The Super-Kamiokande Collaboration

# Search for Cosmic-ray Boosted Sub-GeV Dark Matter using Recoil Protons at
Super-Kamiokande

K. Abe  Kamioka Observatory, Institute for Cosmic Ray Research, University of
Tokyo, Kamioka, Gifu 506-1205, Japan  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  Y. Hayato
Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,
Kamioka, Gifu 506-1205, Japan  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  K. Hiraide  Kamioka
Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka,
Gifu 506-1205, Japan  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  K. Ieki  M. Ikeda
Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,
Kamioka, Gifu 506-1205, Japan  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  J. Kameda  Kamioka
Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka,
Gifu 506-1205, Japan  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  Y. Kanemura  R. Kaneshima
Y. Kashiwagi  Kamioka Observatory, Institute for Cosmic Ray Research,
University of Tokyo, Kamioka, Gifu 506-1205, Japan  Y. Kataoka  Kamioka
Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka,
Gifu 506-1205, Japan  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  S. Miki  Kamioka
Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka,
Gifu 506-1205, Japan  S. Mine  Kamioka Observatory, Institute for Cosmic Ray
Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan  Department of
Physics and Astronomy, University of California, Irvine, Irvine, CA
92697-4575, USA  M. Miura  S. Moriyama  Kamioka Observatory, Institute for
Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan  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  Y. Nakano  Kamioka Observatory, Institute for
Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan  M.
Nakahata  Kamioka Observatory, Institute for Cosmic Ray Research, University
of Tokyo, Kamioka, Gifu 506-1205, Japan  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  S.
Nakayama  Kamioka Observatory, Institute for Cosmic Ray Research, University
of Tokyo, Kamioka, Gifu 506-1205, Japan  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  Y.
Noguchi  K. Okamoto  K. Sato  Kamioka Observatory, Institute for Cosmic Ray
Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan  H. Sekiya
Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,
Kamioka, Gifu 506-1205, Japan  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  H. Shiba  K. Shimizu
Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo,
Kamioka, Gifu 506-1205, Japan  M. Shiozawa  Kamioka Observatory, Institute for
Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan  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  Y. Sonoda  Y. Suzuki  Kamioka Observatory,
Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu
506-1205, Japan  A. Takeda  Kamioka Observatory, Institute for Cosmic Ray
Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan  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  Y. Takemoto  Kamioka Observatory, Institute for Cosmic Ray Research,
University of Tokyo, Kamioka, Gifu 506-1205, Japan  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  A. Takenaka  Kamioka Observatory, Institute for Cosmic Ray Research,
University of Tokyo, Kamioka, Gifu 506-1205, Japan  H. Tanaka  Kamioka
Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka,
Gifu 506-1205, Japan  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  S. Watanabe  Kamioka
Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka,
Gifu 506-1205, Japan  T. Yano  Kamioka Observatory, Institute for Cosmic Ray
Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan  S. Han  Research
Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of
Tokyo, Kashiwa, Chiba 277-8582, Japan  T. Kajita  Research Center for Cosmic
Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa,
Chiba 277-8582, Japan  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  ILANCE, CNRS - University
of Tokyo International Research Laboratory, Kashiwa, Chiba 277-8582, Japan  K.
Okumura  Research Center for Cosmic Neutrinos, Institute for Cosmic Ray
Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan  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  T. Tashiro  T. Tomiya  X. Wang  J. Xia  S. Yoshida  Research Center for
Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo,
Kashiwa, Chiba 277-8582, Japan  G. D. Megias  Institute for Cosmic Ray
Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan  P. Fernandez
L. Labarga  N. Ospina  B. Zaldivar  Department of Theoretical Physics,
University Autonoma Madrid, 28049 Madrid, Spain  B. W. Pointon  Department of
Physics, British Columbia Institute of Technology, Burnaby, BC, V5G 3H2,
Canada  TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3, Canada  E. Kearns
Department of Physics, Boston University, Boston, MA 02215, USA  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  J. L. Raaf  Department of Physics, Boston
University, Boston, MA 02215, USA  L. Wan  Corresponding author
Email address<EMAIL_ADDRESS>(L. Wan) Department of Physics, Boston University,
Boston, MA 02215, USA  T. Wester  Department of Physics, Boston University,
Boston, MA 02215, USA  J. Bian  N. J. Griskevich  Department of Physics and
Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA  W. R.
Kropp  Deceased.  Department of Physics and Astronomy, University of
California, Irvine, Irvine, CA 92697-4575, USA  S. Locke  Department of
Physics and Astronomy, University of California, Irvine, Irvine, CA
92697-4575, USA  M. B. Smy  H. W. Sobel  Department of Physics and Astronomy,
University of California, Irvine, Irvine, CA 92697-4575, USA  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  V. Takhistov  Department of Physics and Astronomy, University of
California, Irvine, Irvine, CA 92697-4575, USA  High Energy Accelerator
Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan  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  A. Yankelevich  Department of Physics and Astronomy, University of
California, Irvine, Irvine, CA 92697-4575, USA  J. Hill  Department of
Physics, California State University, Dominguez Hills, Carson, CA 90747, USA
R. G. Park  Institute for Universe and Elementary Particles, Chonnam National
University, Gwangju 61186, Korea  B. Bodur  Department of Physics, Duke
University, Durham NC 27708, USA  K. Scholberg  C. W. Walter  Department of
Physics, Duke University, Durham NC 27708, USA  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  L. Bernard  A. Coffani  O. Drapier  S. El Hedri  A. Giampaolo  Th. A.
Mueller  A. D. Santos  P. Paganini  B. Quilain  Ecole Polytechnique,
IN2P3-CNRS, Laboratoire Leprince-Ringuet, F-91120 Palaiseau, France  T.
Ishizuka  Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka
811-0295, Japan  T. Nakamura  Department of Physics, Gifu University, Gifu,
Gifu 501-1193, Japan  J. S. Jang  GIST College, Gwangju Institute of Science
and Technology, Gwangju 500-712, Korea  J. G. Learned  Department of Physics
and Astronomy, University of Hawaii, Honolulu, HI 96822, USA  K. Choi
Institute for Basic Science (IBS), Daejeon, 34126, Korea  S. Cao  Institute
For Interdisciplinary Research in Science and Education, ICISE, Quy Nhon,
55121, Vietnam  L. H. V. Anthony  D. Martin  M. Scott  A. A. Sztuc  Y. Uchida
Department of Physics, Imperial College London , London, SW7 2AZ, United
Kingdom  V. Berardi  M. G. Catanesi  E. Radicioni  Dipartimento
Interuniversitario di Fisica, INFN Sezione di Bari and Università e
Politecnico di Bari, I-70125, Bari, Italy  N. F. Calabria  L. N. Machado  G.
De Rosa  Dipartimento di Fisica, INFN Sezione di Napoli and Università di
Napoli, I-80126, Napoli, Italy  G. Collazuol  F. Iacob  M. Lamoureux  M.
Mattiazzi  Dipartimento di Fisica, INFN Sezione di Padova and Università di
Padova, I-35131, Padova, Italy  L. Ludovici  INFN Sezione di Roma and
Università di Roma “La Sapienza”, I-00185, Roma, Italy  M. Gonin  G. Pronost
ILANCE, CNRS - University of Tokyo International Research Laboratory, Kashiwa,
Chiba 277-8582, Japan  C. Fujisawa  Y. Maekawa  Y. Nishimura  Department of
Physics, Keio University, Yokohama, Kanagawa, 223-8522, Japan  M. Friend  T.
Hasegawa  T. Ishida  T. Kobayashi  M. Jakkapu  T. Matsubara  T. Nakadaira
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki
305-0801, Japan  K. Nakamura  High Energy Accelerator Research Organization
(KEK), Tsukuba, Ibaraki 305-0801, Japan  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  Y. Oyama
K. Sakashita  T. Sekiguchi  T. Tsukamoto  High Energy Accelerator Research
Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan  T. Boschi  F. Di
Lodovico  J. Gao  A. Goldsack  T. Katori  J. Migenda  M. Taani  Department of
Physics, King’s College London, London, WC2R 2LS, UK  S. Zsoldos  Department
of Physics, King’s College London, London, WC2R 2LS, UK  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  Y. Kotsar  H. Ozaki  A. T. Suzuki  Department of Physics, Kobe
University, Kobe, Hyogo 657-8501, Japan  Y. Takeuchi  Department of Physics,
Kobe University, Kobe, Hyogo 657-8501, Japan  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  C.
Bronner  J. Feng  T. Kikawa  M. Mori  Department of Physics, Kyoto University,
Kyoto, Kyoto 606-8502, Japan  T. Nakaya  Department of Physics, Kyoto
University, Kyoto, Kyoto 606-8502, Japan  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  R. A.
Wendell  Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
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  K. Yasutome  Department of Physics, Kyoto
University, Kyoto, Kyoto 606-8502, Japan  S. J. Jenkins  N. McCauley  P. Mehta
K. M. Tsui  Department of Physics, University of Liverpool, Liverpool, L69
7ZE, United Kingdom  Y. Fukuda  Department of Physics, Miyagi University of
Education, Sendai, Miyagi 980-0845, Japan  Y. Itow  Institute for Space-Earth
Environmental Research, Nagoya University, Nagoya, Aichi 464-8602, Japan
Kobayashi-Maskawa Institute for the Origin of Particles and the Universe,
Nagoya University, Nagoya, Aichi 464-8602, Japan  H. Menjo  K. Ninomiya
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya,
Aichi 464-8602, Japan  J. Lagoda  S. M. Lakshmi  M. Mandal  P. Mijakowski  Y.
S. Prabhu  J. Zalipska  National Centre For Nuclear Research, 02-093 Warsaw,
Poland  M. Jia  J. Jiang  C. K. Jung  M. J. Wilking  C. Yanagisawa  also at
BMCC/CUNY, Science Department, New York, New York, 1007, USA.  Department of
Physics and Astronomy, State University of New York at Stony Brook, NY
11794-3800, USA  M. Harada  H. Ishino  S. Ito  H. Kitagawa  Department of
Physics, Okayama University, Okayama, Okayama 700-8530, Japan  Y. Koshio
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
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  F. Nakanishi  S. Sakai  Department of Physics,
Okayama University, Okayama, Okayama 700-8530, Japan  G. Barr  D. Barrow
Department of Physics, Oxford University, Oxford, OX1 3PU, United Kingdom  L.
Cook  Department of Physics, Oxford University, Oxford, OX1 3PU, United
Kingdom  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  S. Samani  Department of Physics,
Oxford University, Oxford, OX1 3PU, United Kingdom  D. Wark  Department of
Physics, Oxford University, Oxford, OX1 3PU, United Kingdom  STFC, Rutherford
Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington,
OX11 0QX, United Kingdom  F. Nova  Rutherford Appleton Laboratory, Harwell,
Oxford, OX11 0QX, UK  J. Y. Yang  Department of Physics, Seoul National
University, Seoul 151-742, Korea  M. Malek  J. M. McElwee  O. Stone  M. D.
Thiesse  L. F. Thompson  Department of Physics and Astronomy, University of
Sheffield, S3 7RH, Sheffield, United Kingdom  H. Okazawa  Department of
Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu,
Shizuoka, 425-8611, Japan  S. B. Kim  J. W. Seo  I. Yu  Department of Physics,
Sungkyunkwan University, Suwon 440-746, Korea  A. K. Ichikawa  K. D. Nakamura
S. Tairafune  Department of Physics, Faculty of Science, Tohoku University,
Sendai, Miyagi, 980-8578, Japan  K. Nishijima  Department of Physics, Tokai
University, Hiratsuka, Kanagawa 259-1292, Japan  K. Iwamoto  K. Nakagiri
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan  Y.
Nakajima  Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033,
Japan  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  N. Taniuchi  Department of Physics, University
of Tokyo, Bunkyo, Tokyo 113-0033, Japan  M. Yokoyama  Department of Physics,
University of Tokyo, Bunkyo, Tokyo 113-0033, Japan  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  K. Martens  P. de Perio  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  M. R.
Vagins  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  Department of Physics and Astronomy,
University of California, Irvine, Irvine, CA 92697-4575, USA  M. Kuze  S.
Izumiyama  Department of Physics,Tokyo Institute of Technology, Meguro, Tokyo
152-8551, Japan  M. Inomoto  M. Ishitsuka  H. Ito  T. Kinoshita  R. Matsumoto
Y. Ommura  N. Shigeta  M. Shinoki  T. Suganuma  K. Yamauchi  Department of
Physics, Faculty of Science and Technology, Tokyo University of Science, Noda,
Chiba 278-8510, Japan  J. F. Martin  H. A. Tanaka  T. Towstego  Department of
Physics, University of Toronto, ON, M5S 1A7, Canada  R. Akutsu  TRIUMF, 4004
Wesbrook Mall, Vancouver, BC, V6T2A3, Canada  V. Gousy-Leblanc  also at
University of Victoria, Department of Physics and Astronomy, PO Box 1700 STN
CSC, Victoria, BC V8W 2Y2, Canada.  TRIUMF, 4004 Wesbrook Mall, Vancouver, BC,
V6T2A3, Canada  M. Hartz  A. Konaka  N. W. Prouse  TRIUMF, 4004 Wesbrook Mall,
Vancouver, BC, V6T2A3, Canada  S. Chen  B. D. Xu  B. Zhang  Department of
Engineering Physics, Tsinghua University, Beijing, 100084, China  M.
Posiadala-Zezula  Faculty of Physics, University of Warsaw, Warsaw, 02-093,
Poland  D. Hadley  M. Nicholson  M. O’Flaherty  B. Richards  Department of
Physics, University of Warwick, Coventry, CV4 7AL, UK  A. Ali  Department of
Physics, University of Winnipeg, MB R3J 3L8, Canada  TRIUMF, 4004 Wesbrook
Mall, Vancouver, BC, V6T2A3, Canada  B. Jamieson  Department of Physics,
University of Winnipeg, MB R3J 3L8, Canada  Ll. Marti  A. Minamino  G.
Pintaudi  S. Sano  S. Suzuki  K. Wada  Department of Physics, Yokohama
National University, Yokohama, Kanagawa, 240-8501, Japan

###### Abstract

We report a search for cosmic-ray boosted dark matter with protons using the
0.37 megaton$\times$years data collected at Super-Kamiokande experiment during
the 1996-2018 period (SKI-IV phase). We searched for an excess of proton
recoils above the atmospheric neutrino background from the vicinity of the
Galactic Center. No such excess is observed, and limits are calculated for two
reference models of dark matter with either a constant interaction cross-
section or through a scalar mediator. This is the first experimental search
for boosted dark matter with hadrons using directional information. The
results present the most stringent limits on cosmic-ray boosted dark matter
and exclude the dark matter-nucleon elastic scattering cross-section between
$10^{-33}\text{ cm}^{2}$ and $10^{-27}\text{ cm}^{2}$ for dark matter mass
from 1 MeV/$c^{2}$ to 300 MeV/$c^{2}$.

DOI

††preprint: APS/123-QED

There is overwhelming evidence for the existence of dark matter Zwicky (1933);
Blumenthal  _et al._ (1984); Sofue and Rubin (2001); Schumann (2019); Bertone
and Hooper (2018). The properties of the dark matter remain unknown beyond
gravitational interaction, and there are a variety of theoretical models
predicting a wide range of masses for dark matter candidates (e.g. Essig  _et
al._ (2012); Knapen  _et al._ (2017); Smirnov and Beacom (2019)). Despite
significant efforts of highly sensitive direct dark matter detection
experiments to probe interactions of dark matter at the mass range of
GeV/$c^{2}$ to TeV/$c^{2}$, dark matter have been elusive thus far Akerib  _et
al._ (2017); Aprile  _et al._ (2018). Meanwhile, dark matter at the sub-GeV
mass range is poorly explored Feng and Kumar (2008); Boehm and Fayet (2004);
Lin  _et al._ (2012); Hochberg  _et al._ (2015). The conventional direct dark
matter detection experiments focusing on nuclear recoils are not sensitive to
cold sub-GeV dark matter due to insufficient recoil energy, and the
experimental searches of cold sub-GeV dark matter have focused on the Migdal
effect Ibe  _et al._ (2018); Aprile  _et al._ (2019a); Liu  _et al._ (2019a);
Armengaud  _et al._ (2019) and the interaction with electrons Essig  _et al._
(2012); Barak  _et al._ (2020); Arnaud  _et al._ (2020). Besides, if a
fraction of the cold dark matter is boosted to relativistic energies, it can
be efficiently detected in direct detection experiments as well as higher
threshold neutrino detectors Agashe  _et al._ (2014); Necib  _et al._ (2017);
Emken  _et al._ (2018); Hu  _et al._ (2017); Giudice  _et al._ (2018);
Cappiello and Beacom (2019); Argüelles  _et al._ (2022).

A general possibility for dark matter to obtain relativistic energies is via
the upscattering by cosmic-rays, constituting cosmic-ray boosted dark matter
(CRDM) Bringmann and Pospelov (2019); Ema  _et al._ (2019); Cappiello  _et
al._ (2019); Cappiello and Beacom (2019). The upscattering process originates
from the same dark matter-nucleus interactions as direct detection experiments
search for, without requiring additional assumptions or model dependence. Due
to the dark matter density distribution concentrated toward the Galactic
Center (GC) Navarro  _et al._ (1996), the CRDM arriving at the Earth has a
directional preference from the GC. For terrestrial detectors, the CRDM-
nucleon interaction in the Earth can be sizable, and the dark matter can be
scattered multiple times and become attenuated when traveling through the
Earth Ge  _et al._ (2021).

The boosted relativistic component can be observed by the interactions in the
detector with electrons Agashe  _et al._ (2014); Ema  _et al._ (2019) or
hadrons Ema  _et al._ (2021); Cappiello and Beacom (2019). In 2018, the Super-
Kamiokande experiment published the first experimental search for boosted dark
matter in a terrestrial detector with electron recoils Kachulis  _et al._
(2018). Later on, PROSPECT Andriamirado  _et al._ (2021), PandaX-II Cui  _et
al._ (2022), and CDEX-10 Xu  _et al._ (2022) reported their result on CRDM
using nuclear recoils, setting cross-section limits at $10^{-31}-10^{-26}$ cm2
in a dark matter mass region from MeV/$c^{2}$ to GeV/$c^{2}$.

In this analysis, we search for CRDM from MeV/$c^{2}$ to GeV/$c^{2}$ with
recoil protons at the Super-Kamiokande (SK) experiment Fukuda  _et al._
(2003). We use the data collected at SK during the 1996-2018 period (SKI-IV
phases). The large fiducial volume and the directional reconstruction ability
of SK, a water Cherenkov detector, enables a sensitive search for CRDM. The
parameter space we explore extends by more than one order of magnitude beyond
the existing limits Andriamirado  _et al._ (2021); Cui  _et al._ (2022).

Super-Kamiokande is a cylindrical 50 kiloton water Cherenkov detector located
in Kamioka, Japan, under a 2,700 meter water-equivalent rock overburden Fukuda
_et al._ (2003). The detector consists of an inner detector (ID) and an outer
detector (OD) optically separated at 2 m from the detector’s outer wall. There
are 11,129 inward-facing 20-inch PMTs viewing the 32 kton target volume of the
ID, and the OD is viewed by 1,885 outward-facing 8-inch PMTs. The ID is used
to reconstruct the energies, vertices, and to perform the particle
identifications (PID) of the physics events, while the OD is primarily used as
a veto for charged particles entering from outside the detector or identifying
particles that exit the ID.

This analysis uses the fully contained fiducial volume (FCFV) dataset composed
of events that have activity only in the ID (FC) and are reconstructed with
vertices more than 2 m from the ID wall, corresponding to the 22.5 kton
fiducial volume (FV). The total livetime of the dataset is 6050.3 days,
corresponding to an exposure of 0.37 megaton$\times$years. The visible energy,
corresponding to the energy of an electron that would cause the same amount of
light in the detector, of the events is required to be above 30 MeV to remove
spallation backgrounds induced by the cosmic-ray muons. To select recoil
protons without extra activities, we require the candidate events to have only
one single reconstructed Cherenkov ring.

In this FCFV sample, the majority of events are electrons and muons. Electrons
create electromagnetic showers which produce fuzzy rings and can be easily
removed, while muons and protons have a sharp ring edge. To select proton
events from the muon background, we employed a proton fitter that utilizes the
light pattern and ring topology to calculate the proton likelihood, proton
momentum, and track length Fechner  _et al._ (2009). A distinctive feature of
the protons is that they are likely to have hadronic interactions in water and
lose energy by producing secondary particles. If both the secondary particles
and the scattered proton are below Cherenkov threshold, the Cherenkov light
emission is truncated and leaves a narrow proton Cherenkov ring. If the
secondary particles, typically pions, are energetic enough to emit bright
Cherenkov light, the identification of the proton becomes significantly more
difficult, and therefore the reconstruction is less efficient for higher
momentum protons due to the higher hadronic interaction probability.

Since the identification performance depends on proton momentum, we
established a series of kinematic precuts. To remove the majority of high
energy muons, we require the reconstructed proton momentum to be less than 3
GeV/$c$, the visible energy to be less than 400 MeV, and the corrected charge
within $70^{\circ}$ of the direction Abe  _et al._ (2022) to be less than
2,000 photo-electrons. Due to the large mass, protons have a smaller Cherenkov
angle compared to muons at the same momentum, and thus we require the
reconstructed Cherenkov angle of candidate events to be less than 40∘.
Finally, we place a cut on the proton-muon identification likelihood.

To further enhance the proton-muon separation, a multi-variate analysis (MVA)
is employed after the precuts. The input variables include the fitted track
length, the fitted momentum, and the PID likelihood from the proton fitter
Fechner  _et al._ (2009), the charge distribution within and outside of the
Cherenkov ring, the reconstructed Cherenkov angle, the vertex reconstruction
quality, and the number of decay-electrons. More details on the variable
definitions and distributions can be found in the supplementary material Abe
_et al._ (2022).

The structure of the MVA is selected as a multilayer perceptron Hocker  _et
al._ (2007), which is trained with simulated protons and non-proton events
from the atmospheric neutrino MC sample after the precuts. The MVA takes the
eight input variables and outputs an estimator describing how signal- or
background-like an event is. The cut on the MVA estimator is optimized towards
best sensitivity assuming a 0.37 megaton$\times$years exposure and realistic
systematic errors, and the corresponding efficiency is shown in Fig. 1. The
proton reconstruction is only feasible within a momentum window between 1.2
GeV/$c$ and 2.3 GeV/$c$. Below 1.2 GeV/$c$, the Cherenkov light yield is too
low to reconstruct the proton ring. Above 2.3 GeV/$c$, the protons tend to
have hadronic interactions and the secondary particles make extra rings, which
complicates the proton reconstruction. After the precuts and the MVA cut, we
expected 86.0 proton events and 25.7 non-proton events in the final sample
from atmospheric neutrinos.

Figure 1: The selection efficiencies for the proton sample. The red dotted
line indicates the reduction efficiency of the FCFV sample above 30 MeV. The
blue dashed line represents the efficiency after precuts. The green solid line
is the efficiency after the MVA cut.

The systematic uncertainties in this proton sample include uncertainties in
atmospheric neutrino cross-section and flux (26%), proton hadronic interaction
systematics (4%), and detector related systematics (8% for proton events, and
13% for non-proton background events). The major source of the atmospheric
neutrino related uncertainty is the neutral current / charged current ratio
(20%). In summary, we estimated 27% for protons from atmospheric neutrinos,
29% uncertainty for non-proton background events from atmospheric neutrinos,
and 9% in proton signal efficiency. As such, we expected $111.7\pm
10.6\text{(stat.)}\pm 30.7\text{(sys.)}$ events for the searched 0.37
megaton$\times$years livetime in the final sample from atmospheric neutrinos.
Compared with the observation of 126 events, this result is within the
estimated systematic and statistical uncertainty.

The CRDM flux is determined by the dark matter distribution model, the cosmic-
ray model, and the dark matter interaction model. In this analysis, we use the
NFW profile for Galactic dark matter density distribution Navarro  _et al._
(1996). For simplicity, the cosmic-ray flux is assumed to be homogeneous
within a leaky box model cylinder Strong  _et al._ (2007), and the radius and
height of the cylinder are taken as $R=10$ kpc and $h=1$ kpc following Ref.
Bringmann and Pospelov (2019); Ema  _et al._ (2021). The energy spectrum of
cosmic-rays is modeled from 10 MeV to above 50 GeV with Voyager’s observation
Cummings  _et al._ (2016) and different theoretical calculations Boschini  _et
al._ (2017); Tomassetti  _et al._ (2019), as specified in Ref. Ema  _et al._
(2021). For the dark matter nucleon interaction cross-section, we consider two
reference scenarios, one with fermionic dark matter and a scalar mediator, and
one with a constant dark matter-nucleon interaction cross-section. In the
scalar mediator scenario, we employed the flux and cross-section as calculated
in Ref. Ema  _et al._ (2021) with a mediator mass of $m=1$ GeV/$c^{2}$. For
the constant cross-section dark matter model, we make use of a reproduced flux
from Ref. Bringmann and Pospelov (2019), and the cross-section is assumed to
be $10^{-30}$ cm2 at the dark matter-nucleon coupling constant $g=1$.

As SK is a Cherenkov detector, it can reconstruct directions of the recoil
protons, which facilitates the separation of the relatively isotropic
atmospheric neutrino backgrounds from signals that are more peaked in the
direction of the GC. The directional distribution of recoil protons with
regard to the GC is a convolution of the angular resolution of proton rings,
the kinematic correlation between recoil proton direction and the incoming
CRDM, and the model-dependent directional distribution of the CRDM flux. The
reconstructed angular resolution of proton rings is 2.6∘, a subdominant factor
compared to the kinematic angular correlation and the CRDM distribution.
Considering the two reference cross-section models and the different cylinder
sizes for cosmic-ray modeling, we found that the optimal directional cuts from
the GC varies by about $10\%$. For a more general interpretation, we fix the
GC direction cut at $\cos\theta_{GC}>0.6$.

At the large dark matter coupling scale we are probing, the CRDM attenuation
within the Earth is non-negligible, which ensures that the CRDM flux arriving
at the detector comes primarily from above the horizon. To reject the upward-
going atmospheric neutrino backgrounds and to avoid the uncertainty near the
horizon, we apply a zenith angle cut at $-\cos\theta_{z}>0.2$. The efficiency
for such a cut can be obtained by calculating the fraction of live-time the GC
is above the horizon considering the latitude of the observatory site, which
is $0.29$ for SK. After the GC direction cut and the zenith angle cut, the
expected number of backgrounds from atmospheric neutrinos in the proton sample
is expected to be 7.4 (6.5) events with (without) normalization to data.

The GC angular distribution of the MC expectation and data with and without
the zenith cut are shown in Fig. 2. To avoid the systematic bias from the
atmospheric neutrino azimuthal spectra, we employed an on-off source search,
with the on-source at the GC, and the off-source shifted from the on-source by
180∘ in right ascension, as shown in the supplementary material Abe  _et al._
(2022). Applying the cut $-\cos\theta_{z}>0.2$ and $\cos\theta_{GC}>0.6$, the
remaining number of events in the proton data sample is 9 for the on-source
(GC), and 7 for the off-source. Considering the systematic uncertainty, the
upper limit on the number of the CRDM recoil proton events can be calculated
using Rolke method Rolke  _et al._ (2005) as 5.7 events at 90% confidence
level.

Figure 2: The angle between proton ring and the GC for events in the proton
sample, without (upper) and with (lower) the zenith angle cut. The black
points indicate data with statistical uncertainty. The blue bands indicate MC
expectation with systematic uncertainty.

In the absence of an excess in the proton sample, we calculated the upper
limit of the dark matter-nucleon coupling and the interaction cross-section.
Note that the CRDM is produced from the same mechanism of dark matter-nucleon
scattering, and therefore the CRDM flux is also proportional to the cross-
section. Our result covers the sub-GeV dark matter mass from MeV/$c^{2}$ to
GeV/$c^{2}$ at $10^{-33}$ cm2, as shown in Fig. 3.

The recent CRDM search result from PANDAX-II Cui  _et al._ (2022) assuming
constant cross-section is also shown for comparison. Due to the large exposure
of SK and the directional information from the Cherenkov ring, the constraint
from SK is better than the existing limits by a factor of 2.

If the dark matter-nucleon coupling is large enough, the CRDM flux will lose
energy when traveling through the rock overburden above the detector, imposing
an upper bound on the exclusion region. This energy can be calculated with an
analytical approximation considering the nuclear form factor effect Xia  _et
al._ (2022). In the case of SK, due to the higher detection threshold from
proton Cherenkov radiation, the experiment is only sensitive to sub-GeV dark
matter above 0.5 GeV kinematic energy, and the attenuation of the rock
overburden for this energy range is calculated to be below 10% at
$\sigma<10^{-27}$ cm2. Above $10^{-27}$ cm2, the parameter space has been
excluded by an analysis using cosmic microwave background data Xu  _et al._
(2018). The lower end of the search range in dark matter mass at 1 MeV/$c^{2}$
is constrained by the Big Bang nucleosynthesis Reno and Seckel (1988); Krnjaic
and McDermott (2020). At higher dark matter mass, the constraints mainly come
from the direct detection experiment CRESST-III Abdelhameed  _et al._ (2019)
and the Migdal effect searches at CDEX-1B Liu  _et al._ (2019b) and XENON1T
Aprile  _et al._ (2019b).

Figure 3: Constraints on dark matter-nucleon cross-section. Solid lines show
the upper limit while dashed lines indicate the sensitivity. The green lines
are calculated with a constant cross-section model. The blue lines are the
cross-sections at the non-relativistic limit ($\sigma_{NR}$) for scalar
mediator model. The shaded sage green region indicates the PANDAX-II CRDM
exclusion region Cui  _et al._ (2022). The shaded maroon region shows the
CRESST-III exclusion region Abdelhameed  _et al._ (2019) and the shaded grey
region shows the constraints via Migdal effect from CDEX-1B Liu  _et al._
(2019b) and XENON1T Aprile  _et al._ (2019b).

In summary, we report a directional search for the CRDM using a newly
constructed proton sample selected from the data collected at Super-Kamiokande
during the period of 1996-2018 (SKI-IV phases). In the absence of an excess
from dark matter signals above the expected background, we derived new limits
on the dark matter-nucleon interaction cross-section, which are the most
stringent constraint on hadronic coupling of sub-GeV dark matter so far. This
result benefits from the large fiducial volume and directional reconstruction
ability of SK, which motivates further exploration of CRDM and boosted dark
matter in general from the next generation large neutrino detectors with
directional capabilities, such as Hyper-Kamiokande Abe  _et al._ (2011) and
DUNE Abi  _et al._ (2020). The reported proton sample efficiency and direction
distribution can also be interpreted by any theory that predicts an excess of
proton recoils from the direction of the GC.

We thank Dr. Yohei Ema for providing the CRDM flux and insightful discussions.
We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting
Company. The Super-Kamiokande experiment has been built and operated from
funding by the Japanese Ministry of Education, Culture, Sports, Science and
Technology, the U.S. Department of Energy, and the U.S. National Science
Foundation. Some of us have been supported by funds from the National Research
Foundation of Korea NRF‐2009‐0083526 (KNRC) funded by the Ministry of Science,
ICT, and Future Planning and the Ministry of Education (2018R1D1A3B07050696,
2018R1D1A1B07049158), the Japan Society for the Promotion of Science, the
National Natural Science Foundation of China under Grants No. 11620101004, the
Spanish Ministry of Science, Universities and Innovation (grant
PGC2018-099388-B-I00), the Natural Sciences and Engineering Research Council
(NSERC) of Canada, the Scinet and Westgrid consortia of Compute Canada, the
National Science Centre, Poland (2015/18/E/ST2/00758), the Science and
Technology Facilities Council (STFC) and GridPPP, UK, the European Union’s
Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-
Curie grant agreement no.754496, H2020-MSCA-RISE-2018 JENNIFER2 grant
agreement no.822070, and H2020-MSCA-RISE-2019 SK2HK grant agreement no.
872549.

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