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    Energy calibration of LHAASO-KM2A using the cosmic ray Moon shadow

    Zhen Cao1,2,3, F. Aharonian3,4,5,6, Y. X. Bai1,3, Y. W. Bao7, D. Bastieri8, X. J. Bi1,2,3, Y. J. Bi1,3, W. Bian7, A. V. Bukevich9 et al. (LHAASO Collaboration)

    A. V. Bukevich9, C. M. Cai10, W. Y. Cao4, Zhe Cao11,4, J. Chang12, J. F. Chang1,3,11, A. M. Chen7, E. S. Chen1,3, G. H. Chen8, H. X. Chen13, Liang Chen14, Long Chen10, M. J. Chen1,3, M. L. Chen1,3,11, Q. H. Chen10, S. Chen15, S. H. Chen1,2,3, S. Z. Chen1,3, T. L. Chen16, X. B. Chen17, X. J. Chen10, Y. Chen17, N. Cheng1,3, Y. D. Cheng1,2,3, M. C. Chu18, M. Y. Cui12, S. W. Cui19, X. H. Cui20, Y. D. Cui21, B. Z. Dai15, H. L. Dai1,3,11, Z. G. Dai4, Danzengluobu16, Y. X. Diao10, X. Q. Dong1,2,3, K. K. Duan12, J. H. Fan8, Y. Z. Fan12, J. Fang15, J. H. Fang13, K. Fang1,3, C. F. Feng22, H. Feng1, L. Feng12, S. H. Feng1,3, X. T. Feng22, Y. Feng13, Y. L. Feng16, S. Gabici23, B. Gao1,3, C. D. Gao22, Q. Gao16, W. Gao1,3, W. K. Gao1,2,3, M. M. Ge15, T. T. Ge21, L. S. Geng1,3, G. Giacinti7, G. H. Gong24, Q. B. Gou1,3, M. H. Gu1,3,11, F. L. Guo14, J. Guo24, X. L. Guo10, Y. Q. Guo1,3, Y. Y. Guo12, Y. A. Han25, O. A. Hannuksela18, M. Hasan1,2,3, H. H. He1,2,3,†, H. N. He12, J. Y. He12, X. Y. He12, Y. He10, S. Hernández-Cadena7, B. W. Hou1,2,3, C. Hou1,3, X. Hou26, H. B. Hu1,2,3, S. C. Hu1,3,27, C. Huang17, D. H. Huang10, J. J. Huang1,2,3, T. Q. Huang1,3, W. J. Huang21, X. T. Huang22, X. Y. Huang12, Y. Huang1,3,27, Y. Y. Huang17, X. L. Ji1,3,11, H. Y. Jia10, K. Jia22, H. B. Jiang1,3, K. Jiang11,4, X. W. Jiang1,3, Z. J. Jiang15, M. Jin10, S. Kaci7, M. M. Kang28, I. Karpikov9, D. Khangulyan1,3, D. Kuleshov9, K. Kurinov9, B. B. Li19, Cheng Li11,4, Cong Li1,3, D. Li1,2,3, F. Li1,3,11, H. B. Li1,2,3, H. C. Li1,3, Jian Li4, Jie Li1,3,11, K. Li1,3, L. Li29, R. L. Li12, S. D. Li14,2, T. Y. Li7, W. L. Li7, X. R. Li1,3, Xin Li11,4, Y. Li7, Y. Z. Li1,2,3, Zhe Li1,3, Zhuo Li30, E. W. Liang31, Y. F. Liang31, S. J. Lin21, B. Liu12, C. Liu1,3, D. Liu22, D. B. Liu7, H. Liu10, H. D. Liu25, J. Liu1,3, J. L. Liu1,3, J. R. Liu10, M. Y. Liu16, R. Y. Liu17, S. M. Liu10, W. Liu1,3, X. Liu10, Y. Liu8, Y. Liu10, Y. N. Liu24, Y. Q. Lou24, Q. Luo21, Y. Luo7, H. K. Lv1,3, B. Q. Ma25,30, L. L. Ma1,3, X. H. Ma1,3, J. R. Mao26, Z. Min1,3, W. Mitthumsiri32, G. B. Mou33, H. J. Mu25, A. Neronov23, K. C. Y. Ng18, M. Y. Ni12, L. Nie10, L. J. Ou8, P. Pattarakijwanich32, Z. Y. Pei8, J. C. Qi1,2,3, M. Y. Qi1,3, J. J. Qin4, A. Raza1,2,3,*, C. Y. Ren12, D. Ruffolo32, A. Sáiz32, D. Semikoz23, L. Shao19, O. Shchegolev9,34, Y. Z. Shen17, X. D. Sheng1,3, Z. D. Shi4, F. W. Shu29, H. C. Song30, Yu. V. Stenkin9,34, V. Stepanov9, Y. Su12, D. X. Sun4,12, H. Sun22, Q. N. Sun1,3, X. N. Sun31, Z. B. Sun35, N. H. Tabasam22, J. Takata36, P. H. T. Tam21, H. B. Tan17, Q. W. Tang29, R. Tang7, Z. B. Tang11,4, W. W. Tian2,20, C. N. Tong17, L. H. Wan21, C. Wang35, G. W. Wang4, H. G. Wang8, J. C. Wang26, K. Wang30, Kai Wang17, Kai Wang36, L. P. Wang1,2,3, L. Y. Wang1,3, L. Y. Wang19, R. Wang22, W. Wang21, X. G. Wang31, X. J. Wang10, X. Y. Wang17, Y. Wang10, Y. D. Wang1,3, Z. H. Wang28, Z. X. Wang15, Zheng Wang1,3,11, D. M. Wei12, J. J. Wei12, Y. J. Wei1,2,3, T. Wen1,3, S. S. Weng33, C. Y. Wu1,3, H. R. Wu1,3, Q. W. Wu36, S. Wu1,3, X. F. Wu12, Y. S. Wu4, S. Q. Xi1,3, J. Xia4,12, J. J. Xia10, G. M. Xiang14,2, D. X. Xiao19, G. Xiao1,3, Y. L. Xin10, Y. Xing14, D. R. Xiong26, Z. Xiong1,2,3, D. L. Xu7, R. F. Xu1,2,3, R. X. Xu30, W. L. Xu28, L. Xue22, D. H. Yan15, T. Yan1,3, C. W. Yang28, C. Y. Yang26, F. F. Yang1,3,11, L. L. Yang21, M. J. Yang1,3, R. Z. Yang4, W. X. Yang8, Z. H. Yang7, Z. G. Yao1,3, X. A. Ye12, L. Q. Yin1,3, N. Yin22, X. H. You1,3, Z. Y. You1,3, Q. Yuan12, H. Yue1,2,3, H. D. Zeng12, T. X. Zeng1,3,11, W. Zeng15, X. T. Zeng21, M. Zha1,3, B. B. Zhang17, B. T. Zhang1,3, C. Zhang17, F. Zhang10, H. Zhang7, H. M. Zhang31, H. Y. Zhang15, J. L. Zhang20, Li Zhang15, P. F. Zhang15, P. P. Zhang4,12, R. Zhang12, S. R. Zhang19, S. S. Zhang1,3, W. Y. Zhang19, X. Zhang33, X. P. Zhang1,3, Yi Zhang1,12, Yong Zhang1,3, Z. P. Zhang4, J. Zhao1,3, L. Zhao11,4, L. Z. Zhao19, S. P. Zhao12, X. H. Zhao26, Z. H. Zhao4, F. Zheng35, W. J. Zhong17, B. Zhou1,3, H. Zhou7, J. N. Zhou14, M. Zhou29, P. Zhou17, R. Zhou28, X. X. Zhou1,2,3, X. X. Zhou10, B. Y. Zhu4,12, C. G. Zhu22, F. R. Zhu10, H. Zhu20, K. J. Zhu1,2,3,11, Y. C. Zou36, X. Zuo1,3, and F. Akram37,‡ (LHAASO Collaboration)

    • 1Key Laboratory of Particle Astrophysics and Experimental Physics Division and Computing Center, Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China
    • 2University of Chinese Academy of Sciences, 100049 Beijing, China
    • 3TIANFU Cosmic Ray Research Center, Chengdu, Sichuan, China
    • 4University of Science and Technology of China, 230026 Hefei, Anhui, China
    • 5Yerevan State University, 1 Alek Manukyan Street, Yerevan 0025, Armenia
    • 6Max-Planck-Institut for Nuclear Physics, P.O. Box 103980, 69029 Heidelberg, Germany
    • 7Tsung-Dao Lee Institute andSchool of Physics and Astronomy, Shanghai Jiao Tong University, 200240 Shanghai, China
    • 8Center for Astrophysics, Guangzhou University, 510006 Guangzhou, Guangdong, China
    • 9Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow, Russia
    • 10School of Physical Science and Technology and School of Information Science and Technology, Southwest Jiaotong University, 610031 Chengdu, Sichuan, China
    • 11State Key Laboratory of Particle Detection and Electronics, China
    • 12Key Laboratory of Dark Matter and Space Astronomy and Key Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, 210023 Nanjing, Jiangsu, China
    • 13Research Center for Astronomical Computing, Zhejiang Laboratory, 311121 Hangzhou, Zhejiang, China
    • 14Shanghai Astronomical Observatory, Chinese Academy of Sciences, 200030 Shanghai, China
    • 15School of Physics and Astronomy, Yunnan University, 650091 Kunming, Yunnan, China
    • 16Key Laboratory of Cosmic Rays (Tibet University), Ministry of Education, 850000 Lhasa, Tibet, China
    • 17School of Astronomy and Space Science, Nanjing University, 210023 Nanjing, Jiangsu, China
    • 18Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China
    • 19Hebei Normal University, 050024 Shijiazhuang, Hebei, China
    • 20Key Laboratory of Radio Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, 100101 Beijing, China
    • 21School of Physics and Astronomy (Zhuhai) and School of Physics (Guangzhou) and Sino-French Institute of Nuclear Engineering and Technology (Zhuhai), Sun Yat-sen University, 519000 Zhuhai and 510275 Guangzhou, Guangdong, China
    • 22Institute of Frontier and Interdisciplinary Science, Shandong University, 266237 Qingdao, Shandong, China
    • 23APC, Université Paris Cité, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, 119 75205 Paris, France
    • 24Department of Engineering Physics and Department of Physics and Department of Astronomy, Tsinghua University, 100084 Beijing, China
    • 25School of Physics and Microelectronics, Zhengzhou University, 450001 Zhengzhou, Henan, China
    • 26Yunnan Observatories, Chinese Academy of Sciences, 650216 Kunming, Yunnan, China
    • 27China Center of Advanced Science and Technology, Beijing 100190, China
    • 28College of Physics, Sichuan University, 610065 Chengdu, Sichuan, China
    • 29Center for Relativistic Astrophysics and High Energy Physics, School of Physics and Materials Science and Institute of Space Science and Technology, Nanchang University, 330031 Nanchang, Jiangxi, China
    • 30School of Physics and Kavli Institute for Astronomy and Astrophysics, Peking University, 100871 Beijing, China
    • 31Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science and Technology, Guangxi University, 530004 Nanning, Guangxi, China
    • 32Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
    • 33School of Physics and Technology, Nanjing Normal University, 210023 Nanjing, Jiangsu, China
    • 34Moscow Institute of Physics and Technology, 141700 Moscow, Russia
    • 35National Space Science Center, Chinese Academy of Sciences, 100190 Beijing, China
    • 36School of Physics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
    • 37Centre for High Energy Physics, University of the Punjab, Lahore, Pakistan

    • *Contact author: aliraza@ihep.ac.cn
    • †Contact author: hhh@ihep.ac.cn
    • ‡Contact author: faisal.chep@pu.edu.pk

    Phys. Rev. D 112, 123051 – Published 29 December, 2025

    DOI: https://doi.org/10.1103/gc7n-ypqw

    Abstract

    We present a precise measurement of the westward rigidity-dependent shift of the Moon’s shadow using three and a half years of cosmic ray data collected by the kilometer square array (KM2A) of the Large High Altitude Air Shower Observatory (LHAASO) experiment. These measurements enable us to calibrate the detector energy response in the range of 20 to 260 TeV, with results showing excellent agreement with the energy response derived from Monte Carlo (MC) simulations of the KM2A detector. We also measure a best-fit parameter ε=0.015±0.08, corresponding to a 95% CI of [−14%,+17%] for the energy scale estimation. This result establishes the exceptional accuracy of the KM2A-MC in simulating the detector’s response within this energy range.

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