PHYSICAL REVIEW LETTERS 120, 221301 (2018)
Editors' Suggestion

Search for Boosted Dark Matter Interacting with Electrons in Super-Kamiokande
C. Kachulis,4 K. Abe,1,38 C. Bronner,1 Y. Hayato,1,38 M. Ikeda,1 K. Iyogi,1 J. Kameda,1,38 Y. Kato,1 Y. Kishimoto,1,38
Ll. Marti,1 M. Miura,1,38 S. Moriyama,1,38 M. Nakahata,1,38 Y. Nakano,1 S. Nakayama,1,38 Y. Okajima,1 A. Orii,1
G. Pronost,1 H. Sekiya,1,38 M. Shiozawa,1,38 Y. Sonoda,1 A. Takeda,1,38 A. Takenaka,1 H. Tanaka,1 S. Tasaka,1
T. Tomura,1,38 R. Akutsu,2 T. Kajita,2,38 K. Kaneyuki,2,38,* Y. Nishimura,2 K. Okumura,2,38 K. M. Tsui,2 L. Labarga,3
P. Fernandez,3 F. d. M. Blaszczyk,4 J. Gustafson,4 E. Kearns,4,38 J. L. Raaf,4 J. L. Stone,4,38 L. R. Sulak,4 S. Berkman,5
S. Tobayama,5 M. Goldhaber,6,* M. Elnimr,7 W. R. Kropp,7 S. Mine,7 S. Locke,7 P. Weatherly,7 M. B. Smy,7,38
H. W. Sobel,7,38 V. Takhistov,7,† K. S. Ganezer,8 J. Hill,8 J. Y. Kim,9 I. T. Lim,9 R. G. Park,9 A. Himmel,10 Z. Li,10
E. O’Sullivan,10 K. Scholberg,10,38 C. W. Walter,10,38 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 R. P. Litchfield,15 W. Y. Ma,15 Y. Uchida,15 M. O. Wascko,15 S. Cao,16 M. Friend,16
T. Hasegawa,16 T. Ishida,16 T. Ishii,16 T. Kobayashi,16 T. Nakadaira,16 K. Nakamura,16,38 Y. Oyama,16 K. Sakashita,16
T. Sekiguchi,16 T. Tsukamoto,16 KE. Abe,17 M. Hasegawa,17 A. T. Suzuki,17 Y. Takeuchi,17,38 T. Yano,17 T. Hayashino,18
T. Hiraki,18 S. Hirota,18 K. Huang,18 M. Jiang,18 KE. Nakamura,18 T. Nakaya,18,38 B. Quilain,18 N. D. Patel,18
R. A. Wendell,18,38 L. H. V. Anthony,19 N. McCauley,19 A. Pritchard,19 Y. Fukuda,20 Y. Itow,21,22 M. Murase,21 F. Muto,21
P. Mijakowski,23 K. Frankiewicz,23 C. K. Jung,24 X. Li,24 J. L. Palomino,24 G. Santucci,24 C. Vilela,24 M. J. Wilking,24
C. Yanagisawa,24,‡ S. Ito,25 D. Fukuda,25 H. Ishino,25 A. Kibayashi,25 Y. Koshio,25,38 H. Nagata,25 M. Sakuda,25 C. Xu,25
Y. Kuno,26 D. Wark,27,33 F. Di Lodovico,28 B. Richards,28 R. Tacik,29,42 S. B. Kim,30 A. Cole,31 L. Thompson,31
H. Okazawa,32 Y. Choi,34 K. Ito,35 K. Nishijima,35 M. Koshiba,36 Y. Totsuka,36,* Y. Suda,37 M. Yokoyama,37,38
R. G. Calland,38 M. Hartz,38 K. Martens,38 C. Simpson,38,27 Y. Suzuki,38 M. R. Vagins,38,7 D. Hamabe,39 M. Kuze,39
T. Yoshida,39 M. Ishitsuka,40 J. F. Martin,41 C. M. Nantais,41 H. A. Tanaka,41 A. Konaka,42 S. Chen,43
L. Wan,43 Y. Zhang,43 R. J. Wilkes,44 and A. Minamino45(Super-Kamiokande Collaboration)
1

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, Madrid 28049, 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
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
7
Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697-4575, USA
8
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
9
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
10
Department of Physics, Duke University, Durham, North Carolina 27708, USA
11
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
12
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
13
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, 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
16High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan17
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan18
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
19
Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom
20
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
21
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
22
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya, Aichi 464-8602, Japan
23
National Centre For Nuclear Research, Warsaw 00-681, Poland
24
Department of Physics and Astronomy, State University of New York at Stony Brook, New York 11794-3800, USA
25
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
26
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
27
Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom
28
School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, United Kingdom
29
Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan S4SOA2, Canada

20031-9007=18=120(22)=221301(8)221301-1

Published by the American Physical Society

PHYSICAL REVIEW LETTERS 120, 221301 (2018)30

Department of Physics, Seoul National University, Seoul 151-742, Korea
Department of Physics and Astronomy, University of Sheffield, Sheffield S10 2TN, United Kingdom
32
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka 425-8611, Japan
33
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington OX11 0QX, United Kingdom
34
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
35
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
36
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
37
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
38
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
39
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan40
Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan
41
Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
42
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T2A3, Canada
43
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
44
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
45
Faculty of Engineering, Yokohama National University, Yokohama 240-8501, Japan
31(Received 16 November 2017; revised manuscript received 23 March 2018; published 30 May 2018)
A search for boosted dark matter using 161.9 kt yr of Super-Kamiokande IV data is presented. We search
for an excess of elastically scattered electrons above the atmospheric neutrino background, with a visibleenergy between 100 MeV and 1 TeV, pointing back to the Galactic center or the Sun. No such excess isobserved. Limits on boosted dark matter event rates in multiple angular cones around the Galactic centerand Sun are calculated. Limits are also calculated for a baseline model of boosted dark matter produced
from cold dark matter annihilation or decay. This is the first experimental search for boosted dark matterfrom the Galactic center or the Sun interacting in a terrestrial detector.
DOI: 10.1103/PhysRevLett.120.221301

While there has long been ample evidence for the
existence of dark matter [1–5], the specific properties andidentity of dark matter remain elusive. The ΛCDM cosmology, which consists of long-lived dark matter that was
nonrelativistic (“cold”) at freeze-out and a cosmologicalconstant Λ, which corresponds to dark energy, has been well
supported by cosmological observations [6]. Under thiscosmology, the dark matter abundance has been measured
by the observation of the cosmic microwave background toaccount for about 25% of the energy density of the Universe[7,8]. However, despite numerous direct and indirect detection searches, as well as searches for dark matter produced atparticle accelerators, there has thus far been no definitive
observation of particle dark matter [9–17].
With the properties of dark matter so uncertain, various
possibilities must be considered. One possibility is that somedark matter is, in fact, not cold but is highly relativisticand has been produced at late times, thus denoted “boosted”
dark matter [18–25]. Boosted dark matter could exist as a
subdominant dark matter component, with a dominant cold

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.

dark matter component accounting for most of the dark
matter energy density of the Universe. In this way, boosted
dark matter can remain consistent with ΛCDM. The subdominant boosted dark matter can be the same particle as thedominant cold dark matter, or it can be a different, lighter
particle. Boosted dark matter can be produced from thedominant cold dark matter through a variety of processes,
including annihilation [26,27], semiannihilation [28–32],
number-changing 3 → 2 self-annihilation [33–35], anddecay [22,36]. Boosted dark matter can then be observed
through its scattering off electrons or nuclei in large-volume
terrestrial detectors [37,38]. Current direct detection limits
can be evaded in multicomponent models by having only the
boosted dark matter species couple directly to standard
model particles [18,22–24] or in boosted dark matter singlecomponent models by invoking a spin-dependent dark
matter-nucleon cross section [24].
This Letter reports the results of a search for boosted
dark matter coupling to electrons in Super-Kamiokande(SK), with the boosted dark matter originating in the
Galactic center or the Sun and with scattered electronenergies ranging from 100 MeV to 1 TeV. This is the firsttime that this class of high-energy “electron elastic scatterlike” events has been studied at SK. The search is
performed on 2628.1 days of SK-IV data, which corresponds to 161.9 kt yr exposure. The analysis is designed to
be independent of the particular model of the coupling

221301-2

PHYSICAL REVIEW LETTERS 120, 221301 (2018)
between boosted dark matter and electrons. This way, theresults can be applied to any model that predicts a source ofparticles from the Galactic center or Sun which would
scatter electrons to energies greater than 100 MeV.
The SK detector [39] is a water Cherenkov detector
located 1000 m below Mt. Ikenoyama in Gifu, Japan. It
consists of a 50 kt cylindrical tank of water, which is
divided into a 32 kt (22.5 kt fiducial) inner detector (ID)surrounded by an outer detector (OD). The ID and the OD
are optically separated by black Tyvek sheeting, and the ID
is observed by 11 129 inward-facing 20-inch photomultiplier tubes (PMTs), while the OD is observed by 1885
outward-facing 8-inch PMTs. The ID provides most of theinformation used in event reconstruction, while the OD isused as an active veto region. Events are classified as fully
contained (FC) if there is activity only in the ID.
Relativistic charged particles in SK produce Cherenkov
rings, which are categorized as e-like for electrons and γ’s
or μ-like for muons.
The search begins with the fully contained fiducialvolume (FCFV) data set. This data set consists of all eventswith no OD activity, a reconstructed vertex inside thefiducial volume, and greater than 100 MeV of e-like
momentum. These are events that originate and deposit
all of their energy in the ID. This is a standard SK data
set used to study atmospheric neutrinos [40]. From thisdata set, we search for elastically scattered electrons byapplying the following analysis cuts: (i) one-ring (ifEvis < 100 GeV), (ii) e-like, (iii) zero decay electrons,and (iv) zero tagged neutrons. The first two cuts search for asingle relativistic electron, while the final two cuts remove
events with a signature of a nuclear interaction. Decay
electrons in e-like events are the result of the π  → μ →e decay chain with the π  coming from a neutrinonucleus interaction. Tagged neutrons originate from neutrons being knocked out of the nucleus following aneutrino-nucleus interaction, thermalizing, and capturing
on hydrogen. Neutron captures are particularly numerous
following neutrino deep inelastic scattering. Neither decay
electrons nor neutron captures should occur following theelastic scatter of an electron by a boosted dark matterparticle. The one-ring cut is not applied for events withvisible energy above 100 GeV, as the ring-counting
algorithm, which is tuned for lower-energy events, becomes
unreliable at such high energies. We choose to restrict thisanalysis to SK-IV data only in order to take advantageof neutron tagging to remove atmospheric neutrino background. While neutron tagging has been used similarly in
SK proton decay searches [41], this is the first time that it
has been applied toward sample purification at energies
greater than about 1 GeV. Event displays of example events
passing the analysis cuts are provided in Supplemental
Material [42].
Because of intricacies of the SK-IV trigger logic, events≳50 GeV often cannot have neutron tagging applied.

Events for which neutron tagging cannot be applied areconsidered a signal if they pass the first three analysis cuts.
Fourteen such events were found by FCFV selection, noneof which passed the first three analysis cuts. This effect isaccounted for in the signal efficiency, background rate, andlimit calculations described below. The effect is minimal,
since the efficiency of the neutron tagging cut is nearly
100%, and the background rate is driven down at suchhigh energies by the sharp dropoff of the atmospheric
neutrino flux.
The efficiency of the analysis cuts was found using asignal MC of 200 000 electrons with energies ranging from30 MeV to 1 TeV. Events were simulated up to 1 m outside
the fiducial volume, and efficiency was defined as thenumber of events passing each cut divided by the number of
events simulated in the fiducial volume (events can migrate
into or out of the fiducial volume during reconstruction).
The efficiency of the FCFV selection and analysis cuts isshown in Fig. 1. The main cause of the reduction ofefficiency with energy is the loss of containment at highenergies; some higher-energy electromagnetic showers areable to penetrate from the FV into the OD and so do notpass the FC selection. The systematic uncertainty on theefficiency is estimated to be about 2%, most of which is due
to uncertainty in the efficiency of the one-ring cut. The
small size of the uncertainty of the FCFV selection and first
three cuts is due to a significant separation between passing
and failing events, so that very few signal events occur near
the boundaries of the cuts. The efficiency of the neutron
tagging cut is found by measuring the rate of false neutron

FIG. 1. Signal efficiency of the FCFV selection and analysis
cuts as a function of the energy. Beginning with the FCFV
selection (dashed-dotted blue curve), the addition of the one-ring(for Evis < 100 GeV, dashed green curve), e-like (dotted red
curve), and finally zero decay electrons and zero tagged neutrons
cuts to arrive at the final efficiency (solid cyan curve) are shown.
The efficiency of the zero decay electrons cut is > 99.99%, sothat the drop from the dotted red line to the solid cyan line is due
solely to the neutron tagging cut.

221301-3

PHYSICAL REVIEW LETTERS 120, 221301 (2018)
TABLE I. Number of events over the entire sky passing each cut in 2628.1 days of SK4 data, simulated ν-MC background expectation,and signal efficiency at representative energy after each cut.
100 MeV < Evis < 1.33 GeV
FCFV& single ring
& e-like& zero decay-e& zero neutrons

1.33 GeV < Evis < 20 GeV

Evis > 20 GeV

Data

ν- MC

ϵsig ð0.5 GeVÞ

Data

ν- MC

ϵsig ð5 GeVÞ

Data

ν- MC

ϵsig ð50 GeVÞ15 206
11 367
5655
5049
4042

14 858.1
10 997.4
5571.55013.83992.9

97.7%
95.8%
94.7%
94.7%
93.0%

4908
2868
1514
1065
658

5109.73161.81644.21207.2
772.6

93.8%
93.3%
93.0%
93.0%
91.3%

118
71
71
13
3

107.5
68.2
68.1
15.7
7.4

84.9%
82.2%
82.2%
82.2%
81.1%

tags in real data recorded by a periodic trigger and, thus, has
minimal systematic uncertainty.
Because the atmospheric neutrino background to thissearch is strongly energy dependent, events are separated
into three samples based on visible energy with ranges
100 MeV < Evis < 1.33 GeV, 1.33 GeV < Evis < 20 GeV,
and Evis > 20 GeV. The number of data events is shownfor each sample in Table I, along with the simulated
atmospheric neutrino Monte Carlo (MC) expectation.
The signal efficiency at representative energies basedon signal electron MC simulation is also shown. The
importance of the decay electron and neutron tagging
cuts is particularly evident in the highest-energy sample(Evis > 20 GeV), where they together reduce the background by about a factor of 10 while having a minimal
effect on the signal efficiency.
Since boosted dark matter is expected to originate inregions of high dark matter density, this search looks for a
signal coming from the Galactic center or the Sun (someboosted dark matter models predict a significant capture
rate of cold dark matter in the Sun, either through a spindependent dark matter-nucleus cross section [20] or
through the combination of a relatively strong dark matter
self-interaction and coupling between cold dark matter andstandard model particles through boosted dark matter loops[23]). Cones are drawn around the signal source, and thenumber of events passing the analysis cuts in each cone iscounted. While the exact relationship between the boosted
dark matter and the scattered electron directions is model
dependent, the scattering is, in general, expected to bestrongly forward, since the energy of the boosted dark
matter and the electron recoil energy are both assumed to bemuch greater than the mass of the electron. Under theseassumptions, the scattering angle of the recoil electron iskinematically constrained to be less than 5.8° at a recoil
energy of 100 MeV, withtheﬃ maximum allowed scatteringpﬃﬃﬃﬃﬃ
angle decreasing as 1= Ee . Thus, since the reconstructed
electron direction was found to have an angular resolution
better than 3° over the entire energy range, it is a goodproxy for the direction of the boosted dark matter.
When the source of the signal is the Galactic center,the optimal size of the search cone is dependent on both the
distribution of the dominant dark matter species in the

Galaxy and the production method of the boosted dark
matter. Production of boosted dark matter through bothdark matter annihilation and decay were considered forthree dark matter halo models: Moore [43], Navarro-FrenkWhite (NFW) [44], and Kravtsov [45]. For each combination of halo model and production method, the signal
MC was reweighted assuming the direction of the scatteredelectron was the same as the direction of the boosted dark
matter. Optimalcone angles were found by maximizing
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
efficiency= background. The optimal half-opening angleof the search cone was found to range from less than 5° toaround 40°, depending on the halo model and boosted dark
matter production method. We therefore used eight searchcones around the Galactic center, ranging from 5° to 40° in
steps of 5°. When the Sun is the signal source, the situation
is much simpler, since it is effectively a point source.
Therefore, a single search cone of 5° around the Sun wasused for the solar search.
A data-driven off-source method was used to estimate
the background due to atmospheric neutrinos for the twolower-energy samples [46]. In order to avoid contaminationfrom a potential signal, the off-source region is definedas everything outside an 80° cone for the Galactic centersearch and everything outside of the 5° search cone for thesolar search. The off-source regions are defined, like thesearch cones, in celestial coordinates for the Galactic centersearch and solar coordinates for the Sun search. For aparticular search cone, each data event in the off-source
region can be assigned two values based on its direction inhorizontal coordinates d̂: T off , which is the fraction of timed̂ spends within the off-source region, and T on , which is thefraction of time d̂ spends within the search cone. The eventis then weighted by the ratio T on =T off . The sum of theseweights gives an estimate of the background in the searchcone, while the square root of the sum of the squares of theweights gives the uncertainty on this estimate. The resulting
estimates are independent of MC calculations, and theiruncertainties range from 3% to 19%, which are smaller thanthe uncertainties on the corresponding estimates based on
MC calculations.
While the off-source method works well for the twolower-energy samples, there are too few events in thehighest-energy sample (Evis > 20 GeV) for it to be

221301-4

Fraction of Events with 0 Tagged Neutrons

PHYSICAL REVIEW LETTERS 120, 221301 (2018)
1
0.9
0.8
0.7
0.6
0.5

Data
MC
Data Fit
MC Fit

0.4
0.3
0.2
0.1
0
10−1

1

10

102

Evis(GeV)

FIG. 2. Neutron tagging cut systematic error estimation. Data
and MC fits are to logarithmic function.

successfully applied. Therefore, the background in thehighest-energy sample was estimated using the 500-yr
SK atmospheric neutrino MC calculation. The MC calculation was livetime normalized and oscillated according tothree-flavor oscillations with nominal oscillation parameters. The systematic uncertainty on the estimated background was found by summing in quadrature the effects of1σ shifts of 75 systematics [40]. The uncertainties in thevalues of oscillation parameters were included as systematics. The total uncertainty in the background was estimated to be 30%. The dominant systematic is theuncertainty related to the neutron tagging cut, which isestimated to be 23%. This systematic accounts for theuncertainty in the efficiency of the neutron tagging algorithm, as well as in the modeling of production andtransport of neutrons in the detector. It was estimatedusing a data-MC comparison of the fraction of events (overthe entire sky) passing the first three analysis cuts that also
had zero tagged neutrons. This comparison is shown in
Fig. 2. Above about 10 GeVof visible energy, there are very
few events in the data, making a data-MC comparison
difficult. To compensate, both the data and MC calculations

were fit to logarithmic functions A þ B logðEvis =GeVÞ, inthe region above 3 GeV. The systematic uncertainty as afunction of the energy was then taken as the difference
between the data fit and the MC fit. The value of theneutron tagging systematic for the background estimateof the highest-energy sample was found by applying
this shift on an event by event basis as a function of thevisible energy of the particular event. While this estimate israther imprecise, the expected background rates in thesignal cones above 20 GeV are all below one, meaning thatthe systematic uncertainty on the background estimate isminimal compared to fluctuations associated with Poissoncounting statistics. It is thus only the magnitude of thissystematic that is important; its exact value has minimal
influence on the calculated limits.
The results of the search are shown in Table II. The
observed data are consistent with expected background forboth the Galactic center and Sun searches. In the highestenergy sample, the search is essentially background-free,and no candidates were found in any of the search cones.
Sky maps of the locations of every event passing theanalysis cuts are provided for each energy sample in
Supplemental Material [47]. For each cone and energy
sample, confidence intervals for the observed boosted dark
matter event rate were computed using a Poisson χ 2 statisticthat incorporates the systematic uncertainty on the background estimate through the pull method [48,49]:

 

O
2
χ ðsÞ ¼ minδ 2 E − O þ O ln
þδ ;
E
2

ð1Þ

where E ¼ bð1 þ δσÞ þ s, b is the estimated number ofbackground events with systematic uncertainty σ, s is thenumber of signal events being tested, δ is the systematicpull that is minimized over, and O is the observed numberof events. Note that, for the two lower-energy samples, thebackground systematic uncertainty σ is due to statisticalfluctuations associated with the off-source method, while

TABLE II. Estimated backgrounds, numbers of events in data, and signal event rate limits for each cone and each energy sample. The
event rate limits are at the 90% confidence level.
100 MeV < Evis < 1.33 GeV

1.33 MeV < Evis < 20 GeV

Evis > 20 GeV

Searchcone

Expected
bckg

Data

Sig rate limitðkt yrÞ−1

Expected
bckg

Data

Sig rate limitðkt yrÞ−1

Expected
bckg

Data

Sig rate limitðkt yrÞ−1

GC 5°
GC 10°GC 15°GC 20°GC 25°GC 30°
GC 35°
GC 40°

8.4  0.7
32.0  1.9
72.5  3.5
126.5  5.4
196.8  7.6
283.7  10.1
384.8  12.8
499.6  15.9

5
24
69
125
202
285
375
494

0.017
0.023
0.078
0.123
0.201
0.214
0.187
0.249

1.6  0.3
6.3  0.84
13.6  1.6
23.3  2.3
35.4  3.3
49.3  4.3
68.1  5.4
90.2  6.9

1
5
11
18
31
48
67
90

0.018
0.026
0.032
0.028
0.049
0.081
0.101
0.124

0.016  0.005
0.060  0.018
0.14  0.04
0.25  0.07
0.37  0.11
0.53  0.16
0.70  0.21
0.90  0.27

0
0
0
0
0
0
0
0

0.015
0.015
0.014
0.014
0.013
0.012
0.011
0.011

Sun 5°

7.59  0.18

5

0.017

1.25  0.07

1

0.020

0.015  0.004

0

0.015

221301-5

PHYSICAL REVIEW LETTERS 120, 221301 (2018)
for the highest-energy sample it is due to uncertainties in
the MC production. The test statistic Δχ 2 was calculated bysubtracting the global minimum χ 2 . To find the confidence
level at which a particular value of s is allowed, themeasured value of Δχ 2 at that value of s was comparedto the Δχ 2 distribution of a large number of toy MC
calculations produced assuming that level of signal. Since
the s ¼ 0 hypothesis is allowed at 90% confidence for all
search cones and energy samples, the upper ends of the
90% confidence intervals are interpreted as 90% upper
limits and presented in Table II.
To demonstrate the application of this result to a
specific model, limits were calculated on a baseline
boosted dark matter model with the Galactic center as
the signal source [18]. This model introduces two darkfermions ψ A and ψ B and a massive dark photon γ 0 , with anassumed mass ordering mA > mB > mγ0 . The particle ψ A
is proposed to be the dominant cold dark matter in the
Universe and does not couple directly to standard model
particles. The particle ψ B is the boosted dark matter andcouples to standard model particles through the exchangeof the dark photon γ 0 . The coupling between γ 0 and ψ B isset by a coupling constant g0 , which is proposed to belarge but perturbative, while the coupling between γ 0 ande− is scaled from γ − e− coupling by the constant ε.
Limits were calculated for two scenarios of ψ B production: one where ψ B is produced through annihilation ofψ A with ψ̄ A and another where ψ B is produced throughthe decay of ψ A . In the annihilation scenario, thethermal annihilation cross section is set to hσ AĀ→BB̄ vi ¼
5 × 10−26 cm3 =s in order to achieve the observed relicdensity ΩA ≈ 0.2 through an assisted freeze-out scenario[18,26]. The energy of ψ B is equal to mA in this scenario.
In the decay scenario, the decay lifetime of ψ A , τdecay , istaken to be a free parameter, and the energy of ψ B is
assumed to be mA =2.
Limits were calculated separately for the Moore, NFW,
and Kravtsov galactic halo models, using the results from adifferent cone for each fit. For the annihilation scenario, the
5° cone was used for the Moore model, the 10° cone for the
NFW model, and the 40° cone for the Kravtsov model. For
the decay scenario, the 40° cone was used for all threegalactic halo models. These cones were selected using thecone optimization technique described earlier. For eachhalo model, signal MC events were reweighted based on
the values of mA , mB , mγ0 , ε, and g0 at the particular point inparameter space being tested. This reweighting accounts forthe model-dependent recoil electron energy spectrum, as
well as the model-dependent smearing between the boosted
dark matter direction and the recoil electron direction. The
effect of boosted dark matter scattering off of both electronsand protons in Earth is also accounted for, though this effectis negligible for the majority of the allowed parameter
space. A binned χ 2 statistic was then computed similar tothe one described above:

2

χ ¼

3
X
i

 


Oi
2
þ δi ; ð2Þ
minδi 2 Ei − Oi þ Oi ln
Eiwith variables defined as before, summed over three bins
corresponding to the three energy samples. The Δχ 2 test
statistic was then calculated by subtracting the global
minimum χ 2 . Confidence intervals were found by comparing the measured Δχ 2 values with the distributions of Δχ 2
values found by many toy Monte Carlo simulations
produced at each point. Ninety-percent confidence intervals
were computed in the ε vs mA plane for the annihilation
scenario, and the ε=τdecay vs mA plane for the decay
scenario, with mB , m0γ , and g0 set to representative valuesof mB ¼ 200 MeV, m0γ ¼ 20 MeV, and g0 ¼ 0.5, respectively. Since the ε ¼ 0 points, which correspond to no
signal, are allowed at 90% confidence, the resulting
confidence intervals are interpreted as upper limits.
These limits are shown for the Moore, NFW, andKravtsov halo models in Fig. 3.
In summary, we have searched for evidence of boosted
dark matter by looking for high-energy elastically scatteredelectrons that point back to the Galactic center or the Sun.
We have found no such evidence. This is the first study ofhigh-energy electron elastic scatterlike events at SK. The
use of decay electron and tagged neutron cuts significantly
reduced background in the highest-energy sample, allowing

FIG. 3. 90% confidence interval upper limits for mB ¼
200 MeV, m0γ ¼ 20 MeV, and g0 ¼ 0.5, for boosted dark matterproduced by annihilation (top) and decay (bottom).

221301-6

PHYSICAL REVIEW LETTERS 120, 221301 (2018)
for an effectively background-free search in that energy
range. Our results are presented in a modelindependent way, which makes them applicable not only
to boosted dark matter but to any theory that predicts anexcess of particles from the Galactic center or Sun that would
elastically scatter electrons to energies above 100 MeV.
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. Some ofus have been supported by funds from the National Research
Foundation of Korea NRF-2009-0083526 (KNRC) fundedby the Ministry of Science, ICT, and Future Planning, theEuropean Union H2020 RISE-GA641540-SKPLUS, theJapan Society for the Promotion of Science, the National
Natural Science Foundation of China under Grant
No. 11235006, the National Science and Engineering
Research Council (NSERC) of Canada, the Scinet andWestgrid consortia of Compute Canada, and the National
Science Centre, Poland (2015/17/N/ST2/04064 and 2015/
18/E/ST2/00758).

*

Deceased.
Also at Department of Physics and Astronomy, UCLA,
California 90095-1547, USA.
‡
Also at BMCC/CUNY, Science Department, New York,New York, USA.
[1] F. Zwicky, Helv. Phys. Acta 6, 110 (1933) [Gen. Relativ.
Gravit. 41, 207 (2009)].
[2] V. C. Rubin, N. Thonnard, and W. K. Ford, Jr, Astrophys. J.
238, 471 (1980).
[3] G. R. Blumenthal, S. M. Faber, J. R. Primack, and M. J.
Rees, Nature (London) 311, 517 (1984).
[4] K. G. Begeman, A. H. Broeils, and R. H. Sanders, Mon.
Not. R. Astron. Soc. 249, 523 (1991).
[5] G. Bertone, D. Hooper, and J. Silk, Phys. Rep. 405, 279(2005).
[6] K. Bamba, S. Capozziello, S. Nojiri, and S. D. Odintsov,
Astrophys. Space Sci. 342, 155 (2012).
[7] P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys.
594, A13 (2016).
[8] G. Hinshaw et al. (WMAP Collaboration), Astrophys. J.
Suppl. Ser. 208, 19 (2013).
[9] D. S. Akerib et al. (LUX Collaboration), Phys. Rev. Lett.
112, 091303 (2014).
[10] Z. Ahmed et al. (CDMS-II Collaboration), Science 327,
1619 (2010).
[11] E. Aprile et al. (XENON100 Collaboration), Phys. Rev.
Lett. 109, 181301 (2012).
[12] S. Desai et al. (Super-Kamiokande Collaboration), Phys.
Rev. D 70, 083523 (2004); 70, 109901(E) (2004).
[13] M. G. Aartsen et al. (IceCube Collaboration), Eur. Phys. J. C
77, 627 (2017).
†[14] S. Adrian-Martinez et al. (ANTARES Collaboration), J.
Cosmol. Astropart. Phys. 11 (2013) 032.
[15] V. Khachatryan et al. (CMS Collaboration), Eur. Phys. J. C
75, 235 (2015).
[16] G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C 75,
299 (2015); 75, 408(E) (2015).
[17] J. Goodman, M. Ibe, A. Rajaraman, W. Shepherd,
T. M. P. Tait, and H.-B. Yu, Phys. Rev. D 82, 116010(2010).
[18] K. Agashe, Y. Cui, L. Necib, and J. Thaler, J. Cosmol.
Astropart. Phys. 10 (2014) 062.
[19] J. Huang and Y. Zhao, J. High Energy Phys. 02 (2014)077.
[20] J. F. Cherry, M. T. Frandsen, and I. M. Shoemaker, Phys.
Rev. Lett. 114, 231303 (2015).
[21] A. Bhattacharya, R. Gandhi, and A. Gupta, J. Cosmol.
Astropart. Phys. 03 (2015) 027.
[22] J. Kopp, J. Liu, and X.-P. Wang, J. High Energy Phys. 04(2015) 105.
[23] K. Kong, G. Mohlabeng, and J.-C. Park, Phys. Lett. B 743,
256 (2015).
[24] J. Berger, Y. Cui, and Y. Zhao, J. Cosmol. Astropart. Phys.
02 (2015) 005.
[25] D. Kim, J.-C. Park, and S. Shin, Phys. Rev. Lett. 119,161801 (2017).
[26] G. Belanger and J.-C. Park, J. Cosmol. Astropart. Phys. 03(2012) 038.
[27] H. S. Cheon, S. K. Kang, and C. S. Kim, Phys. Lett. B 675,
203 (2009); 698, 324(E) (2011).
[28] F. D’Eramo and J. Thaler, J. High Energy Phys. 06 (2010)109.
[29] T. Hambye, J. High Energy Phys. 01 (2009) 028.
[30] T. Hambye and M. H. G. Tytgat, Phys. Lett. B 683, 39(2010).
[31] C. Arina, T. Hambye, A. Ibarra, and C. Weniger, J. Cosmol.
Astropart. Phys. 03 (2010) 024.
[32] G. Belanger, K. Kannike, A. Pukhov, and M. Raidal, J.
Cosmol. Astropart. Phys. 04 (2012) 010.
[33] E. D. Carlson, M. E. Machacek, and L. J. Hall, Astrophys. J.
398, 43 (1992).
[34] A. A. de Laix, R. J. Scherrer, and R. K. Schaefer, Astrophys.
J. 452, 495 (1995).
[35] Y. Hochberg, E. Kuflik, T. Volansky, and J. G. Wacker,
Phys. Rev. Lett. 113, 171301 (2014).
[36] A. Bhattacharya, R. Gandhi, A. Gupta, and S. Mukhopadhyay,
J. Cosmol. Astropart. Phys. 05 (2017) 002.
[37] L. Necib, J. Moon, T. Wongjirad, and J. M. Conrad, Phys.
Rev. D 95, 075018 (2017).
[38] H. Alhazmi, K. Kong, G. Mohlabeng, and J.-C. Park, J.
High Energy Phys. 04 (2017) 158.
[39] Y. Fukuda et al. (Super-Kamiokande Collaboration),
Nucl. Instrum. Methods Phys. Res., Sect. A 501, 418(2003).
[40] R. Wendell et al. (Super-Kamiokande Collaboration), Phys.
Rev. D 81, 092004 (2010).
[41] K. Abe et al. (Super-Kamiokande Collaboration), Phys.
Rev. D 95, 012004 (2017).
[42] See Supplemental Material at http://link.aps.org/
supplemental/10.1103/PhysRevLett.120.221301 for event
displays of example events passing the analysis cuts.

221301-7

PHYSICAL REVIEW LETTERS 120, 221301 (2018)[43] B. Moore, T. R. Quinn, F. Governato, J. Stadel, and G. Lake,
Mon. Not. R. Astron. Soc. 310, 1147 (1999).
[44] J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J.
462, 563 (1996).
[45] A. V. Kravtsov, A. A. Klypin, J. S. Bullock, and J. R.
Primack, Astrophys. J. 502, 48 (1998).
[46] T. P. Li and Y. Q. Ma, Astrophys. J. 272, 317 (1983).

[47] See Supplemental Material at http://link.aps.org/
supplemental/10.1103/PhysRevLett.120.221301 for sky
maps of events passing analysis cuts.
[48] G. L. Fogli, E. Lisi, A. Marrone, D. Montanino, and A.
Palazzo, Phys. Rev. D 66, 053010 (2002).
[49] C. Patrignani et al. (Particle Data Group), Chin. Phys. C 40,
100001 (2016).

221301-8