida,15
M. O. Wascko,15 V. Berardi,16 M. G. Catanesi,16 R. A. Intonti,16 E. Radicioni,16 N. F. Calabria,17 L. N. Machado,17
G. De Rosa,17 G. Collazuol,18 F. Iacob,18 M. Lamoureux,18 N. Ospina,18 L. Ludovici,19 T. Boschi,20,† F. Di Lodovico,20
S. Molina Sedgwick,20,† S. Zsoldos,20 Y. Nishimura,21 S. Cao,22 M. Friend,22 T. Hasegawa,22 T. Ishida,22 T. Ishii,22T. Kobayashi,22 T. Nakadaira,22 K. Nakamura,22,44 Y. Oyama,22 K. Sakashita,22 T. Sekiguchi,22 T. Tsukamoto,22 KE. Abe,23
M. Hasegawa,23 Y. Isobe,23 H. Miyabe,23 Y. Nakano,23 T. Shiozawa,23 T. Sugimoto,23 A. T. Suzuki,23 Y. Takeuchi,23,44
S. Yamamoto,23 A. Ali,24 Y. Ashida,24 T. Hayashino,24 T. Hiraki,24 S. Hirota,24 K. Huang,24 K. Ieki,24 M. Jiang,24
T. Kikawa,24 M. Mori,24 A. Murakami,24 KE. Nakamura,24 T. Nakaya,24,44 N. D. Patel,24 K. Suzuki,24 S. Takahashi,24
K. Tateishi,24 R. A. Wendell,24,44 N. McCauley,25 P. Mehta,25 A. Pritchard,25 K. M. Tsui,25 Y. Fukuda,26 Y. Itow,27,28
H. Menjo,27 G. Mitsuka,27 M. Murase,27 F. Muto,27 T. Niwa,27 K. Sato,27 T. Suzuki,27 M. Taani,27,‡ M. Tsukada,27
P. Mijakowski ,29 K. Frankiewicz,29 J. Hignight,30 C. K. Jung,30 X. Li,30 J. L. Palomino,30 G. Santucci,30 C. Vilela,30
M. J. Wilking,30 C. Yanagisawa,30,§ D. Fukuda,31 K. Hagiwara,31 M. Harada,31 T. Horai,31 H. Ishino,31 S. Ito,31 T. Kayano,31
A. Kibayashi,31 Y. Koshio,31,44 W. Ma,31 T. Mori,31 H. Nagata,31 N. Piplani,31 M. Sakuda,31 S. Seiya,31 Y. Takahira,31
C. Xu,31 R. Yamaguchi,31 Y. Kuno,32 G. Barr,33 D. Barrow,33 L. Cook,33,44 C. Simpson,33,44 D. Wark,33,39 F. Nova,34
R. Tacik,35,48 J. Y. Yang,36 A. Cole,37 S. J. Jenkins,37 J. McElwee,37 M. Thiesse,37 L. Thompson,37 H. Okazawa,38
S. B. Kim,40 Y. Choi,40 K. Ito,41 K. Nishijima,41 K. Iwamoto,42 M. Koshiba,42 Y. Suda,43 M. Yokoyama,43,44
R. G. Calland,44 A. Goldsack,44,33 K. Martens,44 M. Murdoch,44 Y. Suzuki,44 M. R. Vagins,44,6 D. Hamabe,45 M. Kuze,45
Y. Okajima,45 M. Tanaka,45 T. Yoshida,45 M. Inomoto,46 M. Ishitsuka,46 R. Matsumoto,46 K. Ohta,46 M. Shinoki,46
J. F. Martin,47 C. M. Nantais,47 H. A. Tanaka,47 T. Towstego,47 M. Hartz,48 A. Konaka,48 P. de Perio,48 N. W. Prouse,48
S. Chen,49 B. D. Xu,49 Y. Zhang,49 B. Richards,50 K. Connolly,51 R. J. Wilkes,51 B. Jamieson,52 J. Walker,52 P. Giorgio,53
A. Minamino,53 K. Okamoto,53 and G. Pintaudi53(The Super-Kamiokande Collaboration)
1

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,
Kamioka, Gifu 506-1205, Japan
2
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo,
Kashiwa, Chiba 277-8582, Japan3
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
4
Department of Physics, Boston University, Boston, Massachusetts 02215, USA
5
Department of Physics and Astronomy, University of British Columbia,
Vancouver, British Columbia V6T1Z4, Canada
6
Department of Physics and Astronomy, University of California,
Irvine, Irvine, California 92697-4575, USA
7
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
8
Institute for Universe and Elementary Particles, Chonnam National University, Gwangju 61186, Korea
9
Department of Physics, Duke University, Durham, North Carolina 27708, USA
10
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France
11
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan

2470-0010=2020=102(7)=072002(14)072002-1

Published by the American Physical Society

K. ABE et al.

PHYS. REV. D 102, 072002 (2020)
12

Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
GIST College, Gwangju Institute of Science and Technology, Gwangju 61005, Korea
14
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
15
Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
16
Dipartimento Interuniversitario di Fisica, INFN Sezione di Bari and Università e Politecnico di Bari,
I-70125 Bari, Italy
17
Dipartimento di Fisica, INFN Sezione di Napoli and Università di Napoli, I-80126 Napoli, Italy
18
Dipartimento di Fisica, INFN Sezione di Padova and Università di Padova, I-35131 Padova, Italy
19
INFN Sezione di Roma and Università di Roma “La Sapienza”, I-00185 Roma, Italy
20
Department of Physics, King’s College London, London WC2R 2LS, United Kingdom
21
Department of Physics, Keio University, Yokohama, Kanagawa 223-8522, Japan
22
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
23
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
24
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
25
Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom
26
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
27
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
28
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University,
Nagoya, Aichi 464-8602, Japan
29
National Centre For Nuclear Research, 02-093 Warsaw, Poland
30
Department of Physics and Astronomy, State University of New York at Stony Brook,
New York 11794-3800, USA
31
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
32
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
33
Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom
34
Rutherford Appleton Laboratory, Harwell, Oxford OX11 0QX, United Kingdom
35
Department of Physics, University of Regina,
3737 Wascana Parkway, Regina, Saskatchewan S4SOA2, Canada
36
Department of Physics, Seoul National University, Seoul 08826, Korea
37
Department of Physics and Astronomy, University of Sheffield, S3 7RH Sheffield, United Kingdom
38
Department of Informatics in Social Welfare, Shizuoka University of Welfare,
Yaizu, Shizuoka 425-8611, Japan
39
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory,
Warrington OX11 0QX, United Kingdom
40
Department of Physics, Sungkyunkwan University, Suwon 16419, Korea
41
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
42
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
43
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
44
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes
for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8583, Japan
45
Department of Physics,Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan46
Department of Physics, Faculty of Science and Technology, Tokyo University of Science,
Noda, Chiba 278-8510, Japan47
Department of Physics, University of Toronto, Ontario M5S 1A7, Canada
48
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T2A3, Canada
49
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
50
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
51
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
52
Department of Physics, University of Winnipeg, Manitoba R3J 3L8, Canada
53
Department of Physics, Yokohama National University, Yokohama, Kanagawa 240-8501, Japan
13(Received 12 May 2020; accepted 9 September 2020; published 9 October 2020)
We present a search for an excess of neutrino interactions due to dark matter in the form of weaklyinteracting massive particles (WIMPs) annihilating in the Galactic center or halo based on the data set of*

Also at Department of Physics and Astronomy, UCLA, California 90095-1547, USA.
Currently at Queen Mary University of London, London E1 4NS, United Kingdom.
‡
Also at School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom.
§
Also at BMCC/CUNY, Science Department, New York, New York, USA.
†072002-2

INDIRECT SEARCH FOR DARK MATTER FROM THE GALACTIC …

PHYS. REV. D 102, 072002 (2020)

Super-Kamiokande-I, -II, -III and -IV taken from 1996 to 2016. We model the neutrino flux, energy, andflavor distributions assuming WIMP self-annihilation is dominant to νν̄, μþ μ− , bb̄, or W þ W −. The excess isin comparison to atmospheric neutrino interactions which are modeled in detail and fit to data. Limits on
the self-annihilation cross section hσ A Vi are derived for WIMP masses in the range 1 GeV to 10 TeV,
reaching as low as 9.6 × 10−23 cm3 s−1 for 5 GeV WIMPs in bb̄ mode and 1.2 × 10−24 cm3 s−1 for 1 GeV
WIMPs in νν̄ mode. The obtained sensitivity of the Super-Kamiokande detector to WIMP masses below
several tens of GeV is the best among similar indirect searches to date.
DOI: 10.1103/PhysRevD.102.072002

I. INTRODUCTION
There is compelling evidence that ordinary baryonicmatter composes only 5% of the total energy density of the
Universe, which is dominated by dark energy (68%) anddark matter (27%) whose nature is unknown [1]. Some
well-motivated candidates for particle dark matter (DM)arise within supersymmetric extensions of the Standard
Model [2,3]. These particles belong to a collective groupreferred to as weakly interacting massive particles(WIMPs). The lightest supersymmetric particle, the neutralino (χ), has been considered one of the most promising
WIMP candidates. However, the analysis presented here
would also be valid for any other dark matter candidate
annihilating into Standard Model particles.
WIMPs present in the Galactic halo may be observed
directly via elastic scattering off nuclei in detectors [4,5]or indirectly through detection of the products of theirannihilations (or decays) into Standard Model particles,
including neutrinos [6–10]. It is expected that dark matterparticles will accumulate in massive celestial objects likestars or planets and be bound by their gravitational
potentials [11]. Previous searches for WIMP-induced
neutrinos from the Sun and Earth cores, based on datacollected with the Super-Kamiokande (SK) detector, haveshown no excess of dark-matter-induced neutrinos over theatmospheric neutrino background [12–14].
In this study, we assume that dark matter particles
concentrate in the central regions of galaxies, as predictedby many halo models [15–20]. We search for neutrinos
from WIMP annihilation in the center of the Milky Way
and from its halo. This search with neutrinos is complementary to other indirect searches relying on annihilation
products like γ, eþ =e− , or p̄ [21]. The experimental
advantage of neutrinos is that they travel unimpeded andundeflected from their origin. However, their low interaction cross section puts them at a disadvantage relative tothese other annihilation products.

Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
and DOI. Funded by SCOAP3.

We constrain the thermally averaged self-annihilation
cross section hσ A Vi for WIMP pair annihilation for masses
from 1 GeV to 10 TeV. This is the first search for WIMPs
from the Milky Way based on data acquired by the SuperKamiokande detector and extending to dark matter masses
below 10 GeV.
The Super-Kamiokande detector is nearly 100% efficientfor detecting neutrino interactions above ∼100 MeV. The
dominant background is atmospheric neutrino interactions,which have been well studied with our detector. We havemade precise measurements of the flux, angular distribution, and energy spectra of atmospheric neutrinos [22]. We
also have a detailed model of systematic uncertainties [23].
Below we present results of two different approaches toanalyzing the same data sample: a full fit employing bothdata and Monte Carlo templates (combined fit), and amethod comparing observed event rates from a region
around the Galactic center to those in a region located in the
opposite part of the sky (on-source/off-source analysis).
The first method fits for a simulated WIMP-induced
neutrino contribution to the Super-Kamiokande data
together with the expected atmospheric neutrino background component. Various WIMP annihilation channels
and masses are tested. All event categories of detected
neutrino interactions used in recent atmospheric analyses[23], binned in angle and momentum, are used in the fit.
The second method provides a check that is entirely data
driven. We compare the number of events in a certain
angular region around the Galactic center (on-source) andin a region of the same size but shifted by 180° in rightascension (off-source). As the atmospheric neutrino background equally affects both regions, any excess of events inthe on-source data would indicate an additional source ofneutrinos from the area around the Galactic center.
II. DARK MATTER ANNIHILATION
IN THE MILKY WAY
The energy spectrum of neutrinos from the annihilationof dark matter WIMPs and the branching ratio (BR) for
their production is unknown and must be modeled. In thefollowing analysis we consider direct annihilation into pairsof neutrinos, χχ → νν̄, as well as annihilation into pairsof μþ μ− , bb̄, and W þ W − . Each annihilation mode is

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PHYS. REV. D 102, 072002 (2020)1
ϕνe ≃ ϕ0νe − s2
4

ð1Þ

1
1
ϕντ ≃ ϕνμ ¼ ðϕ0νμ þ ϕ0ντ Þ þ s2 ;
2
8

ð2Þ

and

104
103

E2 ⋅ dN/dE [per ann. GeV]

considered separately assuming 100% BR irrespective of
the actual nature of DM annihilation. In the bb̄ and W þ W −channels, neutrinos are mainly created in decays of mesons
produced during the hadronization of the primary annihilation products. In the μþ μ− channel neutrinos are produced
directly in the decays of the muons. In the νν̄ channel, amonoenergetic spectrum and equal fluxes of DM-induced
neutrinos of every flavor are assumed, and the energy ofthe neutrinos equals the mass of the annihilating dark
matter particles.
Neutrinos that travel over galactic distances experience
multiple oscillations and arrive at the detector with a flavor
composition that is predictable based on the values of theneutrino mixing parameters [24,25]. In applying oscillations to DM-induced neutrinos we followed the approachpresented in Ref. [26], adopting parameter values ofsin2 2 θ12 ¼ 0.86, sin2 2θ23 ¼ 1.0 (maximal mixing), andθ13 ≃ 0 to check how long-distance oscillations affect theneutrino production spectra and their flavor ratios at the
Earth. The resulting neutrino fluxes at the detector can be
described with the following effective formulas:

102

bb
+ WW
+ μμ

10
1
10-1
10-2
10-3 -1
10

1

Eν [GeV]102

10FIG. 1. Differential muon neutrino energy spectra for a WIMP
mass of 100 GeV after taking into account neutrino oscillations
throughout the Galaxy. Fluxes have been calculated based on
DarkSUSY [27,28] and Eqs. (1) and (2).

the primary analysis presented in this paper the NFW
model is used as a benchmark. The expected impact ofchanging the halo model is studied with a secondary
analysis that requires fewer computational resources.
The DM density distribution in the NFW model can be
written asρðrÞ ¼

ϕ0νe;μ;τρ0;
ðr=rs Þ½1 þ ðr=rs Þ2

ð3Þ

104

Moore
NFW
Kravtsov103
102

ρ(r) [GeV/cm3]

where
are the initial fluxes and s2 is defined as20
sin 2θ12 ð2ϕνe − ϕ0νμ − ϕ0ντ Þ [26]. Note that the above formulas lead to an equal flux of neutrino flavors at the Earth,that is, flux ratios of 1∶1∶1 for νe :νμ :ντ , for the typicalscenario of neutrino production via the decays of light mesons
and muons in which the initial flavor ratio is 1∶2∶0 at the
production point. The DarkSUSY [27,28] simulation package
was used to obtain the differential neutrino energy spectra
for the DM annihilation channels considered, as shown in
Fig. 1, after taking into account neutrino oscillations.
The expected flux of DM annihilation products depends
on the density distribution of DM particles in the
Milky Way. There are various models describing thestructure of the DM halo obtained on the basis of N-bodysimulations [29] and gravitational lensing observations[30]. The predictions of the Navarro-Frenk-White(NFW) [15], the Kravtsov et al. [16] and the Moore et al.
[17] models of the expected DM density ρ in the halo areshown in Fig. 2, assuming a flat DM density profile for the
innermost regions of the Galaxy. The Moore model
anticipates a high-density cusp in the center of the
Milky Way, while the Kravtsov model yields a flatter
density profile. The NFW profile is between these two
extreme predictions and is similar to other commonly
considered models such as the Einasto profile [18,19]. In

Mχ=100 GeV

Solar System Position

10
1
10-1

10-2
10-3
10-2

10-1

1
r [kpc]10102FIG. 2. Dark matter density (ρ) as a function of distance (r)from the GC for different DM density distribution profiles:
Moore [17], NFW [15], and Kravtsov [16]. The vertical grayline indicates the solar system position, Rsc ¼ 8.5 kpc. The
normalizations are chosen to match the local density of DM
expected at the position of the solar system from the local rotation
curves, for NFW ρðRsc Þ ¼ 0.3 GeV cm−3 (0.27 for Moore, 0.37
for Kravtsov) [9].

072002-4

INDIRECT SEARCH FOR DARK MATTER FROM THE GALACTIC …
where r is the distance from the center of the Galaxy andrs ¼ 20 kpc is the scale radius. The normalization is set so
as to match the DM density at the radius of the solar system(Rsc ¼ 8.5 kpc) expected from rotation curves and corresponds to ρðRsc Þ ¼ 0.3 GeV cm−3 for the NFW profile[8,9]. Though some models based on recent observations
suggest that ρðRsc Þ may deviate slightly from this value[31], the impact on the present analysis is expected to be
negligible.
The annihilation intensity J a (numerical flux per solid
angle) at an angle ψ with respect to the Galactic center (GC)direction is proportional to the line-of-sight (l) integral of
the DM density squared (as two DM particles are required
for annihilation) [8,9],
J a ðψÞ ¼

1
Rsc ρ2sc

Z l
0

max

where ρ2sc ¼ ρ2 ðRsc Þ and Rsc are used as scaling parameters
to make J a dimensionless. The upper limit of integration,lmax ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ðR2MW − sin2 ψR2sc Þ þ Rsc cos ψ;ð5Þ

depends on the assumed size of the Milky Way halo, RMW .
However, contributions beyond the size of the visible
stellar halo (20–30 kpc) are negligible. The dependence ofJ a ðψÞ on the angular distance from the GC is shownin Fig. 3.
The average value of the intensity of DM annihilation
products received at the Earth from a cone with halfangle ψ around the GC, that spans a field of view ofΔΩ ¼ 2πð1 − cos ψÞ, can be cast as
105

Moore
NFW
Kravtsov

104

Ja(ψ)

103
102

10

1
10-1
0

1
J a ðΔΩÞ ¼
ΔΩ

50

100

150

ψ, angular distance from GC [°]FIG. 3. Intensity of annihilation products versus angular distance from the Galactic center for various DM halo profiles.

Z 1
cos ψ

J ðψ 0 Þ2πdðcos ψ 0 Þ:

ð6ÞThen, the neutrino flux at the Earth can be related to theaverage intensity of DM annihilation products as [8,9]dϕν hσ A Vi
R ρ2 dNJ a ðΔΩÞ sc sc2;¼
2
dE
4πMχ dE

ð7Þ

where Mχ is the assumed mass of the DM particle, thefactor 1=2 is needed for self-conjugate WIMPs, and 1=4π
is for isotropic emission. Here dN=dE is the differential
neutrino multiplicity per one annihilation (cf. Fig. 1).

 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ2ρR2sc − 2lRsc cos ψ þ l2dl;
ð4ÞPHYS. REV. D 102, 072002 (2020)

III. SUPER-KAMIOKANDE DETECTOR
AND DATA SAMPLESSuper-Kamiokande is a 50 kton water Cherenkov detector located at the Kamioka Observatory operated by theInstitute for Cosmic Ray Research of the University ofTokyo [32]. It is used to search for proton decay as well as
to investigate atmospheric, man-made and extraterrestrial
neutrinos, including solar neutrinos and those producedin supernovae bursts. The detector consists of an innercylindrical volume (inner detector, ID) and an outer part(outer detector, OD), which plays the role of a veto region
for penetrating particles. The detection of neutrinos relies
on observation of charged particles (primarily leptons)
produced in ν interactions inside or outside the ID’s
22.5 kton fiducial volume. Cherenkov radiation fromcharged particles in the water is emitted in a characteristic
conical pattern, projected onto the detector walls, andrecorded by photomultipliers. The detected light patternallows for the reconstruction of the particle energy anddirection and provides differentiation between electromagnetic showers (e-like) and muon-type non-showering particles (μ-like).
The sample of neutrino interactions in which we search
for WIMP-induced neutrinos consists mainly of interactions of atmospheric neutrinos, which are the main
background of this search. Based on the topology andenergy of the detected events, atmospheric neutrinos can be
assigned to three main categories: fully contained (FC),partially contained (PC), and upward-going muons (UP-μ).
The FC events have a reconstructed neutrino interaction
vertex inside the fiducial volume and particles produced in
the parent neutrino interaction stop inside the ID. The true
neutrino energy of FC events is in the range of hundreds of
MeV up to several GeV. The true neutrino energy of PC
events, which have particles exiting into the OD, ranges
from 1 GeV to 100 GeV with a median energy of 10 GeV.
Neutrinos of higher energies (10 GeV to a few TeV) aredetected as upward-going muons due to muon neutrino
interactions in the surrounding rock. Downward-going
muons entering from outside the detector are removed

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K. ABE et al.
TABLE I.

PHYS. REV. D 102, 072002 (2020)

Summary of atmospheric neutrino data and MC event samples in the SK-I, SK-II, SK-III, and SK-IV data sets.
SK-I

SK-II

SK-III

SK-IV

Data

MC

Data

MC

Data

MC

Data

MC

Fully Contained (FC) sub-GeV
e-like, single-ring
0 decay-e
1 decay-e

2965
299

2933.9
301.6

1577
168

1541.3
161.0

1094
117

1043.7
104.6

4658
590

4744.9575.8

μ-like, single-ring
0 decay-e
1 decay-e
2 decay-e

1017
2006
148

1008.52046.2
147.2

564
1045
86

550.0
1081.2
82.5

340
744
58

356.2
745.6
60.4

922
4216
395

907.6
4142.4395.6

π 0 -likesingle-ring
multi-ring

163
493

165.4
489.0

115
245

106.0
259.0

53
178

53.4
173.6

247
804

244.7
807.0

Fully Contained (FC) Multi-GeV
Single-ringνe -likeν̄e -like
μ-like

193
651
699

168.1
663.4
720.3

82
320
400

84.8
339.6
387.4

66
212
237

60.8
232.8
252.4

364
959
1229

359.2
949.8
1207.2Multi-ringνe -likeν̄e -like
μ-like
other

224
212
610
519

228.1
215.5
615.3
509.4

162
116
344
296

155.0
124.7
336.5
291.7

80
64
230
173

85.4
67.4
226.9
166.5

441
353
1126
820

442.3
366.1
1118.5
818.4

Partially Contained (PC)
Stopping
Through-going

141
793

142.8
787.2

81
356

75.3
372.6

55
308

53.1
309.1

289
1344

297.7
1412.1

432.3

433.2

203.1

211.1

191.7

169.0

627.1

641.8

1410.6422.0

1349.8
497.0

616.4
193.6

640.8
190.0

508.3
205.8

459.5
239.8

2497.4409.2

2448.7382.3

Upward-going muons (UP-μ)Stopping
Through-goingNon-showering
Showeringfrom the analysis samples as they cannot be separated fromdownward-going cosmic-ray muons.
The FC, PC, and UP-μ event classes can be further
divided into more specific subcategories, as listed inTable I. The main criteria for dividing FC events are thetype of the primary ring (e-like vs μ-like), the number ofreconstructed rings (single-ring or multi-ring), the number of electrons from muon decays, the presence of π 0 ,and the likelihood to be ν̄e . If the reconstructed momentum of the primary lepton is below 1.33 GeV, the event isclassified as sub-GeV, and multi-GeV otherwise. The
PC events either stop in or escape the veto region and arethus divided into PC-stopping and PC-through-going.
Similarly, UP-μ events are categorized as “stopping” inthe detector or “through-going.” The most energetic
muons induce showers while passing through the detector. Therefore, “through-going” UP-μ events are further
categorized as “showering” and “non-showering.” A
detailed description of the event classification can befound elsewhere [23].

Since this search covers a wide range of neutrinoenergies, all of the SK atmospheric neutrino data andtheir corresponding subsamples are taken into account in
the analysis. The search is based on data from the SK-I
(1996–2001), SK-II (2002–2005), SK-III (2006–2008),
and SK-IV (2008–2016) run periods. Data used in thiswork were collected until June 2016 and correspond to a
total livetime of 5325.8 live-days for FC and PC events and5629.1 live-days for UP-μ events.
The Monte Carlo (MC) simulation of the detector
response is based on a GEANT3 model [33]. Neutrino
interactions are modeled with the NEUT generator [34] andthe background flux is taken from Ref. [35]. In thisanalysis, MC corresponding to 500 years of livetime
separately for SK-I, -II, -III and -IV sets (2000 years oflivetime in total) is used.
IV. COMBINED FIT
In this search it is assumed that the neutrino datacollected with the SK detector can be described by two

072002-6

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PHYS. REV. D 102, 072002 (2020)

FIG. 4. Illustration of the DM annihilation signal for M χ ¼ 5 GeV=c2 (blue solid line) and M χ ¼ 50 GeV=c2 (blue dotted line) into apair of bb̄ quarks. The samples used in the fit are presented. SK data (black points with errors), the “best-fit” atmospheric MC after
oscillations (red solid), and the DM-induced neutrino signals are shown with respect to the direction of the Galactic center (cos θGC ¼ 1
corresponds to the direction of the GC). The signal normalization corresponds to the 90% C.L. upper limit for the given WIMP mass
hypothesis, but has been multiplied by 10 for visibility. In the fitting procedure, the angular distributions shown in the figure are alsobinned in lepton momentum.

components: WIMP-induced neutrinos (the signal) andatmospheric neutrinos (the background). In the combined
fit analysis we search for a signal excess in the atmospheric neutrino data sample that is compatible with aneutrino source from the GC by introducing DM signal
templates and fitting them together with the atmosphericbackground assuming a variety of WIMP masses. The
spectra and directional distributions of signal events arecorrelated across all of the event subsamples. This isdifferent from previous SK searches for DM-induced
neutrinos that were based only on the angular informationof UP-μ events [13,14].
Monte Carlo event samples are used to simulate bothsignal and background. The standard simulation of atmospheric neutrino interactions used in SK’s oscillation studies
is used to estimate the background and includes simulated
tau neutrino interactions [36]. In order to simulate thesignal, a separate and independent sample of events fromthe atmospheric MC is reweighted to the angular andenergy distributions expected for DM-induced neutrinos
for a given WIMP mass and annihilation channel.
The Monte Carlo samples allow DM-induced signal
simulation for νμ ν̄μ with energies 100 MeV ≤ Eν ≤ 10 TeV,for νe ν̄e in 100 MeV ≤ Eν ≤ 80 GeV, and for ντ ν̄τ in
100 MeV ≤ Eν ≤ 150 GeV. These upper limits are determined by event statistics in the atmospheric MC. For
WIMP masses (M χ ) greater than several hundreds ofGeV, the detected event rate is dominated by interactionsin the rock rather than the detector volume, and therefore
only muon neutrinos are used to simulate the high-energy
part of the DM-induced neutrino energy spectrum.
Although the analysis in this energy range lacks contributions from other neutrino flavors, it has the advantage of thebest pointing resolution.
The signal and background contributions are comparedagainst the data for various WIMP masses and annihilation
channels using the “pull” χ 2 [37] method based on Poisson
probabilities,

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PHYS. REV. D 102, 072002 (2020)

FIG. 5. Fitted number of DM-induced neutrinos of all flavors from annihilation into bb̄, μþ μ− , W þ W − , and νν̄ as a function of the
WIMP mass. Also shown are the expected sensitivities for the zero-signal case.





X
X
X
ATM
i
DM
i
data
Nn
1þ
1þ
− N data
χ ¼2
f n ϵi þ βN ngn ϵin þ N n ln
2nþX ϵi 2
i

σi

i

i

;


N data
n
P
P i
N ATM
ð1 þ i f in ϵi Þ þ βN DMnn ð1 þ
i gn ϵi Þð8Þis the atmospheric
where n indexes the analysis bins, N ATMnneutrino background expectation including oscillations,
N DM
is the simulated DM-induced neutrino contribution,nand N datais the number of observed events in the nth bin.
n
The parameter β represents the normalization of thesimulated signal. Determining the “best-fit” β is the main
goal of this analysis. Systematic errors are incorporated into
the fit via parameters ϵi , where i is the systematic error
index. Here f in (gin ) represents the fractional change in the
background (signal) MC in bin n for a σ i change in the ithsystematic error. Note that systematic uncertainties related
to the detector, data selection, and neutrino interactions are
fully correlated between the signal and background. Thatis, f in ¼ gin for those errors. Atmospheric neutrino flux
errors, on the other hand, have no impact on the signal andgin ¼ 0 for those errors, accordingly. This analysis only
considers DM-induced neutrinos from the GC and halo anddoes not include other sources. During the fit, Eq. (8) is
minimized with respect2 to the ϵi at each point in parameter
space according to ∂χ∂ϵi ¼ 0 [37]. The “best-fit point” isdefined as the global minimum χ 2 on the grid of all tested
points. The index i covers systematic uncertainties from
Ref. [23] considered in the atmospheric neutrino analysis of
SK data, but adjusted for the GC angular binning scheme
used in this analysis.
The atmospheric neutrino background N ATM
depends onnthe values of the neutrino oscillation parameters θ23 , θ12 , θ13 ,Δm223 , Δm212 , and δCP . The values of these parameters are notdetermined in this analysis as a given GC coordinate does
not correspond to a fixed travel path length in the Earth andtherefore provides little sensitivity to neutrino oscillations.
Accordingly, the oscillation parameters are set to δCP ¼ 0,
sin2 2θ23 ¼ 1.0, Δm223 ¼ 2.44 × 10−3 eV2 [38], sin2 2θ13 ¼
0.092 [39], sin2 θ12 ¼ 0.32, and Δm212 ¼ 7.46 × 10−5 eV2072002-8

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PHYS. REV. D 102, 072002 (2020)

FIG. 6. Upper limit on the fitted number of DM-induced neutrinos of all flavors from annihilation into bb̄, μþ μ− , W þ W − , and νν̄ as afunction of the mass of the DM particles. The expected (median) limit assuming no signal is shown by the dashed line and the region
containing 68.3% (95.5%) of the expected limits is shown by the green (yellow) band.

[40]. However, the uncertainty on each oscillation parameteris included in the fit via systematic error parameters which
prediction.
effectively change the N ATMn
There are 19 data samples used in this analysis,
including both e-like and μ-like event categories. All of
the samples listed in Table I are used in the search. In total,
there are 520 analysis bins (n ¼ 520) as each sample isbinned in momentum and the cosine of the angle between
the event direction and the direction of the Galactic center(cos θGC ). The momentum binning is the same as in otherSK atmospheric ν analyses [23]. The definition of the event
direction depends on the number of rings in the event. In thecase of the single-ring events, the angle to the GC is
calculated using the observed Cherenkov ring direction.
For events with multiple rings, the direction of the event isobtained as the momentum-weighted average direction
taken over all ring directions. The angular resolution of
sub-GeV events strongly depends on the parent neutrinoenergy and is roughly tens of degrees on average (Fig. 32 in
Ref. [41]). At higher energies, the true neutrino direction ismore accurately determined due to the high Lorentz boostof the interaction products.
An illustration of the samples used in the fit is shown in
Fig. 4. The samples in the first column use only one angularbin and several momentum bins due to the poor angularresolution at low neutrino energy and lepton momentum.
All other samples use multiple angular and momentum
bins, though the latter have been merged together in the
figure. The data are simultaneously fit in all neutrino
flavors. Tau neutrinos end up mainly categorized as
multi-GeV single-ring and multi-ring e-like events dueto the complex final state of secondary particles producedin ντ interactions and τ decay. Depending on M χ and theannihilation mode, the signal appears in different samplesof Fig. 4. Even samples containing no signal contribution
constrain the background rate and associated systematic
errors, which impacts all bins in the analysis.
V. RESULTS OF COMBINED FIT ANALYSISFor each tested WIMP mass and annihilation channel,
we try to determine the value of β that governs the allowed
contribution to the SK data from the simulated signal. The
fitted number of DM-induced neutrino events accounting
for the “best-fit” signal normalization β is shown in Fig. 5
along with the expected limits as calculated by MC under
the assumption of no WIMP signal (denoted as 90% and
99% C.L. sensitivities).

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PHYS. REV. D 102, 072002 (2020)

FIG. 7. Local p-value for the fitted number of WIMP-induced neutrinos for bb̄, μþ μ− , W þ W − , and νν̄ annihilation channels as afunction of the mass of the DM particles. Results based on data are shown as solid thick lines with points. For comparison, the expectedvalues assuming different hσ A Vi are also shown.

It should be noted that the points in Fig. 5 are notindependent, as the same set of data is used for each M χ
hypothesis. Accordingly, a correlated rise is seen in allannihilation channels at low WIMP masses as parts of theannihilation spectra from neighboring M χ overlap in someanalysis bins. At higher WIMP masses the results fall into
the unphysical region, where the fitted number of WIMPs isnegative. A strong excess across all annihilation channels
that exceeds the background-only expectation around a
given WIMP mass is expected for a real signal as contributions from dark-matter-induced neutrinos partially overlap
between different annihilation signal templates. However,there is no such signal contribution allowed by the data.
The final fit result is translated into an upper 90% C.L.
limit on the fitted number of DM-induced neutrinos using a
Bayesian approach [42] to adjust results which fall into
the unphysical region. Figure 6 shows the result together
with the sensitivity assuming no WIMP contribution. The
1 − 2σ uncertainty was derived from pseudo-MC data sets
constructed without any WIMP-induced neutrinos.
Prior to fitting the data, MC studies assuming a WIMP
signal were used to determine a significance threshold forthe analysis. An excess above the atmospheric backgroundwith a local p-value greater than 3σ was chosen as thecriterion for a possible WIMP signal. Figure 7 shows thep-value distributions for the obtained fit results. There is a
∼2σ excess observed in the Mχ ¼ 5 GeV bb̄ channel(2.08σ), for the Mχ ¼ 1 GeV μþ μ− (1.74σ) channel, andfor the Mχ ¼ 2 GeV νν̄ (1.82σ) channel. Though all
p-values are consistent with no WIMP contribution, additional checks were performed for the most significant
result.
A fit in which the position of the GC was treated as a freeparameter moving in right ascension (RA), but fixed in
declination (DEC), was performed for the bb̄ annihilation
channel and Mχ ¼ 5 GeV. Fixing the declination allows
us to use the same systematic uncertainties, as they dependon the zenith angle, which itself is proportional to thedeclination. This additional analysis found a similar signal
excess of approximately 2σ for a WIMP signal, but for a
GC position of RA in range from 210° to 260°, though thetrue GC position is at 266°. Accordingly, we find no
indication of a signal consistent with the expectation for
DM from the GC halo in this channel.

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PHYS. REV. D 102, 072002 (2020)

10-17
SK bb
+ SK W W
SK μ +μ -

-18

10

-19

<σA V> [cm3s-1 ]10

IceCube86 bb
Eur. Phys. J. C 77 (2017)+ IceCube86 W W
IceCube86 μ+μIceCube86 ν ν
ANTARES b b
Phys. Lett. B 805 (2020)+ ANTARES W W
ANTARES μ+μANTARES ν ν

SK νν

-20

10

10-21
10-22
-23

10

10-24
-25

10

expectation for thermal relic scenario
-26

10

1

3

102

10

104

10
2

Mχ [GeV/c ]FIG. 8. Upper limits at 90% C.L. on the hσ A Vi versus WIMP mass (the region above the lines is excluded), for dark matter annihilating
through νν̄, bb̄, W þ W − , and μþ μ− into neutrinos, assuming the NFW halo profile. SK limits, obtained in the combined fit andcorresponding to a total livetime of 5325.8 (5629.1) live-days for FC and PC (UP-μ) events, are compared with published results from
IceCube (1005 live-days) [44] and ANTARES (3170 live-days) [45].

selected limits from γ search experiments [46–48] isprovided in the Supplemental Material along with a tablecontaining SK hσ A Vi limit values [49].
VI. ON-SOURCE/OFF-SOURCE ANALYSISThe on-source/off-source analysis provides a data-driven
cross-check of the analysis shown in the previous section,
albeit with weaker sensitivity. It has the advantage of being
able to estimate the background directly from data. Equally
sized on- and off-source regions are defined in rightascension and declination, as shown in Fig. 9. Most of50

DEC [°]

Based on the limit on the number of DM-induced
neutrinos, the corresponding limit on the diffuse flux isderived as a function of M χ using Eq. (7) and translated intoa limit on the DM self-annihilation cross section hσ A Vi.
The latter is shown in Fig. 8 and compared to selected
results of other neutrino experiments. The line at hσ A Vi ¼
3 × 10−26 cm3 s−1 is the expectation for WIMPs produced
thermally during the evolution of the Universe [43].
Despite the smaller effective area of the SK detector whencompared to the IceCube detector [44], the limits obtainedin this analysis are stronger due to the fact that the SK
detector can probe the GC with upward-going events. At
the location of the SK detector, the GC is below the horizonfor ∼64% of the year, while for IceCube it is always
above the horizon and can only be directly probed withdownward-going events which typically suffer from morebackgrounds from cosmic-ray muons. ANTARES is operating in the same hemisphere as SK and its limits [45]are stronger than the ones obtained here for M χ >50–500 GeV (depending on the annihilation mode) due
to the larger effective area of its detector. Weaker constraints from ANTARES observed for Mχ < 500 GeV forbb̄ and for Mχ < 100–150 GeV for W þ W − =μþ μ− annihilation channels are due to the different detection thresholds
between ANTARES and SK. In this M χ range, a substantial
part of the DM-induced neutrino signal is expected below
several tens of GeV (cf. Fig. 1), a region that is well coveredby the SK detector. A comparison of these results with

on-source

off-source

0
GC

−50

−100

0

RA [°]

100

FIG. 9. The on-source/off-source regions defined in equatorial
coordinates.

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PHYS. REV. D 102, 072002 (2020)

Event class
FC sub-GeV
FC multi-GeV
PC
UP-μOptimal size [°]NFW

Moo reKravtsov

60
30
20
10

60
25
10
5

60
55
45
40

the signal is expected to come from the on-source region
centered around the GC (266° RA, −29° DEC) while anindependent background estimation is obtained from theoff-source region, which is offset 180° in right ascension
but at the same declination. Note that the atmospheric
neutrino background is expected to be the same in bothregions as they correspond to identical zenith angles inSK’s local coordinate system. Therefore, the expected
number of events in the on-source region can be interpretedsig
as N ON ¼ N bkg
on þ N on , while for the off-source it issig
sig
N OFF ¼ N bkg(N bkg ) stands for theoff þ N off . Here N
number of signal (background) neutrinos in the on-source(off-source) regions. In this analysis we subtract the
number of off-source events from the on-source observasig
tion: N ON − N OFF ¼ N sigon − N off . This number effectively
sig
sig
equals N on as N off is expected to be significantly smaller
than N sig
on assuming a true source from the GC halo. The
result of this subtraction is directly proportional to hσ A Vi.
Systematic uncertainties related to the background should
equally effect the on- and off-source regions and therefore
cancel in the subtraction.
The angular size of the onpﬃﬃﬃﬃand off-source regions isdetermined to maximize S= B, where S stands for thenumber of expected signal events and B for the number ofbackground events. This optimization is performed with thesame signal and background Monte Carlo used in the
combined fit. As the angular resolution of an event depends
on the neutrino energy, the optimal size of the on- and offsource regions differs between the FC sub-GeV, FC multiGeV, PC, and UP-μ event samples, as shown in Table II for
the three considered halo profiles.
The number N ON − N OFF is obtained for each subcategory of events and similar numbers of events are observedin both the on- and off-source regions for all classes.
Figure 10 shows the asymmetry, A ¼ ðN ON − N OFF Þ=ðN ON þ N OFF Þ, for the benchmark NFW model and all
event categories.
As no asymmetry in the event rate is observed, weconstrain hσ A Vi by introducing information on the halomodel, the mass of the DM particles, and the annihilation
channel. Limits are calculated for M χ in the range from
1 GeV to 10 TeV for the bb̄, μþ μ− , W þ W − , and νν̄annihilation channels, as shown in Fig. 11. In contrast to the

Fully Contained (FC) Sub-GeV
e-like 0 decay-ee-like 1 decay-e
Single-ring π0-like20
μ-like 0 decay-e
μ-like 1 decay-e
μ-like 2 decay-e
Multi-ring π0-like
Fully Contained (FC) Multi-GeV15
νe-likeνe-like
μ-likeMultiRing νe-like
MultiRing νe-like10
MultiRing μ-like
MultiRing Other
Partially Contained (PC)
Stopping
Through-going 5
Upward-going Muons (UP-μ)Stopping
Through-going Non-showering
Through-going Showering

0

−0.5

0

0.5

A=(N -NOFF)/(N +NOFF)
ON

ON

FIG. 10. Observed asymmetry between the number of neutrino
events in the on- and off-source regions across the event
subcategories for the NFW halo model. Errors on the points
are statistical.

combined fit analysis, which is based only on the NFW
halo profile, the limits here are presented also for the Moore
and Kravtsov profiles in order to demonstrate the impact of
the halo model choice. Differences between the benchmark
NFW model and the Moore and Kravtsov models can reachan order of magnitude, due to large discrepancies in thepredicted densities of the DM particles in the inner parts of
the Galaxy.
Figure 12 compares the results of this analysis with theconstraints from the combined fit presented in Sec. V.
The combined fit analysis yields limits that are roughly
10−17

bb+ WW
μ+μνν

10−18
10−19

<σAv> [cm3s-1]

TABLE II. Optimal size of on-source and off-source regions
assuming DM annihilation for the NFW, Moore, and Kravtsov
halo profiles.

Kravtsov
NFW
Moore

10−20
10−21
10−22
10−23
10−24
10−25

expectation for thermal relic scenario

− 26

10

1

10

102

3

10

104

Mχ [GeV/c2]

FIG. 11. Upper limits at 90% C.L. on the DM self-annihilation
cross section hσ A Vi as a function of M χ for the bb̄ (blue), W þ W −(maroon), μþ μ− (purple), and νν̄ (orange) annihilation channels
as obtained in the on-source/off-source analysis. The influence ofthe halo model choice is shown as bands around the results for thebenchmark NFW profile.

072002-12

INDIRECT SEARCH FOR DARK MATTER FROM THE GALACTIC …
10-17
combined fit bb+ combined fit W W
combined fit μ+μcombined fit νν

-18

10

<σA v> [cm3s-1]

10-19

on/off bb+ on/off W W
on/off μ+μon/off νν

10-20
10-21
10-22
10-23
10-24
10-25

expectation for thermal relic scenario

-26

10

1

10

102
Mχ [GeV/c2]

3

10

104

FIG. 12. Upper limits at 90% C.L. on the DM self-annihilation
cross section hσ A Vi as a function of Mχ for the combined fit(solid) and on-source off-source (dashed) analyses for the bb̄
(blue), W þ W − (maroon), μþ μ− (purple), and νν̄ (orange) annihilation channels assuming the NFW profile.

PHYS. REV. D 102, 072002 (2020)

the data are consistent with the expectation fromatmospheric neutrino backgrounds. The strongest exclusion is obtained for WIMP masses below several tensof GeV in the bb̄, νν̄, and μþ μ− channels in the combined
fit. Limits on hσ A Vi reach as low as 9.6 × 10−23 cm3 s−1
for 5 GeV WIMPs in the bb̄ channel and 1.2 ×
10−24 cm3 s−1 for 1 GeV WIMPs in the νν̄ channel.
These are the strongest indirect limits among similar
WIMP-induced neutrino searches to date. Strong constraints on GeV-scale M χ reflect the long exposure andthe discrimination power of multiple subsamples reconstructed using the Super-Kamiokande detector. A complementary and completely data-driven result thatcompared event rates from the angular region near the
GC and one of the same size but located in the opposite
direction also found no evidence of an excess beyond thebackground expectation.
ACKNOWLEDGMENTS

The analyses presented above show no excess of
DM-induced neutrinos from the Galactic center or its halo;

We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment has been built and operated fromfunding by the Japanese Ministry of Education, Culture,
Sports, Science and Technology, the U.S. Department ofEnergy, and the U.S. National Science Foundation. Someof us have been supported by funds from the National
Research Foundation of Korea NRF-2009-0083526(KNRC) funded by the Ministry of Science, ICT, andFuture Planning and the Ministry of Education(2018R1D1A3B07050696,
2018R1D1A1B07049158),
the Japan Society for the Promotion of Science, theNational Natural Science Foundation of China underGrants No. 11235006, the Spanish Ministry of Science,
Universities and Innovation (Grant No. PGC2018-099388B-I00), the Natural Sciences and Engineering ResearchCouncil (NSERC) of Canada, the Scinet and Westgrid
consortia of Compute Canada, the National ScienceCentre, Poland (2015/18/E/ST2/00758), the Science andTechnology Facilities Council (STFC) and GridPPP,
UK, the European Union’s H2020-MSCA-RISE-2018
JENNIFER2 Grant Agreement No. 822070, and H2020MSCA-RISE-2019 SK2HK Grant Agreement No. 872549.

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1 order of magnitude stronger than the on-source/off-source
approach for bb̄, μþ μ− , and W þ W − . However, for low
WIMP masses, the obtained limits are of similar strength,
as the signal is mostly present in the sub-GeV samples. The
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VII. SUMMARY

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limits from other indirect DM search experiments.

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