The LHAASO Collaboration Corresponding Author:]
<EMAIL_ADDRESS>(K. Jia)
<EMAIL_ADDRESS>(J. Li)
<EMAIL_ADDRESS>(X.J. Bi)
<EMAIL_ADDRESS>(L.Q. Gao)
<EMAIL_ADDRESS>(X.Y. Huang)
<EMAIL_ADDRESS>(W.L. Li)
<EMAIL_ADDRESS>(C.G. Zhu)

# Constraints on Ultra Heavy Dark Matter Properties from Dwarf Spheroidal
Galaxies with LHAASO Observations

Zhen Cao  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  F. Aharonian  Dublin Institute for Advanced Studies, 31
Fitzwilliam Place, 2 Dublin, Ireland  Max-Planck-Institut for Nuclear Physics,
P.O. Box 103980, 69029 Heidelberg, Germany  Q. An  State Key Laboratory of
Particle Detection and Electronics, China  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Axikegu  School of Physical
Science and Technology & School of Information Science and Technology,
Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  Y.X. Bai  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.W. Bao  School of Astronomy and Space Science,
Nanjing University, 210023 Nanjing, Jiangsu, China  D. Bastieri  Center for
Astrophysics, Guangzhou University, 510006 Guangzhou, Guangdong, China  X.J.
Bi  Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  Y.J. Bi  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  J.T. Cai  Center for
Astrophysics, Guangzhou University, 510006 Guangzhou, Guangdong, China  Q. Cao
Hebei Normal University, 050024 Shijiazhuang, Hebei, China  W.Y. Cao
University of Science and Technology of China, 230026 Hefei, Anhui, China  Zhe
Cao  State Key Laboratory of Particle Detection and Electronics, China
University of Science and Technology of China, 230026 Hefei, Anhui, China  J.
Chang  Key Laboratory of Dark Matter and Space Astronomy & Key Laboratory of
Radio Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
210023 Nanjing, Jiangsu, China  J.F. Chang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  State Key
Laboratory of Particle Detection and Electronics, China  A.M. Chen  Tsung-Dao
Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong
University, 200240 Shanghai, China  E.S. Chen  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Liang Chen  Key
Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  Lin Chen
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
Long Chen  School of Physical Science and Technology & School of Information
Science and Technology, Southwest Jiaotong University, 610031 Chengdu,
Sichuan, China  M.J. Chen  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  M.L. Chen  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  Q.H. Chen
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
S.H. Chen  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  S.Z. Chen  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  T.L. Chen  Key Laboratory of
Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  Y. Chen  School of Astronomy and Space Science, Nanjing University,
210023 Nanjing, Jiangsu, China  N. Cheng  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Y.D. Cheng
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  M.Y. Cui  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  S.W. Cui  Hebei
Normal University, 050024 Shijiazhuang, Hebei, China  X.H. Cui  National
Astronomical Observatories, Chinese Academy of Sciences, 100101 Beijing, China
Y.D. Cui  School of Physics and Astronomy (Zhuhai) & School of Physics
(Guangzhou) & Sino-French Institute of Nuclear Engineering and Technology
(Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong,
China  B.Z. Dai  School of Physics and Astronomy, Yunnan University, 650091
Kunming, Yunnan, China  H.L. Dai  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  State Key Laboratory of
Particle Detection and Electronics, China  Z.G. Dai  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Danzengluobu  Key Laboratory
of Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  D. della Volpe  Département de Physique Nucléaire et Corpusculaire,
Faculté de Sciences, Université de Genève, 24 Quai Ernest Ansermet, 1211
Geneva, Switzerland  X.Q. Dong  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  University of
Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research
Center, 610000 Chengdu, Sichuan, China  K.K. Duan  Key Laboratory of Dark
Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  J.H. Fan  Center for Astrophysics, Guangzhou University, 510006
Guangzhou, Guangdong, China  Y.Z. Fan  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  J. Fang  School
of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China  K.
Fang  Key Laboratory of Particle Astrophysics & Experimental Physics Division
& Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  C.F. Feng  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  L. Feng  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  S.H. Feng  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  X.T.
Feng  Institute of Frontier and Interdisciplinary Science, Shandong
University, 266237 Qingdao, Shandong, China  Y.L. Feng  Key Laboratory of
Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  S. Gabici  APC, Universit’e Paris Cit’e, CNRS/IN2P3, CEA/IRFU,
Observatoire de Paris, 119 75205 Paris, France  B. Gao  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  C.D.
Gao  Institute of Frontier and Interdisciplinary Science, Shandong University,
266237 Qingdao, Shandong, China  L.Q. Gao  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Q. Gao  Key
Laboratory of Cosmic Rays (Tibet University), Ministry of Education, 850000
Lhasa, Tibet, China  W. Gao  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  W.K. Gao  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  University of Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  M.M. Ge
School of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan,
China  L.S. Geng  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  G. Giacinti  Tsung-Dao Lee Institute & School
of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai,
China  G.H. Gong  Department of Engineering Physics, Tsinghua University,
100084 Beijing, China  Q.B. Gou  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  M.H. Gu  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  F.L. Guo
Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  X.L. Guo
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
Y.Q. Guo  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.Y. Guo  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  Y.A. Han  School
of Physics and Microelectronics, Zhengzhou University, 450001 Zhengzhou,
Henan, China  H.H. He  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  University of Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  H.N. He  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  J.Y. He  Key
Laboratory of Dark Matter and Space Astronomy & Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023
Nanjing, Jiangsu, China  X.B. He  School of Physics and Astronomy (Zhuhai) &
School of Physics (Guangzhou) & Sino-French Institute of Nuclear Engineering
and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275
Guangzhou, Guangdong, China  Y. He  School of Physical Science and Technology
& School of Information Science and Technology, Southwest Jiaotong University,
610031 Chengdu, Sichuan, China  M. Heller  Département de Physique Nucléaire
et Corpusculaire, Faculté de Sciences, Université de Genève, 24 Quai Ernest
Ansermet, 1211 Geneva, Switzerland  Y.K. Hor  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  B.W. Hou  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  C. Hou  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  X. Hou  Yunnan Observatories, Chinese Academy of
Sciences, 650216 Kunming, Yunnan, China  H.B. Hu  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Q. Hu  University
of Science and Technology of China, 230026 Hefei, Anhui, China  Key Laboratory
of Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  S.C. Hu  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  D.H. Huang  School of Physical Science and Technology & School
of Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  T.Q. Huang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  W.J. Huang  School of Physics
and Astronomy (Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute
of Nuclear Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000
Zhuhai & 510275 Guangzhou, Guangdong, China  X.T. Huang  Institute of Frontier
and Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  X.Y. Huang  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  Y. Huang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
University of Chinese Academy of Sciences, 100049 Beijing, China  Tianfu
Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Z.C. Huang  School
of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
X.L. Ji  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  State Key Laboratory of Particle Detection and
Electronics, China  H.Y. Jia  School of Physical Science and Technology &
School of Information Science and Technology, Southwest Jiaotong University,
610031 Chengdu, Sichuan, China  K. Jia  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China<EMAIL_ADDRESS>K. Jiang  State Key Laboratory of Particle
Detection and Electronics, China  University of Science and Technology of
China, 230026 Hefei, Anhui, China  X.W. Jiang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Z.J. Jiang
School of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan,
China  M. Jin  School of Physical Science and Technology & School of
Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  M.M. Kang  College of Physics, Sichuan University,
610065 Chengdu, Sichuan, China  T. Ke  Key Laboratory of Particle Astrophysics
& Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  D. Kuleshov  Institute for
Nuclear Research of Russian Academy of Sciences, 117312 Moscow, Russia  K.
Kurinov  Institute for Nuclear Research of Russian Academy of Sciences, 117312
Moscow, Russia  Moscow Institute of Physics and Technology, 141700 Moscow,
Russia  B.B. Li  Hebei Normal University, 050024 Shijiazhuang, Hebei, China
Cheng Li  State Key Laboratory of Particle Detection and Electronics, China
University of Science and Technology of China, 230026 Hefei, Anhui, China
Cong Li  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  D. Li  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  University of
Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research
Center, 610000 Chengdu, Sichuan, China  F. Li  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  State Key
Laboratory of Particle Detection and Electronics, China  H.B. Li  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  H.C. Li  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  H.Y. Li  University of
Science and Technology of China, 230026 Hefei, Anhui, China  Key Laboratory of
Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  J. Li  University of Science and Technology of China, 230026 Hefei,
Anhui, China  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  Jian Li  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Jie Li  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  K. Li  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  W.L. Li  Institute of Frontier and Interdisciplinary
Science, Shandong University, 266237 Qingdao, Shandong, China  W.L. Li  Tsung-
Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong
University, 200240 Shanghai, China  X.R. Li  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Xin Li
State Key Laboratory of Particle Detection and Electronics, China  University
of Science and Technology of China, 230026 Hefei, Anhui, China  Y.Z. Li  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  Zhe Li  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  Zhuo Li  School of Physics, Peking University,
100871 Beijing, China  E.W. Liang  School of Physical Science and Technology,
Guangxi University, 530004 Nanning, Guangxi, China  Y.F. Liang  School of
Physical Science and Technology, Guangxi University, 530004 Nanning, Guangxi,
China  S.J. Lin  School of Physics and Astronomy (Zhuhai) & School of Physics
(Guangzhou) & Sino-French Institute of Nuclear Engineering and Technology
(Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong,
China  B. Liu  University of Science and Technology of China, 230026 Hefei,
Anhui, China  C. Liu  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  D. Liu  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  H. Liu  School of Physical Science and Technology & School of
Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  H.D. Liu  School of Physics and Microelectronics,
Zhengzhou University, 450001 Zhengzhou, Henan, China  J. Liu  Key Laboratory
of Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  J.L.
Liu  Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  J.Y. Liu  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  M.Y. Liu  Key Laboratory of
Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet,
China  R.Y. Liu  School of Astronomy and Space Science, Nanjing University,
210023 Nanjing, Jiangsu, China  S.M. Liu  School of Physical Science and
Technology & School of Information Science and Technology, Southwest Jiaotong
University, 610031 Chengdu, Sichuan, China  W. Liu  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Y. Liu
Center for Astrophysics, Guangzhou University, 510006 Guangzhou, Guangdong,
China  Y.N. Liu  Department of Engineering Physics, Tsinghua University,
100084 Beijing, China  R. Lu  School of Physics and Astronomy, Yunnan
University, 650091 Kunming, Yunnan, China  Q. Luo  School of Physics and
Astronomy (Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of
Nuclear Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000
Zhuhai & 510275 Guangzhou, Guangdong, China  H.K. Lv  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  B.Q.
Ma  School of Physics, Peking University, 100871 Beijing, China  L.L. Ma  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  X.H. Ma  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  J.R. Mao  Yunnan
Observatories, Chinese Academy of Sciences, 650216 Kunming, Yunnan, China  Z.
Min  Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  W. Mitthumsiri  Department of Physics, Faculty of
Science, Mahidol University, 10400 Bangkok, Thailand  H.J. Mu  School of
Physics and Microelectronics, Zhengzhou University, 450001 Zhengzhou, Henan,
China  Y.C. Nan  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  A. Neronov  APC, Universit’e Paris Cit’e,
CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, 119 75205 Paris, France  Z.W. Ou
School of Physics and Astronomy (Zhuhai) & School of Physics (Guangzhou) &
Sino-French Institute of Nuclear Engineering and Technology (Zhuhai), Sun Yat-
sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong, China  B.Y. Pang
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  P.
Pattarakijwanich  Department of Physics, Faculty of Science, Mahidol
University, 10400 Bangkok, Thailand  Z.Y. Pei  Center for Astrophysics,
Guangzhou University, 510006 Guangzhou, Guangdong, China  M.Y. Qi  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.Q. Qi  Hebei Normal University, 050024
Shijiazhuang, Hebei, China  B.Q. Qiao  Key Laboratory of Particle Astrophysics
& Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  J.J. Qin  University of
Science and Technology of China, 230026 Hefei, Anhui, China  D. Ruffolo
Department of Physics, Faculty of Science, Mahidol University, 10400 Bangkok,
Thailand  A. Sáiz  Department of Physics, Faculty of Science, Mahidol
University, 10400 Bangkok, Thailand  D. Semikoz  APC, Universit’e Paris Cit’e,
CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, 119 75205 Paris, France  C.Y.
Shao  School of Physics and Astronomy (Zhuhai) & School of Physics (Guangzhou)
& Sino-French Institute of Nuclear Engineering and Technology (Zhuhai), Sun
Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong, China  L.
Shao  Hebei Normal University, 050024 Shijiazhuang, Hebei, China  O.
Shchegolev  Institute for Nuclear Research of Russian Academy of Sciences,
117312 Moscow, Russia  Moscow Institute of Physics and Technology, 141700
Moscow, Russia  X.D. Sheng  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  F.W. Shu  Center for
Relativistic Astrophysics and High Energy Physics, School of Physics and
Materials Science & Institute of Space Science and Technology, Nanchang
University, 330031 Nanchang, Jiangxi, China  H.C. Song  School of Physics,
Peking University, 100871 Beijing, China  Yu.V. Stenkin  Institute for Nuclear
Research of Russian Academy of Sciences, 117312 Moscow, Russia  Moscow
Institute of Physics and Technology, 141700 Moscow, Russia  V. Stepanov
Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow,
Russia  Y. Su  Key Laboratory of Dark Matter and Space Astronomy & Key
Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of
Sciences, 210023 Nanjing, Jiangsu, China  Q.N. Sun  School of Physical Science
and Technology & School of Information Science and Technology, Southwest
Jiaotong University, 610031 Chengdu, Sichuan, China  X.N. Sun  School of
Physical Science and Technology, Guangxi University, 530004 Nanning, Guangxi,
China  Z.B. Sun  National Space Science Center, Chinese Academy of Sciences,
100190 Beijing, China  P.H.T. Tam  School of Physics and Astronomy (Zhuhai) &
School of Physics (Guangzhou) & Sino-French Institute of Nuclear Engineering
and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275
Guangzhou, Guangdong, China  Q.W. Tang  Center for Relativistic Astrophysics
and High Energy Physics, School of Physics and Materials Science & Institute
of Space Science and Technology, Nanchang University, 330031 Nanchang,
Jiangxi, China  Z.B. Tang  State Key Laboratory of Particle Detection and
Electronics, China  University of Science and Technology of China, 230026
Hefei, Anhui, China  W.W. Tian  University of Chinese Academy of Sciences,
100049 Beijing, China  National Astronomical Observatories, Chinese Academy of
Sciences, 100101 Beijing, China  C. Wang  National Space Science Center,
Chinese Academy of Sciences, 100190 Beijing, China  C.B. Wang  School of
Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
G.W. Wang  University of Science and Technology of China, 230026 Hefei, Anhui,
China  H.G. Wang  Center for Astrophysics, Guangzhou University, 510006
Guangzhou, Guangdong, China  H.H. Wang  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  J.C. Wang  Yunnan Observatories, Chinese
Academy of Sciences, 650216 Kunming, Yunnan, China  K. Wang  School of
Astronomy and Space Science, Nanjing University, 210023 Nanjing, Jiangsu,
China  L.P. Wang  Institute of Frontier and Interdisciplinary Science,
Shandong University, 266237 Qingdao, Shandong, China  L.Y. Wang  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  P.H. Wang  School of Physical Science and Technology
& School of Information Science and Technology, Southwest Jiaotong University,
610031 Chengdu, Sichuan, China  R. Wang  Institute of Frontier and
Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong,
China  W. Wang  School of Physics and Astronomy (Zhuhai) & School of Physics
(Guangzhou) & Sino-French Institute of Nuclear Engineering and Technology
(Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275 Guangzhou, Guangdong,
China  X.G. Wang  School of Physical Science and Technology, Guangxi
University, 530004 Nanning, Guangxi, China  X.Y. Wang  School of Astronomy and
Space Science, Nanjing University, 210023 Nanjing, Jiangsu, China  Y. Wang
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
Y.D. Wang  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Y.J. Wang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  Z.H. Wang  College of
Physics, Sichuan University, 610065 Chengdu, Sichuan, China  Z.X. Wang  School
of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China
Zhen Wang  Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai
Jiao Tong University, 200240 Shanghai, China  Zheng Wang  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  D.M. Wei
Key Laboratory of Dark Matter and Space Astronomy & Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023
Nanjing, Jiangsu, China  J.J. Wei  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  Y.J. Wei  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  T. Wen  School of Physics and Astronomy, Yunnan University,
650091 Kunming, Yunnan, China  C.Y. Wu  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  H.R. Wu
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  S. Wu  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  X.F. Wu  Key Laboratory of
Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  Y.S. Wu  University of Science and Technology of China, 230026 Hefei,
Anhui, China  S.Q. Xi  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  J. Xia  University of Science and Technology
of China, 230026 Hefei, Anhui, China  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  J.J. Xia  School
of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
G.M. Xiang  University of Chinese Academy of Sciences, 100049 Beijing, China
Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  D.X. Xiao
Hebei Normal University, 050024 Shijiazhuang, Hebei, China  G. Xiao  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  G.G. Xin  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  Y.L. Xin  School of Physical
Science and Technology & School of Information Science and Technology,
Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  Y. Xing  Key
Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences, 200030 Shanghai, China  Z. Xiong
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  D.L. Xu  Tsung-Dao Lee Institute & School of Physics and
Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China  R.F. Xu  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  R.X. Xu  School of Physics, Peking University, 100871 Beijing,
China  W.L. Xu  College of Physics, Sichuan University, 610065 Chengdu,
Sichuan, China  L. Xue  Institute of Frontier and Interdisciplinary Science,
Shandong University, 266237 Qingdao, Shandong, China  D.H. Yan  School of
Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China  J.Z.
Yan  Key Laboratory of Dark Matter and Space Astronomy & Key Laboratory of
Radio Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
210023 Nanjing, Jiangsu, China  T. Yan  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  C.W. Yang
College of Physics, Sichuan University, 610065 Chengdu, Sichuan, China  F.
Yang  Hebei Normal University, 050024 Shijiazhuang, Hebei, China  F.F. Yang
Key Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  State Key Laboratory of Particle Detection and
Electronics, China  H.W. Yang  School of Physics and Astronomy (Zhuhai) &
School of Physics (Guangzhou) & Sino-French Institute of Nuclear Engineering
and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai & 510275
Guangzhou, Guangdong, China  J.Y. Yang  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  L.L. Yang  School of Physics and Astronomy
(Zhuhai) & School of Physics (Guangzhou) & Sino-French Institute of Nuclear
Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai &
510275 Guangzhou, Guangdong, China  M.J. Yang  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  R.Z. Yang
University of Science and Technology of China, 230026 Hefei, Anhui, China
S.B. Yang  School of Physics and Astronomy, Yunnan University, 650091 Kunming,
Yunnan, China  Y.H. Yao  College of Physics, Sichuan University, 610065
Chengdu, Sichuan, China  Z.G. Yao  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  Y.M. Ye  Department of
Engineering Physics, Tsinghua University, 100084 Beijing, China  L.Q. Yin  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  N. Yin  Institute of Frontier and Interdisciplinary
Science, Shandong University, 266237 Qingdao, Shandong, China  X.H. You  Key
Laboratory of Particle Astrophysics & Experimental Physics Division &
Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  Z.Y. You  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  University of
Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research
Center, 610000 Chengdu, Sichuan, China  Y.H. Yu  University of Science and
Technology of China, 230026 Hefei, Anhui, China  Q. Yuan  Key Laboratory of
Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  H. Yue  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  University of Chinese Academy of Sciences,
100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000 Chengdu,
Sichuan, China  H.D. Zeng  Key Laboratory of Dark Matter and Space Astronomy &
Key Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese
Academy of Sciences, 210023 Nanjing, Jiangsu, China  T.X. Zeng  Key Laboratory
of Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China
State Key Laboratory of Particle Detection and Electronics, China  W. Zeng
School of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan,
China  M. Zha  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  B.B. Zhang  School of Astronomy and Space Science,
Nanjing University, 210023 Nanjing, Jiangsu, China  F. Zhang  School of
Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
H.M. Zhang  School of Astronomy and Space Science, Nanjing University, 210023
Nanjing, Jiangsu, China  H.Y. Zhang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray
Research Center, 610000 Chengdu, Sichuan, China  J.L. Zhang  National
Astronomical Observatories, Chinese Academy of Sciences, 100101 Beijing, China
L.X. Zhang  Center for Astrophysics, Guangzhou University, 510006 Guangzhou,
Guangdong, China  Li Zhang  School of Physics and Astronomy, Yunnan
University, 650091 Kunming, Yunnan, China  P.F. Zhang  School of Physics and
Astronomy, Yunnan University, 650091 Kunming, Yunnan, China  P.P. Zhang
University of Science and Technology of China, 230026 Hefei, Anhui, China  Key
Laboratory of Dark Matter and Space Astronomy & Key Laboratory of Radio
Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023
Nanjing, Jiangsu, China  R. Zhang  University of Science and Technology of
China, 230026 Hefei, Anhui, China  Key Laboratory of Dark Matter and Space
Astronomy & Key Laboratory of Radio Astronomy, Purple Mountain Observatory,
Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China  S.B. Zhang
University of Chinese Academy of Sciences, 100049 Beijing, China  National
Astronomical Observatories, Chinese Academy of Sciences, 100101 Beijing, China
S.R. Zhang  Hebei Normal University, 050024 Shijiazhuang, Hebei, China  S.S.
Zhang  Key Laboratory of Particle Astrophysics & Experimental Physics Division
& Computing Center, Institute of High Energy Physics, Chinese Academy of
Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  X. Zhang  School of Astronomy and Space Science,
Nanjing University, 210023 Nanjing, Jiangsu, China  X.P. Zhang  Key Laboratory
of Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  Y.F.
Zhang  School of Physical Science and Technology & School of Information
Science and Technology, Southwest Jiaotong University, 610031 Chengdu,
Sichuan, China  Yi Zhang  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  Key Laboratory of
Dark Matter and Space Astronomy & Key Laboratory of Radio Astronomy, Purple
Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu,
China  Yong Zhang  Key Laboratory of Particle Astrophysics & Experimental
Physics Division & Computing Center, Institute of High Energy Physics, Chinese
Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center,
610000 Chengdu, Sichuan, China  B. Zhao  School of Physical Science and
Technology & School of Information Science and Technology, Southwest Jiaotong
University, 610031 Chengdu, Sichuan, China  J. Zhao  Key Laboratory of
Particle Astrophysics & Experimental Physics Division & Computing Center,
Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing,
China  Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  L.
Zhao  State Key Laboratory of Particle Detection and Electronics, China
University of Science and Technology of China, 230026 Hefei, Anhui, China
L.Z. Zhao  Hebei Normal University, 050024 Shijiazhuang, Hebei, China  S.P.
Zhao  Key Laboratory of Dark Matter and Space Astronomy & Key Laboratory of
Radio Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,
210023 Nanjing, Jiangsu, China  Institute of Frontier and Interdisciplinary
Science, Shandong University, 266237 Qingdao, Shandong, China  F. Zheng
National Space Science Center, Chinese Academy of Sciences, 100190 Beijing,
China  B. Zhou  Key Laboratory of Particle Astrophysics & Experimental Physics
Division & Computing Center, Institute of High Energy Physics, Chinese Academy
of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research Center, 610000
Chengdu, Sichuan, China  H. Zhou  Tsung-Dao Lee Institute & School of Physics
and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China  J.N.
Zhou  Key Laboratory for Research in Galaxies and Cosmology, Shanghai
Astronomical Observatory, Chinese Academy of Sciences, 200030 Shanghai, China
M. Zhou  Center for Relativistic Astrophysics and High Energy Physics, School
of Physics and Materials Science & Institute of Space Science and Technology,
Nanchang University, 330031 Nanchang, Jiangxi, China  P. Zhou  School of
Astronomy and Space Science, Nanjing University, 210023 Nanjing, Jiangsu,
China  R. Zhou  College of Physics, Sichuan University, 610065 Chengdu,
Sichuan, China  X.X. Zhou  School of Physical Science and Technology & School
of Information Science and Technology, Southwest Jiaotong University, 610031
Chengdu, Sichuan, China  C.G. Zhu  Institute of Frontier and Interdisciplinary
Science, Shandong University, 266237 Qingdao, Shandong, China  F.R. Zhu
School of Physical Science and Technology & School of Information Science and
Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China  H.
Zhu  National Astronomical Observatories, Chinese Academy of Sciences, 100101
Beijing, China  K.J. Zhu  Key Laboratory of Particle Astrophysics &
Experimental Physics Division & Computing Center, Institute of High Energy
Physics, Chinese Academy of Sciences, 100049 Beijing, China  University of
Chinese Academy of Sciences, 100049 Beijing, China  Tianfu Cosmic Ray Research
Center, 610000 Chengdu, Sichuan, China  State Key Laboratory of Particle
Detection and Electronics, China  X. Zuo  Key Laboratory of Particle
Astrophysics & Experimental Physics Division & Computing Center, Institute of
High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
Tianfu Cosmic Ray Research Center, 610000 Chengdu, Sichuan, China  [

###### Abstract

In this work we try to search for signals generated by ultra-heavy dark matter
at the Large High Altitude Air Shower Observatory (LHAASO) data. We look for
possible gamma-ray by dark matter annihilation or decay from 16 dwarf
spheroidal galaxies in the field of view of LHAASO. Dwarf spheroidal galaxies
are among the most promising targets for indirect detection of dark matter
which have low fluxes of astrophysical $\gamma$-ray background while large
amount of dark matter. By analyzing more than 700 days observational data at
LHAASO, no significant dark matter signal from 1 TeV to 1 EeV is detected.
Accordingly we derive the most stringent constraints on the ultra-heavy dark
matter annihilation cross-section up to EeV. The constraints on the lifetime
of dark matter in decay mode are also derived.

Introduction— Various kinds of astronomical evidence suggest the existence of
massive dark matter (DM) in the universe [1], which comprises approximately
85$\%$ of all matter [2]. However, DM cannot be explained by the Standard
Model of particle physics [3, 4]. Therefore, one of the most important tasks
in fundamental physics is to detect and reveal the nature of DM particles.
Most searches primarily focus on weakly interacting massive particles (WIMPs)
or ultra-light DM. However, no conclusive DM signal has been observed up to
now [5, 6, 7, 8, 9]. On the other hand, ultra-heavy dark matter (UHDM; 10 TeV
$\lesssim M_{\chi}\lesssim m_{pl}\approx 10^{16}$ TeV) represents a potential
alternative DM candidate that could be generated through various mechanisms,
including freeze-out, freeze-in, out-of-equilibrium decay, phase transitions,
gravitational particle production, and primordial black holes (see the review
in Ref. [10] and references therein). Some models for UHDM, like composite
dark matter [11, 12], have been proposed to evade the unitarity limit, and
very-high-energy (VHE) gamma-ray may be produced not only via the decay of
UHDM, but also via its self-annihilation [13].

Among different astronomical systems, dwarf spheroidal galaxies (dSphs) are
considered one of the most promising targets for detecting DM signals due to
their relatively short distances, high mass-to-light ratios [14, 15], and
locations far away from complicated emission regions like the Galactic disk.
These properties have instigated extensive research on them utilizing various
astronomical facilities [16, 17, 18, 19, 20, 21, 22, 23]. Importantly, given
the relative proximity of these systems, the angular dimensions of their
signal regions, particularly in scenarios involving decay, may be comparable
to or even surpass the point spread function (PSF) of detection instruments.
Thus, viewing these sources as extended rather than point-like sources may
play a crucial role in the indirect detection of DM [24, 25].

The LHAASO is located in Sichuan Province, China, at an altitude of 4410
meters. It is a multi-purpose and comprehensive extensive air shower array,
designed for the study of cosmic rays and gamma-ray across wide energy ranges,
from 10 TeV to 100 PeV for cosmic rays and from sub-TeV to beyond 1 PeV for
gamma-ray [26]. LHAASO is composed of three sub-arrays: the KiloMeter Squared
Array (KM2A), the Water Cherenkov Detector Array (WCDA), and the Wide Field-
of-view air Cherenkov Telescopes Array (WFCTA). Since its operation, several
important results have been achieved in cosmic-ray and gamma-ray research [27,
28, 29, 30, 31]. The remarkable gamma-ray sensitivity of LHAASO for energies
exceeding 100 TeV [32] presents an opportunity for the exploration of UHDM.
WCDA and KM2A also have good PSFs for VHE gamma-ray [33, 34], enabling them to
potentially discern the spatial extension of dSphs.

In this Letter, we search for VHE $\gamma$-ray signal from dSphs with data
recorded by WCDA and KM2A of LHAASO, and report the stringent constraints on
the UHDM up to EeV.

Gamma-ray Flux from Dark Matter—The expected differential gamma-ray flux from
DM annihilation can be written as

$\displaystyle\frac{{\rm d}F_{\rm anni}}{{\rm d}E{\rm d}\Omega{\rm
d}t}(E,\Omega)=\frac{\left\langle\sigma_{A}v\right\rangle}{8\pi
M^{2}_{\chi}}\frac{{\rm d}N_{\gamma}}{{\rm
d}E}e^{-\tau_{\gamma\gamma}(E)}\times\frac{{\rm d}J}{{\rm d}\Omega}.$ (1)

Similarly, for DM decay, it can be defined as

$\displaystyle\frac{{\rm d}F_{\rm decay}}{{\rm d}E{\rm d}\Omega{\rm
d}t}(E,\Omega)=\frac{1}{4\pi\tau_{\chi}M_{\chi}}\frac{{\rm d}N_{\gamma}}{{\rm
d}E}e^{-\tau_{\gamma\gamma}(E)}\times\frac{{\rm d}D}{{\rm d}\Omega},$ (2)

where $\left\langle\sigma_{A}v\right\rangle$ is the velocity-weighted DM
annihilation cross-section, $\tau_{\chi}$ is the DM decay lifetime, and
$M_{\chi}$ is the mass of the DM particle. ${\rm d}N_{\gamma}/{\rm d}E$ is the
gamma-ray energy spectrum resulting from DM annihilation (decay), as
calculated using HDMSpectra [35]. The term $\tau_{\gamma\gamma}(E)$ represents
the total attenuation depth resulting from the pair production process
($\gamma\gamma\rightarrow e^{+}e^{-}$), taking into account background photons
from starlight (SL), infrared radiation (IR), and cosmic microwave background
(CMB), as described in Ref. [36]. The last term is the differential J- (D-)
factor, which characterizes the strength of the DM signal. In Eq. 1 and Eq. 2,
${\rm d}J/{\rm d}\Omega=\int\rho^{2}_{DM}(r){\rm d}l$, and ${\rm d}D/{\rm
d}\Omega=\int\rho_{DM}(r){\rm d}l$, where $\rho_{DM}(r)$ refers to the DM
density at distance $r$ from the center of dSphs, and $l$ represents the
distance from a point on the line-of-sight (L.o.S) to the Earth. The J- (D-)
factor is defined as the differential J- (D-) factor integrated over the
region of interest (ROI). In this work, we take the DM density distribution in
dSphs following the Navarro-Frenk-White (NFW) profile [37].

Table 1: The ROI half width and J- (D-) factor for 16 dSphs considered in this
analysis.

Name | $\rm{log_{10}(J_{\theta}/GeV^{2}cm^{-5})}$ | $\rm{\theta_{anni}[deg]}$ | $\rm{log_{10}(D_{\theta}/GeVcm^{-2})}$ | $\rm{\theta_{decay}[deg]}$
---|---|---|---|---
Draco | $18.96_{-0.15}^{+0.16}$ | 1.0 | $19.38_{-0.32}^{+0.24}$ | 2.3
Ursa Minor | $18.79_{-0.11}^{+0.12}$ | 1.0 | $18.68_{-0.15}^{+0.33}$ | 2.1
Ursa Major I | $18.40_{-0.27}^{+0.28}$ | 0.9 | $18.64_{-0.48}^{+0.50}$ | 1.8
Ursa Major II | $19.70_{-0.43}^{+0.43}$ | 1.0 | $19.41_{-0.57}^{+0.43}$ | 2.0
Bootes 1 | $18.39_{-0.37}^{+0.36}$ | 0.9 | $18.77_{-0.54}^{+0.40}$ | 1.8
Canes Venatici I | $17.43_{-0.15}^{+0.16}$ | 0.8 | $18.19_{-0.39}^{+0.40}$ | 1.3
Coma Berenices | $19.26_{-0.43}^{+0.35}$ | 0.9 | $19.12_{-0.73}^{+0.46}$ | 1.8
Leo I | $17.58_{-0.10}^{+0.10}$ | 0.8 | $18.44_{-0.42}^{+0.33}$ | 1.4
Segue 1 | $19.25_{-0.69}^{+0.60}$ | 0.8 | $18.33_{-0.63}^{+0.69}$ | 0.8
Sextans | $17.80_{-0.10}^{+0.10}$ | 1.0 | $18.49_{-0.21}^{+0.28}$ | 1.8
Canes Venatici II | $17.82_{-0.37}^{+0.38}$ | 0.8 | $18.45_{-0.74}^{+0.50}$ | 1.4
Hercules | $17.60_{-0.69}^{+0.53}$ | 0.8 | $17.79_{-0.61}^{+0.62}$ | 1.0
Leo II | $17.72_{-0.17}^{+0.18}$ | 0.8 | $17.85_{-0.40}^{+0.62}$ | 1.0
Willman I | $19.80_{-0.52}^{+0.50}$ | 0.9 | $19.00_{-0.93}^{+0.71}$ | 1.5
Aquarius 2 | $18.57_{-0.57}^{+0.50}$ | 1.1 | $18.53_{-0.68}^{+0.61}$ | 1.3
Leo T | $17.66_{-0.52}^{+0.55}$ | 0.8 | $17.88_{-0.69}^{+0.65}$ | 1.0

With a large field-of-view (FoV) of approximately 2 sr, LHAASO has the ability
to observe about 60$\%$ of the sky each day [32]. The 16 dSphs within the FoV
of LHAASO have been selected as our observation targets, and the coordinates
of these dSphs are shown in Table S1 of the Supplemental Material [38]. To
optimize the size of the ROI for balancing the preference between a larger
area containing more signal and a smaller area with less background (and
nearby sources) contamination, we utilize $\mathcal{S}/\sqrt{B}$ as a metric,
where $\mathcal{S}$ and $B$ are the expected signal and expected background in
the ROI, respectively. Considering the expected signal also depends on the
details of NFW profile [39, 40, 41], we use the publicly available MCMC chains
provided by Ref. [41] to determine the optimal ROI for our instrument and
compute the corresponding J-(D-) factor distribution in our ROI. The details
are discussed in Sec. II of the Supplemental Material. The half-width of the
chosen ROI, the corresponding median J- (D-) factor, and its uncertainty for
each dSph are shown in Table 1. For the observation of WCDA, it is a
conservative case that the ROI selection is consistent with the above value
because WCDA has better angular resolution in the low energy range than KM2A.
Meanwhile, the J- (D-) factor is consistent throughout the analysis.

Observation and Data Analysis—The present work utilizes LHAASO-WCDA data (E
$<$ 20 TeV ) acquired from March 5, 2021 to March 31, 2023. LHAASO-KM2A data
(E $>$ 10 TeV) are utilized, including KM2A 1/2 array data from December 27,
2019 to November 30, 2020, KM2A 3/4 array data from December 1, 2020 to July
19, 2021, and KM2A full array data from July 20, 2021 to February 28, 2022. We
apply the detector simulation, event reconstruction and selection algorithms
detailed in the performance papers of LHAASO sub-arrays [33, 34] for the
analysis of WCDA and KM2A data. The total effective observation time for each
target dSph from WCDA and KM2A are shown in Table S1 of Supplemental Material
[38].

We divide the KM2A data from 10 TeV to 103 TeV into 10 logarithmically evenly
spaced bins according to reconstructed energy. For the WCDA data, events are
divided into 6 groups according to the number of triggered PMT units
($N_{hits}$), i.e. [60,100], [100,200], [200,300], [300,500], [500,800],
[800,2000]. Based on the reconstructed direction, the selected events from
each energy bin in the KM2A dataset and each group of WCDA data are mapped
onto a 2D sky map with a pixel size of 0.1${}^{\circ}\times$0.1∘ in the
equatorial coordinate. We use the “direct integration” method as described in
Ref. [42] to estimate the number of background events per pixel. To eliminate
the contamination of known gamma-ray sources on background estimation, we mask
the Galactic disk region ($|\rm{b}|<10^{\circ}$), known sources given by
TeVCat [43], and first LHAASO catalog [44] (see Fig. S1 of Supplemental
Material [38]).

The expected numbers of gamma-ray events produced by DM in the ROIs are
calculated by folding the gamma-ray flux produced by DM with the WCDA and KM2A
detector response function respectively. More details are discussed in Sec. I
of Supplemental Material [38].

To quantify the excess of gamma-ray signals in the ROIs, we use a 3D binned
likelihood ratio analysis combining WCDA and KM2A data. This method accounts
for both the energy spectrum and the spatial characteristics of the DM
signals, which are different from the background in the ROIs. In this
analysis, we define the 3D likelihood function for the $k$-th dSph as follows:

$\displaystyle{\mathcal{L}}_{k}=\prod\limits_{i,j}{\rm
Poisson}(N_{i,j,k}^{obs};N_{i,j,k}^{exp}+N_{i,j,k}^{bkg})\times{\mathcal{G}}(B_{k};B_{k}^{obs},\sigma_{k}),$
(3)

where

$\begin{split}{\mathcal{G}}(B_{k};B_{k}^{obs},\sigma_{k})=\frac{1}{{\rm
ln}(10)B_{k}^{obs}\sqrt{2\pi}\sigma_{k}}\\\ \times e^{-[{\rm
log_{10}}(B_{k})-{\rm
log_{10}}(B_{k}^{obs})]^{2}/2\sigma_{k}^{2}}.\end{split}$ (4)

The $N_{i,j,k}^{exp}$ is the expected number of gamma-ray from DM annihilation
or decay in the $i$-th energy estimator bin and the $j$-th pixel on the 2D sky
map of the $k$-th dSph. $N_{i,j,k}^{bkg}$ is the estimated background events
from the “direct integration” method, and $N_{i,j,k}^{obs}$ is the observed
number of gamma-ray photons. The term
$\mathcal{G}(B_{k};B_{k}^{obs},\sigma_{k})$ is included for the statistical
uncertainties on the J- (D-) factor of the $k$-th dSph, following Ref. [16,
17], where $B$ equals $J$ for the annihilation case and $B$ equals $D$ for the
decaying case. The larger uncertainties listed in Table 1 are taken as
$\sigma_{k}$ considering the asymmetric distribution of J- (D-) factor
conservatively.

To quantify how well the DM signal fits the observed data, we define the test
statistic of the $k$-th dSph (${TS_{k}}$) as,

$\displaystyle{TS_{k}=-2\rm{ln}(\frac{{\mathcal{L}_{k}}(S=0)}{{\mathcal{L}_{k}}(S_{max})})},$
(5)

where ${S}$ represents the DM signal flux, and $S_{\text{max}}$ is the best-
fit value of the DM signal flux that maximizes the likelihood. To avoid non-
physical values, we set $\left\langle\sigma_{A}v\right\rangle$ and
$\tau_{\chi}$ to be positive during the fitting process. We obtained the
statistical significance of the signal over the null hypothesis (no DM model)
by $\sqrt{TS_{k}}$. Then one-sided 95% confidence level (C.L.) limits on
$\left\langle\sigma_{A}v\right\rangle$ or $\tau_{\chi}$ are set by increasing
the DM signal normalization from its best-fit value until -2${\rm
ln}{\mathcal{L}}$ increases by a value of 2.71 [45].

The combined likelihood analysis of all dSphs is performed by
$\mathcal{L}_{total}=\prod\limits_{k}{\mathcal{L}}_{k}$, with the aim of
improving the overall statistical power and generating stronger constraints on
the DM parameters.

Figure 1: The 95$\%$ C.L. upper limits on the DM annihilation cross-section
for $b\overline{b},\tau^{+}\tau^{-}$ channels and comparing to other
experiments (Fermi-LAT [17], HAWC [19] ,H.E.S.S [20], MAGIC [21], VERITAS
[22], IceCube [46]). The solid black line represents the observed combined
limit of this work. The dashed black line, green band, and yellow band
represent the expected limits and their 1$\sigma$ and 2$\sigma$ uncertainties.
The dashed gray line is Thermal Relic cross-section [47], and the other dashed
colored lines show the results of other experiments.

Figure 2: The 95$\%$ C.L. lower limits on the DM decay lifetime for
$b\overline{b},\tau^{+}\tau^{-}$ channels. The solid black line represents the
LHAASO observed combined limit, and the dashed black line, green band, and
yellow band represent the expected combined limits, 1$\sigma$ and 2$\sigma$
uncertainty based on the mock observation. The limits obtained from Fermi-LAT
[48], MAGIC [49], IceCube [50], LHAASO-KM2A Galactic halo [29] and HAWC [51]
with dashed colored line are also shown for comparison.

Results— We utilize data from 756 days of LHAASO-WCDA and 794 days of LHAASO-
KM2A observations to search for DM signals in 16 dSphs around the Milky Way.
No significant gamma-ray excess was detected from these dSphs. The statistical
significance of DM signals in these dSphs is shown in Sec. III of Supplemental
Material [38]. Therefore, 95$\%$ C.L. limits are placed on the DM annihilation
cross-section or the DM decay lifetime, as shown in Fig. 1 and Fig. 2
respectively. In Fig. S8 of Supplemental Material [38], the 95$\%$ C.L. upper
limits for $\left\langle\sigma_{A}v\right\rangle$ from combined and individual
dSphs are presented, assuming a DM mass range from 1 TeV to 1 EeV with a
100$\%$ branching ratio to specific standard model particles. The combined
upper limits are dominated by sources with large J-factor, small uncertainties
and favorable locations inside the LHAASO FoV, i.e., Ursa Major II, Ursa
Minor, Draco, Willman I, Segue 1 and Coma Berenices.

To assess the consistency between the constraints derived from the observed
data and the expected limits from pure background, we repeat 1000 mock
observations under the null hypothesis, considering the Poisson ﬂuctuation
with the measured background. The expected combined limits and the two-sided
68$\%$ and 95$\%$ containment bands for $b\overline{b}$ and $\tau^{+}\tau^{-}$
are shown in Fig. 1. See also Fig. S10 of the Supplemental Material [38] for
other channels. The fact that observed limits are between the expected limit
bands indicates that the observational data are consistent with Poisson
ﬂuctuation with the background. The constraints on high-mass DM consistently
approach the 68% boundary of the anticipated limit bands, suggesting a slight
overestimation of the background in this study and thereby a deficit in the
number of putative signal events inferred in the ROIs. This overestimation is
likely due to the contribution of faint sources which are below our
sensitivity threshold and thus not removed by the mask used in our background
estimation; this issue may be more important for high masses due to the lower
event rates at high energies. Fig. 1 also shows the “Thermal Relic” cross-
section [47] and the limits from other experiments such as Fermi-LAT [17],
HAWC [19], H.E.S.S [20], MAGIC [21], VERITAS [22], and IceCube [46]. The
observations of dSphs by LHAASO could provide better constraints for DM with a
mass heavier than a few hundred TeV.

In Fig. S9 of Supplemental Material [38], the 95$\%$ C.L. lower limits for
$\tau_{\chi}$ are presented for combined and individual dSphs analysis.
Similar to the DM annihilation results, the limits are mainly driven by Ursa
Major II, Ursa Minor, Draco, and Coma Berenices. The expected limits from the
same analysis for mock data are shown in Fig. 2, for $b\overline{b}$ and
$\tau^{+}\tau^{-}$ final states, with the limits from Fermi-LAT [48], MAGIC
[49], IceCube [50], LHAASO-KM2A Galactic halo [29], and HAWC [51]. We also
show constraints for $\tau_{\chi}$ from combined dSphs observation and mock
data in Fig. S10 of Supplemental Material [38] for other channels.

In our analysis, we incorporate the J- (D-) factor likelihood into our
likelihood analysis, leading to a reduction in the constraints on DM
parameters by a factor of 2-6 (see Fig. S6 of Supplemental Material [38]).
Additionally, we factor in the effects of VHE gamma-ray absorption by the
ISRF, resulting in a relaxation of constraints on DM particles with masses
exceeding 1000 TeV by approximately 5-10-fold. Moreover, we consider the
expected morphology of the DM signal, moving beyond a point-like source
approximation. The constraints derived from the extended source analysis based
on the DM density profile are consequently diminished by a factor of 1.5-12,
particularly in the context of DM decay scenarios, conforming a strong effect
of the spatial extension of dSphs on the DM search results [25]. It is
important to acknowledge that the J- (D-) factor correction exclusively
accounts for the statistical uncertainties in the J- (D-) factors and does not
address the systematic uncertainties stemming from the choice of DM profiles
and uncertainties with some presumptions about Jeans equation. While factors
such as departures from spherical symmetry, velocity anisotropy of the DM
halo, the influence of contaminating foreground stars, and variations in the
DM profile are considered, the predicted J- (D-) factors and constraints may
undergo alterations by a few-fold [52, 53, 17, 54, 55, 56, 57, 58].

Our results extend for the first time the mass range of the limits on the
$\left\langle\sigma_{A}v\right\rangle$ to 1 EeV with the best constraints
above a few hundred TeV. Fermi-LAT [17], H.E.S.S [20], MAGIC [21], and VERITAS
[22] exhibit more stringent limits at lower DM masses, since the effective
area of LHAASO would decay rapidly at low energy. We have comparable limits to
HAWC [19] for masses up to several hundred TeV and consistently have better
constraints than those from IceCube [46] across all mass ranges. For the DM
decay lifetime, our constraints are weaker than those based on galactic halo
data by KM2A [29], since the D-factor in the selected dSphs is smaller, and
the effects of attenuation by pair production are more significant considering
the large distances of dSphs from the Earth compared to the galactic halo. In
general, our constraints on the DM decay lifetime are also less stringent
compared to those determined by HAWC [51], MAGIC [49], Fermi-LAT [48], and
IceCube [50] through the observation of Virgo cluster, Perseus cluster, and
the galactic halo with larger D-factors and subdominant effects of
attenuation. However, the combined limits from dSphs, considering the
uncertainties of the DM distribution and the spatial extension of the expected
signal, could also provide a complementary set of reliable limits.

Conclusion and Outlook— We investigate DM annihilation and decay signals from
16 dSphs within the LHAASO FoV using data collected by WCDA and KM2A. No
significant gamma-ray excess is observed from these sources. Consequently, we
establish individual and combined constraints on
$\left\langle\sigma_{A}v\right\rangle$ and $\tau_{\chi}$ across five channels
($b\overline{b},t\overline{t},\mu^{+}\mu^{-},\tau^{+}\tau^{-},W^{+}W^{-}$).

In this analysis, we treat the selected dSphs as extended sources in the 3D
likelihood analysis framework to consider the spatial distribution of the DM
density within the dSphs. We optimize the size of ROIs and recalculate the J-
(D-) factor and their uncertainties corresponding to the ROIs. To make the
analysis more comprehensive and reliable, the absorption effect of ISRF on VHE
gamma-ray is considered, and the statistical uncertainty of the J- (D-) factor
is incorporated as a nuisance parameter in the likelihood analysis.

Our results represent the first-ever constraint on
$\left\langle\sigma_{A}v\right\rangle$, extending the mass of DM to 1 EeV. The
combined limits are the most stringent constraints for
$\left\langle\sigma_{A}v\right\rangle$ above a few hundred TeV. Meanwhile, we
stress that the impact of spatial extension from dSphs is a necessary
condition when deriving DM limits from dSphs with future instruments. As more
WCDA and KM2A data will be collected, the development of algorithms to enhance
energy and angular resolution for LHAASO , and improvements in kinematics
measurements to reduce the uncertainty of the DM density distribution, LHAASO
is expected to become more sensitive and to improve its limits in the future.

Acknowledgements— We would like to thank all staff members who work at the
LHAASO site above 4400 meters above sea level year-round to maintain the
detector and keep the water recycling system, electricity power supply and
other components of the experiment operating smoothly. We are grateful to
Chengdu Management Committee of Tianfu New Area for the constant financial
support for research with LHAASO data. This research work is supported by the
following grants: The National Key R$\&$D program of China No.2018YFA0404201,
No.2018YFA0404202, No.2018YFA0404203, No.2018YFA0404204, National Natural
Science Foundation of China No.12175248, No.12322302, Department of Science
and Technology of Sichuan Province, China No.2021YFSY0030, Project for Young
Scientists in Basic Research of Chinese Academy of Sciences No.YSBR-061, the
Chinese Academy of Sciences, the Program for Innovative Talents and
Entrepreneur in Jiangsu, and in Thailand by the National Science and
Technology Development Agency (NSTDA) and the National Research Council of
Thailand (NRCT) under the High-Potential Research Team Grant Program
(N42A650868).

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## Supplemental Material

##  I I. Data Analysis with LHAASO

Table S1 shows the equatorial coordinates and the effective obervation time of
LHAASO for target dSphs in this analysis, where the $\rm T_{WCDA}$ and $\rm
T_{KM2A}$ represent the effective obervation time of LHAASO-WCDA and LHAASO-
KM2A respectively.

Table S1: The associated the right ascension, the declination, and the effective observation time (day) of WCDA and KM2A for 16 dSphs within the LHAASO FoV. Name | Ra[deg] | Dec[deg] |  $\rm T_{WCDA}$[day] |  $\rm T_{KM2A}$ [day]
---|---|---|---|---
Draco | 260.05 | 57.92 | 690.37 | 730.76
Ursa Minor | 227.28 | 67.23 | 701.59 | 739.53
Ursa Major I | 158.71 | 51.92 | 692.51 | 742.17
Ursa Major II | 132.87 | 63.13 | 688.88 | 740.83
Bootes 1 | 210.02 | 14.50 | 699.85 | 742.01
Canes Venatici I | 202.02 | 33.56 | 699.01 | 743.28
Coma Berenices | 186.74 | 23.90 | 696.88 | 744.34
Leo I | 152.12 | 12.30 | 692.19 | 743.02
Segue 1 | 151.77 | 16.08 | 691.72 | 743.06
Sextans | 153.26 | -1.61 | 693.36 | 743.60
Canes Venatici II | 194.29 | 34.32 | 698.15 | 743.81
Hercules | 247.76 | 12.79 | 699.04 | 737.33
Leo II | 168.37 | 22.15 | 693.95 | 744.18
Willman I | 162.34 | 51.05 | 693.45 | 742.21
Aquarius 2 | 338.48 | -9.33 | 666.84 | 728.11
Leo T | 143.72 | 17.05 | 690.84 | 742.51

Fig S1 displays the masked sky map during background estimation in the
equatorial coordinate system. In this work, we mask the Galactic disk region
($|\rm{b}|<10^{\circ}$), known sources given by TeVCat [43] and first LHAASO
catalog [44] with exclusion radius
$R_{excl}=n\cdot\sqrt{\sigma_{ext}^{2}+\sigma_{psf}^{2}}$, where $n=2.5$ is a
constant factor, $\sigma_{ext}$ and $\sigma_{psf}$ denote the sources
extension and the PSF of instruments respectively, as in Ref. [59].

Figure S1: The masked sky map in the equatorial coordinate system.

Detector response for gamma-ray is crucial to relate the DM flux to the number
of events from the dSphs. We investigate the detector response of LHAASO-WCDA
and LHAASO-KM2A to detect gamma-ray as a function of the primary energy and
the incidence direction from same detector simulation procedure in performance
paper[33, 34]. Following Ref. [60], the expected events (${N_{i,j,k}^{DM}}$)
of gamma-ray from DM annihilation or decay in $i$-th energy estimator bin and
$j$-th pixel of 2D sky map for $k$-th dSph in the observation time is
calculated by

${N_{i,j,k}^{DM}=\int_{i}{\rm d}\eta\int_{j}{\rm
d}\Omega(\hat{p^{\prime}})\int{\rm d}tR(\eta,\hat{p^{\prime}},t)},$ (6)

where the $\rm\eta$ is the energy estimator, which represented as the number
of triggered PMTs ($\rm N_{hit}$) for WCDA, and represented as reconstruction
energy for KM2A. The $\hat{p^{\prime}}$ represents the reconstructed direction
according to the direction reconstruction algorithm and $t$ denotes the
observation time. As for the R, it can be described by the following
formation,

${R(\eta,\hat{p^{\prime}},t)=\int{\rm d}E\int_{\hat{p}}{\rm d}\Omega\frac{{\rm
d}F}{{\rm d}E{\rm d}\Omega{\rm
d}t}A(\hat{p},E)P(\hat{p^{\prime}},E;\hat{p})M(\eta,\hat{p};E)}.$ (7)

Here, the $E$ and $\hat{p}$ are the primary energy and primary direction for a
gamma-ray event. The flux term is expected differential gamma-ray flux from DM
annihilation or decay, which is described as Eq.1 and Eq.2 of the Letter.
These three factors are computed for once LHAASO observation, effective
collection area ($A(\hat{p},E)$), point-spread-function
($P(\hat{p^{\prime}},E;\hat{p})$) and energy estimator transfer matrix
($M(\eta,\hat{p};E)$). According to LHAASO official simulation data[33, 34],
the effective area is the product of reference area and efficiency from event
trigger, reconstruction and selection for gamma-ray with primary energy $E$
and primary direction $\hat{p}$. The point spread function and the energy
estimator transfer matrix are the probability distributions of the
reconstructed direction $\hat{p^{\prime}}$ and the observed energy estimator
with primary energy $E$ and primary direction $\hat{p}$ respectively. With the
expected events of gamma-ray from DM, ${N_{i,j,k}^{DM}}$, and estimated
background events, we could get the expected numbers of gamma-ray,
$N_{i,j,k}^{exp}$, in the $i$-th energy estimator ($N_{hit}$ for WCDA and
reconstructed energy for KM2A) bin and the $j$-th pixel on the 2D sky map of
the $k$-th dSph.

##  II II. Calculation for J- (D-) factor and density profile

The observation targets refered in this work are selected from Ref. [41].
Among the 44 dSphs objects studied in Ref. [41], we exclude the 6 dSphs bound
to Andromeda Galaxy (M31) and 15 dSphs that are not in LHAASO’s FoV, where the
declination of dSphs satisfies the range $-20.64^{\circ}$ to $79.36^{\circ}$.
Subsequently, from the remaining 23 dSphs, we select 16 dSphs as our primary
observation targets. The coordinates of these selected dSphs are detailed in
Table S1. Notably, apart from their advantageous locations, these chosen dSphs
exhibit tighter constraints compared to the unselected dSphs. The seven dSphs
within LHAASO’s FoV which the authors of Ref. [41] indicate should be treated
with caution because the MCMC chains include tails or provide only upper
limits in posterior distributions (Draco II, Leo IV, Leo V, Pisces II, Pegasus
III, Segue 2 and Triangulum II), are not selected for the study.

In Eq. 1 and Eq. 2 of the Letter, ${\rm d}J/{\rm d}\Omega$ and ${\rm d}D/{\rm
d}\Omega$ are defined as,

$\displaystyle{\frac{{\rm d}J}{{\rm d}\Omega}=\int\rho^{2}_{DM}(r){\rm d}l},$
(8) $\displaystyle{\frac{{\rm d}D}{{\rm d}\Omega}=\int\rho_{DM}(r){\rm d}l},$
(9)

where the $\rm{\rho_{DM}(r)}$ refers to the DM density profile in the dSphs,
and $l$ represents the distance from a point on the line-of-sight (L.o.S) to
the Earth. The relationship between $r$ and $l$ is described by
$r^{2}=l^{2}+d^{2}-2ldcos\theta$. Here, $d$ represents the distance between
the dSph center and the Earth, while $\theta$ denotes the angle between the
L.o.S and the direction of the dSph center. In this work, Navarro–Frenk–White
(NFW)[37] model is adopted as

$\displaystyle{\rho_{DM}(r)=\frac{\rho_{s}}{(r/r_{s})(1+r/r_{s})^{2}}},$ (10)

where $\rho_{s}$ is the scale density and $r_{s}$ is the scale radius. The
upper limits of integration of $l$ are conservatively estimated with the tidal
radius ($r_{t}$) of dSphs [41], as

$\displaystyle{l_{\pm}=d{\rm cos}(\theta)\pm\sqrt{r_{t}^{2}-d^{2}{\rm
sin}^{2}(\theta)}}.$ (11)

The parameters (i.e. $d$, $r_{t}$, $\rho_{s}$, $r_{s}$) determine the
calculation of the density profile and the J- (D-) factor of dSphs. The Ref
[41] performed a Jeans analysis on the target dSphs, whose DM profiles follow
the NFW profile with these parameters mentioned above. We use their public
available MCMC chains to calculate the distribution of density profile and J-
(D-) for each target dSph. Fig S2 shows the constraints on the differential J-
(D-) profile for two dSphs: the classical dwarf Draco and the ultra-faint
dwarf Ursa Major II. The envelopes show the $\pm 1\sigma$ and median values of
the differential J- (D-) profile as a function of the angular separation from
the center of the dSphs.

Figure S2: Expected differential J- profile (purple) and D- profile (green)
for Draco and Ursa Major II. At each angle the solid and dashed lines show the
median proﬁles and the shaded band corresponds to the $\pm 1\sigma$
distribution as derived in MCMC chains provided by Ref [41]. Table S2: The
corresponding density profile parameters of J- factor for each dSphs [41].

Source | $d/\rm{kpc}$ | ${r_{t}}/\rm{kpc}$ | ${\rm log_{10}(}\rho_{s}/M_{\odot}{\rm kpc^{-3})}$ | ${\rm log_{10}(}r_{s}/{\rm kpc})$
---|---|---|---|---
Draco | 67.40 | 9.07 | 7.45 | 0.17
Ursa Minor | 73.29 | 6.92 | 7.91 | -0.18
Ursa Major I | 95.58 | 8.34 | 7.83 | -0.19
Ursa Major II | 35.12 | 9.35 | 6.79 | 0.72
Bootes 1 | 65.69 | 9.06 | 6.62 | 0.58
Canes Venatici I | 211.09 | 19.82 | 7.20 | 0.14
Coma Berenices | 42.31 | 5.14 | 7.57 | 0.06
Leo I | 266.15 | 23.25 | 7.72 | -0.09
Segue 1 | 23.88 | 3.41 | 6.96 | 0.39
Sextans | 89.63 | 11.88 | 6.32 | 0.65
Canes Venatici II | 166.26 | 29.91 | 6.50 | 0.70
Hercules | 138.16 | 22.21 | 6.17 | 0.82
Leo II | 242.44 | 19.15 | 7.95 | -0.23
Willman I | 44.46 | 8.07 | 7.81 | 0.10
Aquarius 2 | 107.50 | 24.46 | 6.59 | 0.78
Leo T | 380.69 | 25.00 | 6.69 | 0.74

Figure S3: The DM annihilation signal-to-noise ratio as a function of the
angle for the Draco (left) and Ursa Major II (right). The black solid line
represents the median curve of signal-to-noise ratio, and the shaded band
corresponds to the $\pm 1\sigma$ distribution. The maximum value of the median
curve is represented by the green dashed line, corresponding to the optimal
region.

In order to maximize the sensitivity of the signal search, we use
$\mathcal{S}/\sqrt{\mathcal{B}}$ as an indicator to find the optimal region of
interest (ROI) [61], where $\mathcal{S}$ is the 2D signal map, which use the
J- (D-) profile of each dSphs convolved with 2D point spread function (PSF) at
first KM2A energy estimator bin and multiply by the solid angle in each pixel.
$\mathcal{B}$ is background distribution estimated according to the background
estimation method mentioned in data analysis. We sum all signal within
$\theta$ to get $\mathcal{S}$ and sum all background within $\theta$ to get
$\mathcal{B}$, and we vary $\theta$ to maximize
$\mathcal{S}/\sqrt{\mathcal{B}}$. We obtain the variation of the signal-to-
noise ratio($\mathcal{S}/\sqrt{\mathcal{B}}$) with the angle $\theta$, and
select the $\theta$ with the maximum median signal-to-noise ratio as the ROI
size. Fig S3 shows the DM annihilation signal-to-noise ratio as a function of
the $\theta$ for the Draco and Ursa Major II, in which the black solid line
represents the median curve of signal-to-noise ratio, and the maximum value of
the median is represented by the green dashed line, corresponding to the
optimal region. The optimal regions for some dSphs are smaller than the PSF of
KM2A at first KM2A energy estimator bin, in which case we fixed the selected
ROI as 1.58$\sigma$ [62], and use the parameters corresponding to the median
of the J-(D-) factor at the optimal ROI as the parameters of the dark matter
distribution model, as shown in Table S2. The ROI sizes and J- (D-) factors of
the 16 dSphs are shown in Table I in the Letter.

##  III III. Statistical Significance of DM Annihilation and Decay Signals

The significance map of two dSphs, the classical dwarf Draco and the ultra-
faint dwarf Ursa Major II, are calculated by using the Li-Ma formula [61] with
KM2A and WCDA data, as shown in Fig S4. The dashed green and red lines in the
figures indicate the ROI regions for DM decay and annihilation, respectively.

Figure S4: The significance map of Draco (left) and Ursa Major II (right) of
the energy of 10-1000 TeV in the KM2A data (top) and $N_{hit}$ of 60-2000 in
the WCDA data (bottom).

Fig S5 shows the signal signiﬁcance as a function of dark matter particle mass
in the two channels, i.e., $b\overline{b}$ and $\tau^{+}\tau^{-}$. There is no
significant gamma-ray signal excess from the dark matter annihilation or decay
process in this analysis, with the highest significance approaching 2.4
$\sigma$.

Figure S5:  LHAASO-measured signiﬁcance of the dark matter annihilation (top
panel) and decay (bottom panel) signal in two channels, i.e.,
${b\overline{b}}$ and ${\tau^{+}\tau^{-}}$, for the 16 individual dSphs. The
color lines show the signal signiﬁcance for each dSphs as a function of dark
matter particle mass.

##  IV IV. Other supplementary results

In Fig S6, we show comparison of results for the impacts of High Energy gamma-
ray absorption by the Interstellar Radiation Field (ISRF), uncertainty of J-
(D-) factor and morphology processing of dSphs on DM parameter constraints.

In Fig S7, we show comparison of results for the impacts of treating dSphs as
point sources versus extended sources, using WCDA data only, KM2A data only,
and combined WCDA and KM2A data. It is clear that, in the case of KM2A data,
constraints on low-mass dark matter remain consistent between point source and
extended source analyses, which is consistent with the large PSF at lower
energy levels. However, constraints on high-mass dark matter are degraded
significantly in the extended analysis due to the high-quality PSF at higher
energy levels. Similar trends in constraints are observed in the results
obtained from WCDA. As anticipated, the signal originating from decay
processes should exhibit even greater spatial extension compared to that from
annihilation. Thus it is evident that the good PSF of LHAASO could enable us
to take the spatial analysis.

In Fig S8 and Fig S9, we show 95$\%$ C.L. upper limits on the DM annihilation
cross-section and 95$\%$ C.L. lower limits on the DM decay lifetime from
individual analysis of each dSph and combined analysis of all dSphs.

In Fig S10, we show the comparison of observed limits and expected limits from
pure background simulation.

Figure S6:  Comparison of results for the impacts of high energy gamma-ray
absorption by the Interstellar Radiation Field (ISRF), uncertainty of J- (D-)
factor and morphology processing of dSphs on DM parameter constraints. The top
panels represent the compared combined limits of DM annihilation cross-section
of ${b\overline{b}}$ and ${\tau^{+}\tau^{-}}$ channels, while down panels
represent the compared combined limits of DM decay lifetime. The black line
represents the limits of the extended source analysis with J- (D-) factor
uncertainty and the effect of absorption, as the benchmark analysis. The
dashed green line represents the limits of the extended source analysis
considering only the J- (D-) factor uncertainty, and the dashed red line
represents the results of the extended source analysis considering only the
effect of absorption by ISRF. The dashed blue line represents the limits of
the point-like source analysis with J- (D-) factor uncertainty and the effect
of absorption by ISRF.

Figure S7: Comparison of results for the impacts of treating dSphs as point
sources versus extended sources, using WCDA data only, KM2A data only, and
combined WCDA and KM2A data. The 95$\%$ C.L. upper limits on the DM
annihilation cross-section for the $b\overline{b}$ channels are shown in the
left panel. The 95$\%$ C.L. lower limits on the DM lifetime for the
$b\overline{b}$ channels are presented in the right panel.

Figure S8: The results of LHAASO analysis show the 95$\%$ C.L. upper limits on
the DM annihilation cross-section for five channels
($b\overline{b}$,$\tau^{+}\tau^{-}$, $t\overline{t}$,$\mu^{+}\mu^{-}$ and
$W^{+}W^{-}$) using data from 16 dSphs around the Milky Way. The solid red
line represents the combined limits obtained using all of the dSphs, while the
dashed colored lines represent the individual upper limits obtained from each
dSph.

Figure S9: The panels display the 95$\%$ C.L. lower limits on the DM decay
lifetime assuming DM with mass range from 1 TeV to 1 EeV with 100$\%$
branching ratio decay into specific standard model
particles($b\overline{b}$,$\tau^{+}\tau^{-}$, $t\overline{t}$,$\mu^{+}\mu^{-}$
and $W^{+}W^{-}$) for all 16 dSphs. The solid red line represents the combined
limit obtained from the analysis of all dSphs, while the dashed colored lines
correspond to the lower limits obtained from the individual analysis of each
dSph.

Figure S10: The comparison of observed limits and expected limits for the
$t\overline{t},\mu^{+}\mu^{-}$ and $W^{+}W^{-}$ processes. The top three
figures depict the observed and expected 95$\%$ C.L. upper limits on the DM
annihilation cross-section. The bottom three figures represent the observed
95$\%$ C.L. lower limits on the DM decay lifetime. The solid black line
represents the LHAASO observed combined limit, and the dashed black line,
green band, and yellow band represent the expected combined limits, their
1$\sigma$ and 2$\sigma$ uncertainty based on the mock observations.