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  • Letter
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Oscillating features in the electromagnetic structure of the neutron

Nature Physics volume 17, pages 1200–1204 (2021)Cite this article

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Abstract

The complicated structure of the neutron cannot be calculated using first-principles calculations due to the large colour charge of quarks and the self-interaction of gluons. Its simplest structure observables are the electromagnetic form factors1, which probe our understanding of the strong interaction. Until now, a small amount of data has been available for the determination of the neutron structure from the time-like kinematical range. Here we present measurements of the Born cross section of electron–positron annihilation reactions into a neutron and anti-neutron pair, and determine the neutron’s effective form factor. The data were recorded with the BESIII experiment at centre-of-mass energies between 2.00 and 3.08 GeV using an integrated luminosity of 647.9 pb−1. Our results improve the statistics on the neutron form factor by more than a factor of 60 over previous measurements, demonstrating that the neutron form factor data from annihilation in the time-like regime is on par with that from electron scattering experiments. The effective form factor of the neutron shows a periodic behaviour, similar to earlier observations of the proton form factor. Future works—both theoretical and experimental—will help illuminate the origin of this oscillation of the electromagnetic structure observables of the nucleon.

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Fig. 1: Signal-process reaction and schematic of the response within the BESIII detector.
Fig. 2: Results for the Born cross section σB and corresponding form factor ∣G∣ of the neutron.
Fig. 3: Results for the Rnp ratio and form factor ∣G∣ deviation from the dipole law with respect to \(\sqrt{s}\).

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Data availability

Source data are provided with this paper. The raw data used for the plots within this paper and other findings of this study are archived in the Institute of High Energy Physics mass storage silo and are available from the corresponding author upon reasonable request.

Code availability

All algorithms used for data analysis and simulation are archived by the authors and are available on request.

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Acknowledgements

We thank the staff of BEPCII, IHEP Computing Center and Supercomputing Center of USTC for their strong support. This work is supported in part by National Key R&D Program of China under contract nos. 2020YFA0406400 and 2020YFA0406300; National Natural Science Foundation of China (NSFC) under contract nos. 11625523, 11635010, 11735014, 11805124, 11822506, 11835012, 11935015, 11935016, 11935018, 11961141012, 12022510, 12025502, 12035009, 12035013, 12061131003, 11705192, 11950410506 and 12061131003; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under contract nos. U1732263, U1832207, U1832103 and U2032111; CAS Key Research Program of Frontier Sciences under contract no. QYZDJ-SSW-SLH040; 100 Talents Program of CAS; Guangdong Major Project of Basic and Applied Basic Research no. 2020B030103008; Science and Technology Program of Guangzhou (no. 2019050001); INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; ERC under contract no. 758462; European Union Horizon 2020 research and innovation programme under contract no. Marie Skłodowska-Curie grant agreement no. 894790; German Research Foundation DFG under contract no. 443159800; Collaborative Research Center CRC 1044, FOR 2359 and GRK 214; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under contract no. DPT2006K-120470; National Science and Technology fund; Olle Engkvist Foundation under contract no. 200-0605; STFC (United Kingdom); The Knut and Alice Wallenberg Foundation (Sweden) under contract no. 2016.0157; The Royal Society, UK, under contract nos. DH140054 and DH160214; The Swedish Research Council; US Department of Energy under contract nos. DE-FG02-05ER41374 and DE-SC-0012069.

Author information

Author notes

  1. M. N. Achasov, N. Y. Muchnoi & I. B. Nikolaev

    Present address: The Novosibirsk State University, Novosibirsk, Russia

  2. Y. Ban, Yuanning Gao, Z. Huang, Y. J. Mao, Y. X. Song, D. Y. Wang, M. Z. Wang, X. Wang, X. H. Xie, X. Q. Yuan & Y. Zheng

    Present address: State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, People’s Republic of China

  3. G. Chelkov & A. Zhemchugov

    Present address: The Moscow Institute of Physics and Technology, Moscow, Russia

  4. Z. J. Chen, X. Sun, J. S. Yu & Y. Zeng

    Present address: School of Physics and Electronics, Hunan University, Changsha, China

  5. Y. P. Guo, H. J. Li, M. H. Liu, T. Luo, X. Pan, X. L. Wang, X. Wu, H. Xiao, F. Yan, L. Yan & Yi Zhang

    Present address: Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai, People’s Republic of China

  6. M. Himmelreich, S. Nakhoul, F. Nerling & K. Peters

    Present address: Goethe University Frankfurt, Frankfurt am Main, Germany

  7. J. F. Hu & H. N. Li

    Present address: Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou, China

  8. S. Janchiv & J. W. Zhang

    Present address: Institute of Physics and Technology, Ulaanbaatar, Mongolia

  9. O. B. Kolcu

    Present address: Istanbul Arel University, Istanbul, Turkey

  10. S. Nisar

    Present address: Department of Physics, Harvard University, Cambridge, MA, USA

  11. A. Sarantsev

    Present address: The NRC ‘Kurchatov Institute’, PNPI, Gatchina, Russia

  12. H. J. Yang

    Present address: Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology, Institute of Nuclear and Particle Physics, Shanghai, People’s Republic of China

  13. A. Yuncu

    Present address: Bogazici University, Istanbul, Turkey

Authors and Affiliations

  1. Institute of High Energy Physics, Beijing, People’s Republic of China

    M. Ablikim, X. Cai, G. F. Cao, N. Cao, J. F. Chang, W. L. Chang, G. Chen, H. S. Chen, M. L. Chen, Y. B. Chen, H. L. Dai, X. C. Dai, Z. Y. Deng, J. Dong, L. Y. Dong, M. Y. Dong, J. Fang, S. S. Fang, Y. Fang, C. D. Fu, Y. Fu, W. X. Gong, M. H. Gu, C. Y. Guan, K. L. He, Y. K. Heng, Z. L. Hou, H. M. Hu, T. Hu, Y. Hu, Y. P. Huang, Q. Ji, X. B. Ji, X. L. Ji, X. S. Jiang, B. C. Ke, R. Kiuchi, M. G. Kurth, F. Li, G. Li, H. B. Li, Ke Li, L. K. Li, W. D. Li, W. G. Li, H. Liang, L. Z. Liao, B. J. Liu, C. X. Liu, Fang Liu, H. M. Liu, Huanhuan Liu, J. Y. Liu, K. Liu, T. Liu, Z. A. Liu, X. C. Lou, J. D. Lu, J. G. Lu, X. L. Lu, Y. Lu, Y. P. Lu, X. L. Luo, H. L. Ma, M. M. Ma, Q. M. Ma, R. Q. Ma, X. X. Ma, X. Y. Ma, Z. P. Mao, X. H. Mo, Z. Ning, Q. Ouyang, A. Pathak, R. G. Ping, S. Qian, Z. H. Qin, J. F. Qiu, G. Rong, X. Y. Shen, R. S. Shi, X. Shi, W. M. Song, G. X. Sun, H. K. Sun, S. S. Sun, T. Sun, Y. Z. Sun, Z. T. Sun, G. Y. Tang, B. Wang, H. P. Wang, K. Wang, L. L. Wang, Meng Wang, Y. F. Wang, Y. Q. Wang, Z. Wang, Z. Y. Wang, S. P. Wen, J. F. Wu, L. H. Wu, L. J. Wu, Z. Wu, S. Y. Xiao, Y. J. Xiao, Y. G. Xie, T. Y. Xing, G. F. Xu, W. Xu, H. X. Yang, Y. Yang, M. Ye, J. H. Yin, B. X. Yu, G. Yu, C. Z. Yuan, Y. Yuan, B. X. Zhang, H. Y. Zhang, J. W. Zhang, Y. Zhang, J. Z. Zhang, Jianyu Zhang, Jiawei Zhang, L. Zhang, Y. H. Zhang, Yao Zhang, G. Zhao, J. Y. Zhao, J. Z. Zhao, Ling Zhao, Q. Zhao, Y. B. Zhao, J. P. Zheng, L. P. Zhou, Q. Zhou, A. N. Zhu, K. Zhu, K. J. Zhu, Z. A. Zhu, B. S. Zou & J. H. Zou

  2. G.I. Budker Institute of Nuclear Physics (BINP) SB RAS, Novosibirsk, Russia

    M. N. Achasov, N. Y. Muchnoi & I. B. Nikolaev

  3. Uppsala University, Uppsala, Sweden

    P. Adlarson, J. Biernat, W. I. Andersson, T. Johansson, A. Kupsc, J. Pettersson, K. Schoenning, V. Thoren & M. Wolke

  4. Helmholtz Institute Mainz, Mainz, Germany

    S. Ahmed, A. Dbeyssi, P. Larin, F. E. Maas & Ch. Rosner

  5. Ruhr-University Bochum, Bochum, Germany

    M. Albrecht, K. Begzsuren, R. B. de Boer, F. Feldbauer, M. Fritsch, F. H. Heinsius, T. Held, T. Holtmann, S. Jaeger, I. K. Keshk, B. Kopf, M. Kuemmel, M. Kuessner, J. Q. Li, M. Pelizaeus, A. Pitka, X. S. Qin, C. Schnier, U. Wiedner, L. Wollenberg & J. Q. Zhang

  6. Johannes Gutenberg University of Mainz, Mainz, Germany

    R. Aliberti, N. Berger, A. Denig, W. Gradl, C. H. Heinz, P. Kiese, H. Leithoff, M. Lellmann, T. Lenz, S. Maldaner, C. F. Redmer, Y. Schelhaas & P. Weidenkaff

  7. University of Turin, Turin, Italy

    A. Amoroso, F. Bianchi, A. Bortone, M. Destefanis, F. De Mori, M. Greco, L. Lavezzi, M. Maggiora, S. Marcello, S. Sosio, S. Spataro & W. Yuan

  8. INFN, Turin, Italy

    A. Amoroso, F. Bianchi, A. Bortone, W. S. Cheng, F. Cossio, M. Destefanis, F. De Mori, L. Fava, M. Greco, L. Lavezzi, S. Lusso, M. Maggiora, S. Marcello, A. Rivetti, M. Rolo, S. Sosio, S. Spataro & W. Yuan

  9. University of Science and Technology of China, Hefei, People’s Republic of China

    Q. An, C. Q. Feng, Yang Gao, G. S. Huang, M. Irshad, Z. H. Lei, Cheng Li, H. Li, P. L. Li, X. H. Li, H. Liang, D. Liu, J. B. Liu, L. Liu, S. B. Liu, W. M. Liu, H. P. Peng, V. Prasad, H. Qi, H. S. Sang, X. Y. Shan, M. Shao, H. C. Shi, X. D. Shi, Y. J. Sun, Y. K. Sun, Y. X. Tan, J. X. Teng, W. P. Wang, Yue Wang, L. Xia, W. B. Yan, R. X. Yang, H. Zhang, Y. T. Zhang, Yan Zhang, Lei Zhao, Z. G. Zhao, X. R. Zhou & Y. C. Zhu

  10. State Key Laboratory of Particle Detection and Electronics, Beijing, People’s Republic of China

    Q. An, X. Cai, J. F. Chang, M. L. Chen, Y. B. Chen, H. L. Dai, J. Dong, M. Y. Dong, J. Fang, C. Q. Feng, Yang Gao, W. X. Gong, M. H. Gu, Y. K. Heng, T. Hu, G. S. Huang, M. Irshad, X. L. Ji, X. S. Jiang, Z. H. Lei, Cheng Li, F. Li, H. Li, P. L. Li, X. H. Li, H. Liang, D. Liu, J. B. Liu, L. Liu, S. B. Liu, W. M. Liu, Z. A. Liu, X. C. Lou, J. G. Lu, Y. P. Lu, X. L. Luo, X. Y. Ma, X. H. Mo, Z. Ning, Q. Ouyang, H. P. Peng, V. Prasad, H. Qi, S. Qian, Z. H. Qin, X. Y. Shan, M. Shao, H. C. Shi, X. Shi, X. D. Shi, Y. J. Sun, Y. K. Sun, Y. X. Tan, J. X. Teng, K. Wang, W. P. Wang, Yue Wang, Y. F. Wang, Z. Wang, Z. Wu, L. Xia, Y. G. Xie, W. B. Yan, R. X. Yang, M. Ye, B. X. Yu, H. Y. Zhang, J. W. Zhang, Y. H. Zhang, Y. T. Zhang, Yan Zhang, J. Z. Zhao, Lei Zhao, Y. B. Zhao, Z. G. Zhao, J. P. Zheng, X. R. Zhou, K. J. Zhu & Y. C. Zhu

  11. Indian Institute of Technology Madras, Chennai, India

    Anita Lavania, J. Libby & K. Ravindran

  12. University of Jinan, Jinan, People’s Republic of China

    X. H. Bai, Y. Jin & Z. X. Meng

  13. Southeast University, Nanjing, People’s Republic of China

    Y. Bai

  14. Joint Institute for Nuclear Research, Dubna, Russia

    O. Bakina, I. Boyko, G. Chelkov, D. Dedovich, I. Denysenko, A. Guskov, Y. Nefedov, A. Sarantsev & A. Zhemchugov

  15. INFN Laboratori Nazionali di Frascati, Frascati, Italy

    R. B. Ferroli, M. Bertani, A. Calcaterra, G. Felici & P. Patteri

  16. INFN Sezione di Ferrara, Ferrara, Italy

    I. Balossino, D. Bettoni, G. Cibinetto, R. Farinelli, I. Garzia, G. Mezzadri & M. Scodeggio

  17. Peking University, Beijing, People’s Republic of China

    Y. Ban, Yuanning Gao, Z. Huang, Y. J. Mao, Y. X. Song, D. Y. Wang, M. Z. Wang, X. Wang, X. H. Xie, X. Q. Yuan & Y. Zheng

  18. University of Muenster, Muenster, Germany

    J. Bloms, N. Huesken, A. Khoukaz, M. Rump & F. Weidner

  19. Carnegie Mellon University, Pittsburgh, PA, USA

    R. A. Briere

  20. Wuhan University, Wuhan, People’s Republic of China

    H. Cai, X. Dong, K. X. Su, L. Sun, Y. H. Tan, W. H. Wang, Z. Y. Zhang & X. Zhou

  21. University of Chinese Academy of Sciences, Beijing, People’s Republic of China

    G. F. Cao, N. Cao, W. L. Chang, H. S. Chen, X. C. Dai, L. Y. Dong, M. Y. Dong, S. S. Fang, C. Y. Guan, K. L. He, Y. K. Heng, Y. R. Hou, H. M. Hu, T. Hu, X. B. Ji, X. S. Jiang, M. G. Kurth, H. B. Li, W. D. Li, H. Liang, L. Z. Liao, H. M. Liu, J. Y. Liu, Q. Liu, T. Liu, Z. A. Liu, X. C. Lou, J. D. Lu, X. R. Lyu, M. M. Ma, R. Q. Ma, R. T. Ma, X. X. Ma, X. H. Mo, S. L. Olsen, Q. Ouyang, R. G. Ping, W.-B. Qian, C. F. Qiao, G. Rong, X. Y. Shen, R. S. Shi, S. S. Sun, T. Sun, H. P. Wang, Meng Wang, Y. F. Wang, Z. Wang, J. F. Wu, L. J. Wu, Y. J. Xiao, T. Y. Xing, W. Xu, S. L. Yang, Y. Yang, B. X. Yu, G. Yu, C. Z. Yuan, J. W. Zhang, J. Z. Zhang, Jianyu Zhang, Jiawei Zhang, J. Y. Zhao, Y. H. Zheng, L. P. Zhou, Q. Zhou, X. K. Zhou, A. N. Zhu, K. J. Zhu & Z. A. Zhu

  22. Istanbul Bilgi University, Istanbul, Turkey

    S. A. Cetin, O. B. Kolcu & A. Yuncu

  23. Central China Normal University, Wuhan, People’s Republic of China

    D. Y. Chen, Y. G. Gao, Feng Liu, Ke Liu, Y. J. Mo, Y. H. Xie & Z. H. Zhang

  24. Nanjing University, Nanjing, People’s Republic of China

    S. J. Chen, L. M. Gu, S. Jin, T. J. Min, M. Qi, C. W. Wang, J. J. Xu, Y. H. Yang, Lei Zhang & S. F. Zhang

  25. Institute of Modern Physics, Lanzhou, People’s Republic of China

    X. R. Chen, Y. T. Liang, K. H. Qi, Z. Yang & Y. X. Zhao

  26. Hunan University, Changsha, People’s Republic of China

    Z. J. Chen, X. Sun, J. S. Yu & Y. Zeng

  27. Nankai University, Tianjin, People’s Republic of China

    X. F. Cui, C. Dong, L. Gong, X. Y. Jiang, Y. B. Liu, X. N. Ma, S. Q. Qu, P. X. Shen, C. X. Yu, M. G. Zhao, J. Zhu & W. J. Zhu

  28. Liaoning University, Shenyang, People’s Republic of China

    Y. Ding, X. S. Kang, K. Y. Liu & F. C. Ma

  29. Zhengzhou University, Zhengzhou, People’s Republic of China

    S. X. Du, D. M. Li, W. C. Yan & S. J. Zhao

  30. University of Eastern Piedmont, Alessandria, Italy

    L. Fava

  31. University of South China, Hengyang, People’s Republic of China

    Ya Gao, L. Q. Huang, T. Yu, B. Zheng & C. Zhong

  32. University of Ferrara, Ferrara, Italy

    I. Garzia

  33. University of Manchester, Manchester, United Kingdom

    E. M. Gersabeck, J. J. Lane, Y. Pan & D. J. White

  34. University of Minnesota, Minneapolis, MN, USA

    A. Gilman, H. Muramatsu & R. Poling

  35. GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany

    K. Goetzen, M. Himmelreich, R. Kliemt, S. Nakhoul, F. Nerling & K. Peters

  36. Beihang University, Beijing, People’s Republic of China

    S. Gu, T. Y. Qi & L. Yuan

  37. Guangxi University, Nanning, People’s Republic of China

    Y. T. Gu & H. B. Liu

  38. Indiana University, Bloomington, IN, USA

    A. Q. Guo, W. Imoehl & R. E. Mitchell

  39. Nanjing Normal University, Nanjing, People’s Republic of China

    L. B. Guo, C. L. Luo, J. L. Ping, W. Y. Sun, Z. J. Xiao & B. Zhong

  40. Shandong Normal University, Jinan, People’s Republic of China

    R. P. Guo

  41. Fudan University, Shanghai, People’s Republic of China

    Y. P. Guo, H. J. Li, M. H. Liu, T. Luo, X. Pan, T. Y. Qi, C. P. Shen, X. L. Wang, X. Wu, H. Xiao, F. Yan, L. Yan & Yi Zhang

  42. Shandong University, Jinan, People’s Republic of China

    T. T. Han, X. T. Huang, H. B. Jiang, J. B. Jiao, J. L. Li, X. L. Li, Z. Q. Liu, L. L. Ma, F. F. Sui, Meng Wang & X. Y. Zhang

  43. Henan Normal University, Xinxiang, People’s Republic of China

    X. Q. Hao, Q. P. Ji, F. X. Lu, J. F. Sun & G. Zhang

  44. University of Hawaii, Honolulu, HI, USA

    F. A. Harris

  45. Suranaree University of Technology, Nakhon Ratchasima, Thailand

    C. Herold

  46. South China Normal University, Guangzhou, People’s Republic of China

    J. F. Hu & H. N. Li

  47. University of the Punjab, Lahore, Pakistan

    T. Hussain, Q. A. Malik, K. H. Rashid & A. A. Zafar

  48. Huangshan College, Huangshan, People’s Republic of China

    Z. Jiao & H. J. Lu

  49. KVI-CART, University of Groningen, Groningen, The Netherlands

    N. Kalantar-Nayestanaki, R. Kappert, M. Kavatsyuk, J. G. Messchendorp & V. Rodin

  50. Shanxi Normal University, Linfen, People’s Republic of China

    B. C. Ke, H. Li, L. Yang & J. J. Zhang

  51. Justus-Liebig-Universität Giessen, II. Physikalisches Institut, Giessen, Germany

    L. Koch, W. Kühn & J. S. Lange

  52. Qufu Normal University, Qufu, People’s Republic of China

    C. Li

  53. Liaoning Normal University, Dalian, People’s Republic of China

    C. H. Li, C. X. Yue & J. Zhao

  54. Beijing Institute of Petrochemical Technology, Beijing, People’s Republic of China

    Lei Li

  55. Lanzhou University, Lanzhou, People’s Republic of China

    P. R. Li, X. Liu & X. F. Wang

  56. Tsinghua University, Beijing, People’s Republic of China

    S. Y. Li, H. R. Qi & X. L. Zhu

  57. Sun Yat-Sen University, Guangzhou, People’s Republic of China

    Z. Y. Li, C. X. Lin, P. W. Luo, Z. Qian, J. Tang, Ying Wang, Z. Y. You, Z. Y. Yuan, H. H. Zhang & S. Zhang

  58. Sichuan University, Chengdu, People’s Republic of China

    Y. F. Liang & C. J. Tang

  59. Shanxi University, Taiyuan, People’s Republic of China

    F. H. Liu

  60. Henan University of Science and Technology, Luoyang, People’s Republic of China

    Huihui Liu

  61. Soochow University, Suzhou, People’s Republic of China

    S. Liu, D. C. Shan, X. P. Xu & X. Yan

  62. Zhejiang University, Hangzhou, People’s Republic of China

    M. X. Luo

  63. University of Oxford, Oxford, UK

    S. Malde, G. Wilkinson & Y. Zhang

  64. INFN Sezione di Perugia, Perugia, Italy

    A. Mangoni & S. Pacetti

  65. COMSATS University Islamabad, Lahore, Pakistan

    S. Nisar

  66. University of Perugia, Perugia, Italy

    S. Pacetti

  67. Guangxi Normal University, Guilin, People’s Republic of China

    L. Q. Qin, D. H. Wei & Y. X. Yang

  68. Hunan Normal University, Changsha, People’s Republic of China

    W. Shan

  69. Jilin University, Changchun, People’s Republic of China

    W. M. Song

  70. Near East University, Nicosia, North Cyprus, Mersin, Turkey

    I. Uman

  71. North China Electric Power University, Beijing, People’s Republic of China

    Y. D. Wang & X. D. Zhang

  72. Hangzhou Normal University, Hangzhou, People’s Republic of China

    Q. J. Xu

  73. Shanghai Jiao Tong University, Shanghai, People’s Republic of China

    H. J. Yang

  74. China Center of Advanced Science and Technology, Beijing, People’s Republic of China

    M. H. Ye

  75. Xinyang Normal University, Xinyang, People’s Republic of China

    J. L. Zhang

  76. University of Science and Technology Liaoning, Anshan, People’s Republic of China

    S. H. Zhu

Consortia

The BESIII Collaboration

  • M. Ablikim
  • , M. N. Achasov
  • , P. Adlarson
  • , S. Ahmed
  • , M. Albrecht
  • , R. Aliberti
  • , A. Amoroso
  • , Q. An
  • , Anita Lavania
  • , X. H. Bai
  • , Y. Bai
  • , O. Bakina
  • , R. B. Ferroli
  • , I. Balossino
  • , Y. Ban
  • , K. Begzsuren
  • , N. Berger
  • , M. Bertani
  • , D. Bettoni
  • , F. Bianchi
  • , J. Biernat
  • , J. Bloms
  • , A. Bortone
  • , I. Boyko
  • , R. A. Briere
  • , H. Cai
  • , X. Cai
  • , A. Calcaterra
  • , G. F. Cao
  • , N. Cao
  • , S. A. Cetin
  • , J. F. Chang
  • , W. L. Chang
  • , G. Chelkov
  • , D. Y. Chen
  • , G. Chen
  • , H. S. Chen
  • , M. L. Chen
  • , S. J. Chen
  • , X. R. Chen
  • , Y. B. Chen
  • , Z. J. Chen
  • , W. S. Cheng
  • , G. Cibinetto
  • , F. Cossio
  • , X. F. Cui
  • , H. L. Dai
  • , X. C. Dai
  • , A. Dbeyssi
  • , R. B. de Boer
  • , D. Dedovich
  • , Z. Y. Deng
  • , A. Denig
  • , I. Denysenko
  • , M. Destefanis
  • , F. De Mori
  • , Y. Ding
  • , C. Dong
  • , J. Dong
  • , L. Y. Dong
  • , M. Y. Dong
  • , X. Dong
  • , S. X. Du
  • , J. Fang
  • , S. S. Fang
  • , Y. Fang
  • , R. Farinelli
  • , L. Fava
  • , F. Feldbauer
  • , G. Felici
  • , C. Q. Feng
  • , M. Fritsch
  • , C. D. Fu
  • , Y. Fu
  • , Ya Gao
  • , Yang Gao
  • , Yuanning Gao
  • , Y. G. Gao
  • , I. Garzia
  • , E. M. Gersabeck
  • , A. Gilman
  • , K. Goetzen
  • , L. Gong
  • , W. X. Gong
  • , W. Gradl
  • , M. Greco
  • , L. M. Gu
  • , M. H. Gu
  • , S. Gu
  • , Y. T. Gu
  • , C. Y. Guan
  • , A. Q. Guo
  • , L. B. Guo
  • , R. P. Guo
  • , Y. P. Guo
  • , A. Guskov
  • , T. T. Han
  • , X. Q. Hao
  • , F. A. Harris
  • , K. L. He
  • , F. H. Heinsius
  • , C. H. Heinz
  • , T. Held
  • , Y. K. Heng
  • , C. Herold
  • , M. Himmelreich
  • , T. Holtmann
  • , Y. R. Hou
  • , Z. L. Hou
  • , H. M. Hu
  • , J. F. Hu
  • , T. Hu
  • , Y. Hu
  • , G. S. Huang
  • , L. Q. Huang
  • , X. T. Huang
  • , Y. P. Huang
  • , Z. Huang
  • , N. Huesken
  • , T. Hussain
  • , W. I. Andersson
  • , W. Imoehl
  • , M. Irshad
  • , S. Jaeger
  • , S. Janchiv
  • , Q. Ji
  • , Q. P. Ji
  • , X. B. Ji
  • , X. L. Ji
  • , H. B. Jiang
  • , X. S. Jiang
  • , X. Y. Jiang
  • , J. B. Jiao
  • , Z. Jiao
  • , S. Jin
  • , Y. Jin
  • , T. Johansson
  • , N. Kalantar-Nayestanaki
  • , X. S. Kang
  • , R. Kappert
  • , M. Kavatsyuk
  • , B. C. Ke
  • , I. K. Keshk
  • , A. Khoukaz
  • , P. Kiese
  • , R. Kiuchi
  • , R. Kliemt
  • , L. Koch
  • , O. B. Kolcu
  • , B. Kopf
  • , M. Kuemmel
  • , M. Kuessner
  • , A. Kupsc
  • , M. G. Kurth
  • , W. Kühn
  • , J. J. Lane
  • , J. S. Lange
  • , P. Larin
  • , L. Lavezzi
  • , Z. H. Lei
  • , H. Leithoff
  • , M. Lellmann
  • , T. Lenz
  • , C. Li
  • , C. H. Li
  • , Cheng Li
  • , D. M. Li
  • , F. Li
  • , G. Li
  • , H. Li
  • , H. Li
  • , H. B. Li
  • , H. J. Li
  • , H. N. Li
  • , J. L. Li
  • , J. Q. Li
  • , Ke Li
  • , L. K. Li
  • , Lei Li
  • , P. L. Li
  • , P. R. Li
  • , S. Y. Li
  • , W. D. Li
  • , W. G. Li
  • , X. H. Li
  • , X. L. Li
  • , Z. Y. Li
  • , H. Liang
  • , H. Liang
  • , Y. F. Liang
  • , Y. T. Liang
  • , L. Z. Liao
  • , J. Libby
  • , C. X. Lin
  • , B. J. Liu
  • , C. X. Liu
  • , D. Liu
  • , F. H. Liu
  • , Fang Liu
  • , Feng Liu
  • , H. B. Liu
  • , H. M. Liu
  • , Huanhuan Liu
  • , Huihui Liu
  • , J. B. Liu
  • , J. Y. Liu
  • , K. Liu
  • , K. Y. Liu
  • , Ke Liu
  • , L. Liu
  • , M. H. Liu
  • , Q. Liu
  • , S. B. Liu
  • , S. Liu
  • , T. Liu
  • , W. M. Liu
  • , X. Liu
  • , Y. B. Liu
  • , Z. A. Liu
  • , Z. Q. Liu
  • , X. C. Lou
  • , F. X. Lu
  • , H. J. Lu
  • , J. D. Lu
  • , J. G. Lu
  • , X. L. Lu
  • , Y. Lu
  • , Y. P. Lu
  • , C. L. Luo
  • , M. X. Luo
  • , P. W. Luo
  • , T. Luo
  • , X. L. Luo
  • , S. Lusso
  • , X. R. Lyu
  • , F. C. Ma
  • , H. L. Ma
  • , L. L. Ma
  • , M. M. Ma
  • , Q. M. Ma
  • , R. Q. Ma
  • , R. T. Ma
  • , X. N. Ma
  • , X. X. Ma
  • , X. Y. Ma
  • , F. E. Maas
  • , M. Maggiora
  • , S. Maldaner
  • , S. Malde
  • , Q. A. Malik
  • , A. Mangoni
  • , Y. J. Mao
  • , Z. P. Mao
  • , S. Marcello
  • , Z. X. Meng
  • , J. G. Messchendorp
  • , G. Mezzadri
  • , T. J. Min
  • , R. E. Mitchell
  • , X. H. Mo
  • , Y. J. Mo
  • , N. Y. Muchnoi
  • , H. Muramatsu
  • , S. Nakhoul
  • , Y. Nefedov
  • , F. Nerling
  • , I. B. Nikolaev
  • , Z. Ning
  • , S. Nisar
  • , S. L. Olsen
  • , Q. Ouyang
  • , S. Pacetti
  • , X. Pan
  • , Y. Pan
  • , A. Pathak
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  • , M. Pelizaeus
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  • , V. Prasad
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  • , H. R. Qi
  • , K. H. Qi
  • , M. Qi
  • , T. Y. Qi
  • , T. Y. Qi
  • , S. Qian
  • , W.-B. Qian
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  • , S. L. Yang
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  •  & J. H. Zou

Contributions

All the authors have contributed to this publication, being variously involved in the design and construction of the detectors, writing software, calibrating sub-systems, operating the detectors, acquiring data and analysing the processed data.

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The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Hyun-Chul Kim, Galina Pakhlova and Bogdan Wojtsekhowski for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–8, discussion and Tables 1–5.

Source data

Source Data Fig. 2

Source data for Fig. 2.

Source Data Fig. 3

Source data for Fig. 3.

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The BESIII Collaboration. Oscillating features in the electromagnetic structure of the neutron. Nat. Phys. 17, 1200–1204 (2021). https://doi.org/10.1038/s41567-021-01345-6

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