删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

Measurements of the center-of-mass energies of \begin{document}${{\boldsymbol e^+}{\boldsymbol e^

本站小编 Free考研考试/2022-01-01

M. Ablikim 1,
, M. N. Achasov 10,b,
, P. Adlarson 67,
, S. Ahmed 15,
, M. Albrecht 4,
, R. Aliberti 28,
, A. Amoroso 66,66,
, M. R. An 32,
, Q. An 63,49,
, X. H. Bai 57,
, Y. Bai 48,
, O. Bakina 29,
, R. Baldini Ferroli 23,
, I. Balossino 24,
, Y. Ban 38,h,
, K. Begzsuren 26,
, N. Berger 28,
, M. Bertani 23,
, D. Bettoni 24,
, F. Bianchi 66,66,
, J. Bloms 60,
, A. Bortone 66,66,
, I. Boyko 29,
, R. A. Briere 5,
, H. Cai 68,
, X. Cai 1,49,
, A. Calcaterra 23,
, G. F. Cao 1,54,
, N. Cao 1,54,
, S. A. Cetin 53,
, J. F. Chang 1,49,
, W. L. Chang 1,54,
, G. Chelkov 29,a,
, D. Y. Chen 6,
, G. Chen 1,
, H. S. Chen 1,54,
, M. L. Chen 1,49,
, S. J. Chen 35,
, X. R. Chen 25,
, Y. B. Chen 1,49,
, Z. J. Chen 20,i,
, W. S. Cheng 66,
, G. Cibinetto 24,
, F. Cossio 66,
, X. F. Cui 36,
, H. L. Dai 1,49,
, X. C. Dai 1,54,
, A. Dbeyssi 15,
, R. E. de Boer 4,
, D. Dedovich 29,
, Z. Y. Deng 1,
, A. Denig 28,
, I. Denysenko 29,
, M. Destefanis 66,66,
, F. De Mori 66,66,
, Y. Ding 33,
, C. Dong 36,
, J. Dong 1,49,
, L. Y. Dong 1,54,
, M. Y. Dong 1,49,54,
, X. Dong 68,
, S. X. Du 71,
, Y. L. Fan 68,
, J. Fang 1,49,
, S. S. Fang 1,54,
, Y. Fang 1,
, R. Farinelli 24,
, L. Fava 66,66,
, F. Feldbauer 4,
, G. Felici 23,
, C. Q. Feng 63,49,
, J. H. Feng 50,
, M. Fritsch 4,
, C. D. Fu 1,
, Y. Gao 64,
, Y. Gao 38,h,
, Y. Gao 63,49,
, Y. G. Gao 6,
, I. Garzia 24,24,
, P. T. Ge 68,
, C. Geng 50,
, E. M. Gersabeck 58,
, A Gilman 61,
, K. Goetzen 11,
, L. Gong 33,
, W. X. Gong 1,49,
, W. Gradl 28,
, M. Greco 66,66,
, L. M. Gu 35,
, M. H. Gu 1,49,
, Y. T. Gu 13,
, C. Y Guan 1,54,
, A. Q. Guo 22,
, L. B. Guo 34,
, R. P. Guo 40,
, Y. P. Guo 9,f,
, A. Guskov 29,a,
, T. T. Han 41,
, W. Y. Han 32,
, X. Q. Hao 16,
, F. A. Harris 56,
, K. L. He 1,54,
, F. H. Heinsius 4,
, C. H. Heinz 28,
, T. Held 4,
, Y. K. Heng 1,49,54,
, C. Herold 51,
, M. Himmelreich 11,d,
, T. Holtmann 4,
, G. Y. Hou 1,54,
, Y. R. Hou 54,
, Z. L. Hou 1,
, H. M. Hu 1,54,
, J. F. Hu 47,j,
, T. Hu 1,49,54,
, Y. Hu 1,
, G. S. Huang 63,49,
, L. Q. Huang 64,
, X. T. Huang 41,
, Y. P. Huang 1,
, Z. Huang 38,h,
, T. Hussain 65,
, N Husken 22,28,
, W. Ikegami Andersson 67,
, W. Imoehl 22,
, M. Irshad 63,49,
, S. Jaeger 4,
, S. Janchiv 26,
, Q. Ji 1,
, Q. P. Ji 16,
, X. B. Ji 1,54,
, X. L. Ji 1,49,
, Y. Y. Ji 41,
, H. B. Jiang 41,
, X. S. Jiang 1,49,54,
, J. B. Jiao 41,
, Z. Jiao 18,
, S. Jin 35,
, Y. Jin 57,
, M. Q. Jing 1,54,
, T. Johansson 67,
, N. Kalantar-Nayestanaki 55,
, X. S. Kang 33,
, R. Kappert 55,
, M. Kavatsyuk 55,
, B. C. Ke 43,1,
, I. K. Keshk 4,
, A. Khoukaz 60,
, P. Kiese 28,
, R. Kiuchi 1,
, R. Kliemt 11,
, L. Koch 30,
, O. B. Kolcu 53,m,
, B. Kopf 4,
, M. Kuemmel 4,
, M. Kuessner 4,
, A. Kupsc 67,
, M. G. Kurth 1,54,
, W. Kuhn 30,
, J. J. Lane 58,
, J. S. Lange 30,
, P. Larin 15,
, A. Lavania 21,
, L. Lavezzi 66,66,
, Z. H. Lei 63,49,
, H. Leithoff 28,
, M. Lellmann 28,
, T. Lenz 28,
, C. Li 39,
, C. H. Li 32,
, Cheng Li 63,49,
, D. M. Li 71,
, F. Li 1,49,
, G. Li 1,
, H. Li 63,49,
, H. Li 43,
, H. B. Li 1,54,
, H. J. Li 16,
, J. L. Li 41,
, J. Q. Li 4,
, J. S. Li 50,
, Ke Li 1,
, L. K. Li 1,
, Lei Li 3,
, P. R. Li 31,k,l,
, S. Y. Li 52,
, W. D. Li 1,54,
, W. G. Li 1,
, X. H. Li 63,49,
, X. L. Li 41,
, Xiaoyu Li 1,54,
, Z. Y. Li 50,
, H. Liang 1,54,
, H. Liang 63,49,
, H. Liang 27,
, Y. F. Liang 45,
, Y. T. Liang 25,
, G. R. Liao 12,
, L. Z. Liao 1,54,
, J. Libby 21,
, C. X. Lin 50,
, B. J. Liu 1,
, C. X. Liu 1,
, D. Liu 15,63,
, F. H. Liu 44,
, Fang Liu 1,
, Feng Liu 6,
, H. B. Liu 13,
, H. M. Liu 1,54,
, Huanhuan Liu 1,
, Huihui Liu 17,
, J. B. Liu 63,49,
, J. L. Liu 64,
, J. Y. Liu 1,54,
, K. Liu 1,
, K. Y. Liu 33,
, L. Liu 63,49,
, M. H. Liu 9,f,
, P. L. Liu 1,
, Q. Liu 54,
, Q. Liu 68,
, S. B. Liu 63,49,
, Shuai Liu 46,
, T. Liu 1,54,
, W. M. Liu 63,49,
, X. Liu 31,k,l,
, Y. Liu 31,k,l,
, Y. B. Liu 36,
, Z. A. Liu 1,49,54,
, Z. Q. Liu 41,
, X. C. Lou 1,49,54,
, F. X. Lu 50,
, H. J. Lu 18,
, J. D. Lu 1,54,
, J. G. Lu 1,49,
, X. L. Lu 1,
, Y. Lu 1,
, Y. P. Lu 1,49,
, C. L. Luo 34,
, M. X. Luo 70,
, P. W. Luo 50,
, T. Luo 9,f,
, X. L. Luo 1,49,
, X. R. Lyu 54,
, F. C. Ma 33,
, H. L. Ma 1,
, L. L. Ma 41,
, M. M. Ma 1,54,
, Q. M. Ma 1,
, R. Q. Ma 1,54,
, R. T. Ma 54,
, X. X. Ma 1,54,
, X. Y. Ma 1,49,
, F. E. Maas 15,
, M. Maggiora 66,66,
, S. Maldaner 4,
, S. Malde 61,
, Q. A. Malik 65,
, A. Mangoni 23,
, Y. J. Mao 38,h,
, Z. P. Mao 1,
, S. Marcello 66,66,
, Z. X. Meng 57,
, J. G. Messchendorp 55,
, G. Mezzadri 24,
, T. J. Min 35,
, R. E. Mitchell 22,
, X. H. Mo 1,49,54,
, N. Yu. Muchnoi 10,b,
, H. Muramatsu 59,
, S. Nakhoul 11,d,
, Y. Nefedov 29,
, F. Nerling 11,d,
, I. B. Nikolaev 10,b,
, Z. Ning 1,49,
, S. Nisar 8,g,
, S. L. Olsen 54,
, Q. Ouyang 1,49,54,
, S. Pacetti 23,23,
, X. Pan 9,f,
, Y. Pan 58,
, A. Pathak 1,
, A. Pathak 27,
, P. Patteri 23,
, M. Pelizaeus 4,
, H. P. Peng 63,49,
, K. Peters 11,d,
, J. Pettersson 67,
, J. L. Ping 34,
, R. G. Ping 1,54,
, S. Pogodin 29,
, R. Poling 59,
, V. Prasad 63,49,
, H. Qi 63,49,
, H. R. Qi 52,
, K. H. Qi 25,
, M. Qi 35,
, T. Y. Qi 9,
, S. Qian 1,49,
, W. B. Qian 54,
, Z. Qian 50,
, C. F. Qiao 54,
, L. Q. Qin 12,
, X. P. Qin 9,
, X. S. Qin 41,
, Z. H. Qin 1,49,
, J. F. Qiu 1,
, S. Q. Qu 36,
, K. H. Rashid 65,
, K. Ravindran 21,
, C. F. Redmer 28,
, A. Rivetti 66,
, V. Rodin 55,
, M. Rolo 66,
, G. Rong 1,54,
, Ch. Rosner 15,
, M. Rump 60,
, H. S. Sang 63,
, A. Sarantsev 29,c,
, Y. Schelhaas 28,
, C. Schnier 4,
, K. Schoenning 67,
, M. Scodeggio 24,24,
, D. C. Shan 46,
, W. Shan 19,
, X. Y. Shan 63,49,
, J. F. Shangguan 46,
, M. Shao 63,49,
, C. P. Shen 9,
, H. F. Shen 1,54,
, P. X. Shen 36,
, X. Y. Shen 1,54,
, H. C. Shi 63,49,
, R. S. Shi 1,54,
, X. Shi 1,49,
, X. D Shi 63,49,
, J. J. Song 41,
, W. M. Song 27,1,
, Y. X. Song 38,h,
, S. Sosio 66,66,
, S. Spataro 66,66,
, K. X. Su 68,
, P. P. Su 46,
, F. F. Sui 41,
, G. X. Sun 1,
, H. K. Sun 1,
, J. F. Sun 16,
, L. Sun 68,
, S. S. Sun 1,54,
, T. Sun 1,54,
, W. Y. Sun 34,
, W. Y. Sun 27,
, X Sun 20,i,
, Y. J. Sun 63,49,
, Y. K. Sun 63,49,
, Y. Z. Sun 1,
, Z. T. Sun 1,
, Y. H. Tan 68,
, Y. X. Tan 63,49,
, C. J. Tang 45,
, G. Y. Tang 1,
, J. Tang 50,
, J. X. Teng 63,49,
, V. Thoren 67,
, W. H. Tian 43,
, Y. T. Tian 25,
, I. Uman 53,
, B. Wang 1,
, C. W. Wang 35,
, D. Y. Wang 38,h,
, H. J. Wang 31,k,l,
, H. P. Wang 1,54,
, K. Wang 1,49,
, L. L. Wang 1,
, M. Wang 41,
, M. Z. Wang 38,h,
, Meng Wang 1,54,
, W. Wang 50,
, W. H. Wang 68,
, W. P. Wang 63,49,
, X. Wang 38,h,
, X. F. Wang 31,k,l,
, X. L. Wang 9,f,
, Y. Wang 50,
, Y. Wang 63,49,
, Y. D. Wang 37,
, Y. F. Wang 1,49,54,
, Y. Q. Wang 1,
, Y. Y. Wang 31,k,l,
, Z. Wang 1,49,
, Z. Y. Wang 1,
, Ziyi Wang 54,
, Zongyuan Wang 1,54,
, D. H. Wei 12,
, F. Weidner 60,
, S. P. Wen 1,
, D. J. White 58,
, U. Wiedner 4,
, G. Wilkinson 61,
, M. Wolke 67,
, L. Wollenberg 4,
, J. F. Wu 1,54,
, L. H. Wu 1,
, L. J. Wu 1,54,
, X. Wu 9,f,
, Z. Wu 1,49,
, L. Xia 63,49,
, H. Xiao 9,f,
, S. Y. Xiao 1,
, Z. J. Xiao 34,
, X. H. Xie 38,h,
, Y. G. Xie 1,49,
, Y. H. Xie 6,
, T. Y. Xing 1,54,
, G. F. Xu 1,
, Q. J. Xu 14,
, W. Xu 1,54,
, X. P. Xu 46,
, Y. C. Xu 54,
, F. Yan 9,f,
, L. Yan 9,f,
, W. B. Yan 63,49,
, W. C. Yan 71,
, Xu Yan 46,
, H. J. Yang 42,e,
, H. X. Yang 1,
, L. Yang 43,
, S. L. Yang 54,
, Y. X. Yang 12,
, Yifan Yang 1,54,
, Zhi Yang 25,
, M. Ye 1,49,
, M. H. Ye 7,
, J. H. Yin 1,
, Z. Y. You 50,
, B. X. Yu 1,49,54,
, C. X. Yu 36,
, G. Yu 1,54,
, J. S. Yu 20,i,
, T. Yu 64,
, C. Z. Yuan 1,54,
, L. Yuan 2,
, X. Q. Yuan 38,h,
, Y. Yuan 1,
, Z. Y. Yuan 50,
, C. X. Yue 32,
, A. A. Zafar 65,
, X. Zeng Zeng 6,
, Y. Zeng 20,i,
, A. Q. Zhang 1,
, B. X. Zhang 1,
, Guangyi Zhang 16,
, H. Zhang 63,
, H. H. Zhang 27,
, H. H. Zhang 50,
, H. Y. Zhang 1,49,
, J. J. Zhang 43,
, J. L. Zhang 69,
, J. Q. Zhang 34,
, J. W. Zhang 1,49,54,
, J. Y. Zhang 1,
, J. Z. Zhang 1,54,
, Jianyu Zhang 1,54,
, Jiawei Zhang 1,54,
, L. M. Zhang 52,
, L. Q. Zhang 50,
, Lei Zhang 35,
, S. Zhang 50,
, S. F. Zhang 35,
, Shulei Zhang 20,i,
, X. D. Zhang 37,
, X. Y. Zhang 41,
, Y. Zhang 61,
, Y. T. Zhang 71,
, Y. H. Zhang 1,49,
, Yan Zhang 63,49,
, Yao Zhang 1,
, Z. Y. Zhang 68,
, G. Zhao 1,
, J. Zhao 32,
, J. Y. Zhao 1,54,
, J. Z. Zhao 1,49,
, Lei Zhao 63,49,
, Ling Zhao 1,
, M. G. Zhao 36,
, Q. Zhao 1,
, S. J. Zhao 71,
, Y. B. Zhao 1,49,
, Y. X. Zhao 25,
, Z. G. Zhao 63,49,
, A. Zhemchugov 29,a,
, B. Zheng 64,
, J. P. Zheng 1,49,
, Y. H. Zheng 54,
, B. Zhong 34,
, C. Zhong 64,
, L. P. Zhou 1,54,
, Q. Zhou 1,54,
, X. Zhou 68,
, X. K. Zhou 54,
, X. R. Zhou 63,49,
, X. Y. Zhou 32,
, A. N. Zhu 1,54,
, J. Zhu 36,
, K. Zhu 1,
, K. J. Zhu 1,49,54,
, S. H. Zhu 62,
, T. J. Zhu 69,
, W. J. Zhu 9,f,
, W. J. Zhu 36,
, Y. C. Zhu 63,49,
, Z. A. Zhu 1,54,
, B. S. Zou 1,
, J. H. Zou 1,
, (BESIII Collaboration)
, 1.Institute of High Energy Physics, Beijing 100049, China
2.Beihang University, Beijing 100191, China
3.Beijing Institute of Petrochemical Technology, Beijing 102617, China
4.Bochum Ruhr-University, D-44780 Bochum, Germany
5.Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6.Central China Normal University, Wuhan 430079, China
7.China Center of Advanced Science and Technology, Beijing 100190, China
8.COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
9.Fudan University, Shanghai 200443, China
10.G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
11.GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
12.Guangxi Normal University, Guilin 541004, China
13.Guangxi University, Nanning 530004, China
14.Hangzhou Normal University, Hangzhou 310036, China
15.Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
16.Henan Normal University, Xinxiang 453007, China
17.Henan University of Science and Technology, Luoyang 471003, China
18.Huangshan College, Huangshan 245000, China
19.Hunan Normal University, Changsha 410081, China
20.Hunan University, Changsha 410082, China
21.Indian Institute of Technology Madras, Chennai 600036, India
22.Indiana University, Bloomington, Indiana 47405, USA
23.INFN Laboratori Nazionali di Frascati, (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN Sezione di Perugia, I-06100, Perugia, Italy; (C)University of Perugia, I-06100, Perugia, Italy
24.INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
25.Institute of Modern Physics, Lanzhou 730000, China
26.Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia
27.Jilin University, Changchun 130012, China
28.Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
29.Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
30.Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
31.Lanzhou University, Lanzhou 730000, China
32.Liaoning Normal University, Dalian 116029, China
33.Liaoning University, Shenyang 110036, China
34.Nanjing Normal University, Nanjing 210023, China
35.Nanjing University, Nanjing 210093, China
36.Nankai University, Tianjin 300071, China
37.North China Electric Power University, Beijing 102206, China
38.Peking University, Beijing 100871, China
39.Qufu Normal University, Qufu 273165, China
40.Shandong Normal University, Jinan 250014, China
41.Shandong University, Jinan 250100, China
42.Shanghai Jiao Tong University, Shanghai 200240, China
43.Shanxi Normal University, Linfen 041004, China
44.Shanxi University, Taiyuan 030006, China
45.Sichuan University, Chengdu 610064, China
46.Soochow University, Suzhou 215006, China
47.South China Normal University, Guangzhou 510006, China
48.Southeast University, Nanjing 211100, China
49.State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, China
50.Sun Yat-Sen University, Guangzhou 510275, China
51.Suranaree University of Technology, University Avenue 111, Nakhon Ratchasima 30000, Thailand
52.Tsinghua University, Beijing 100084, China
53.Turkish Accelerator Center Particle Factory Group, (A)Istanbul Bilgi University, HEP Res. Cent., 34060 Eyup, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey
54.University of Chinese Academy of Sciences, Beijing 100049, China
55.University of Groningen, NL-9747 AA Groningen, The Netherlands
56.University of Hawaii, Honolulu, Hawaii 96822, USA
57.University of Jinan, Jinan 250022, China
58.University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
59.University of Minnesota, Minneapolis, Minnesota 55455, USA
60.University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany
61.University of Oxford, Keble Rd, Oxford, UK OX13RH
62.University of Science and Technology Liaoning, Anshan 114051, China
63.University of Science and Technology of China, Hefei 230026, China
64.University of South China, Hengyang 421001, China
65.University of the Punjab, Lahore-54590, Pakistan
66.University of Turin and INFN, (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
67.Uppsala University, Box 516, SE-75120 Uppsala, Sweden
68.Wuhan University, Wuhan 430072, China
69.Xinyang Normal University, Xinyang 464000, China
70.Zhejiang University, Hangzhou 310027, China
71.Zhengzhou University, Zhengzhou 450001, China
a.Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
b.Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
c.Also at the NRC "Kurchatov Institute", PNPI, 188300, Gatchina, Russia
d.Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany
e.Also at 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 200240, China
f.Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, China
g.Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA
h.Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
i.Also at School of Physics and Electronics, Hunan University, Changsha 410082, China
j.Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China
k.Also at Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
l.Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, China
m.Currently at Istinye University, 34010 Istanbul, Turkey
Received Date:2020-12-29
Available Online:2021-10-15
Abstract:During the 2016-17 and 2018-19 running periods, the BESIII experiment collected 7.5 fb$ ^{-1} $ of $ e^+e^- $ collision data at center-of-mass energies ranging from 4.13 to 4.44 GeV. These data samples are primarily used for the study of excited charmonium and charmoniumlike states. By analyzing the di-muon process $e^+e^- \to $$ (\gamma_{\rm ISR/FSR}) \mu^+\mu^-$, we measure the center-of-mass energies of the data samples with a precision of 0.6 MeV. Through a run-by-run study, we find that the center-of-mass energies were stable throughout most of the data-collection period.

HTML

--> --> -->
I.INTRODUCTION
The BESIII experiment [1] was designed to study physics in the $ \tau $-charm energy region (2.0 – 4.9 GeV) [2] through $ e^+e^- $ annihilations produced by the BEPCII storage ring [3]. Since it started running in 2008, a variety of data samples have been collected at different center-of-mass (CM) energies for the study of light hadron spectroscopy, charmonium and charmoniumlike states (also called ${XYZ}$ states), charm physics, $ \tau $ physics, various QCD-related studies, and the search for new physics beyond the standard model [4].
The Beam Energy Measurement System (BEMS) [5] was designed to precisely measure BESIII CM energies ($ E_{{\rm{cm}}} $) using a method based on Compton back-scattered photons. However, its capability at high energy ($ E_{{\rm{cm}}} $ above 4 GeV) is degraded by its detection efficiency and limited calibration sources for high-energy gamma rays. Therefore, an alternative algorithm was developed to measure the $ E_{{\rm{cm}}} $ for data samples above 4 GeV. This method uses the well-understood QED process $e^+e^-\to $$ (\gamma_{\rm ISR/FSR}) \mu^+\mu^-$ (the di-muon process), where $ \gamma_{\rm ISR/FSR} $ is a radiative photon due to initial state radiation (ISR) and/or final state radiation (FSR). Using this method, a precision of 0.8 MeV was previously achieved for data from 2011 to 2014 [6].
In this paper, we present the $ E_{\rm cm} $ measurement for the ${{XYZ}}$ data samples taken at BESIII from 2017 to 2019. The method used in Ref. [6] is followed, but the precision of the momentum calibration is improved, and the $ E_{{\rm{cm}}} $ is measured with an uncertainty of 0.6 MeV.
Using the selected di-muon events, $ e^+e^-\to (\gamma_{\rm ISR/FSR}) $$ \mu^+\mu^- $, we determine $ E_{{\rm{cm}}} $ using
$ E_{{\rm{cm}}} = (M_{\rm p}( \mu^+\mu^-) + \Delta M_{\rm ISR/FSR} + \Delta M_{\rm cal})\times c^{2},$
(1)
where $ M_{\rm p}( \mu^+\mu^-) $ is the peak position of the $ \mu^+\mu^- $ invariant mass of selected di-muon events; $ \Delta M_{\rm ISR/FSR} $ is the mass shift due to the emission of ISR or FSR photons, estimated from Monte Carlo (MC) simulation of the di-muon process by turning the ISR/FSR processes on and off in MC generation; and $ \Delta M_{\rm cal} $ is the correction introduced by the momentum calibration of the $ \mu^+\mu^- $ tracks, obtained from an analysis of the process $ e^+e^-\to \gamma_{\rm ISR} J/\psi $.
II.THE BESIII DETECTOR AND DATA SETS
The BESIII detector is described in detail in Ref. [1]. The cylindrical core of the detector covers 93% of the full solid angle and consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), all of which are enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identification modules interleaved with steel. The charged-particle momentum resolution at $ 1\; {\rm GeV}/c $ is $ 0.5% $, and the ${\rm d}E/{\rm d}x$ resolution is $6\%$ for electrons from Bhabha scattering. The EMC measures photon energies with a resolution of $2.5\%$ ($5\%$) at $ 1 $ GeV in the barrel (end cap) region. The time resolution in the TOF barrel region is 68 ps, and that in the end cap region is 60 ps [7-9].
The data samples analyzed in this work are listed in Table 1. They include 16 different CM energies from 4.13 to 4.44 GeV and were collected in two running years: from December 2016 to May 2017 (labelled as "2017XYZ" hereafter, the integrated luminosities are measured using the Bhabha events in Ref. [10]) and from February 2019 to June 2019 (labelled as "2019XYZ" hereafter, the integrated luminosities are estimated by using online monitoring information). The column "Sample" lists the nominal CM energy in MeV used during online data collecting. The true CM energy is generally within a few MeV of the nominal value. Run numbers are used to divide the data into subsamples. Other columns, such as $ \mathcal{L} $ ($ \rm{pb^{-1}} $), are illustrated below.
Sample Run Number $ {\cal{L}} $/$ \rm{pb^{-1}} $ $ M^{\rm cor}(J/\psi) $ $ M_{\rm p}(\mu^{+}\mu^{-}) $ $ E_{\rm cm} $/MeV
4130$ ^2 $ 59163-59573 400 $ 3100.55\pm0.30 $ $ 4130.23\pm0.05 $ $ 4128.78\pm0.05\pm0.36 $
4160$ ^2 $ 59574-59896 400 $ 3100.18\pm0.29 $ $ 4158.89\pm0.05 $ $ 4157.83\pm0.05\pm0.34 $
4190$ ^1 $ 47543-48170 $ 526.70\pm2.16 $ $ 3097.89\pm0.28 $ $ 4187.90\pm0.05 $ $ 4189.12\pm0.05\pm0.34 $
4200$ ^1 $ 48172-48713 $ 526.60\pm2.05 $ $ 3098.17\pm0.27 $ $ 4198.20\pm0.05 $ $ 4199.15\pm0.05\pm0.34 $
4210$ ^1 $ 48714-49239 $ 517.10\pm1.81 $ $ 3097.41\pm0.29 $ $ 4207.67\pm0.06 $ $ 4209.39\pm0.06\pm0.34 $
4220$ ^1 $ 49270-49787 $ 514.60\pm1.80 $ $ 3097.51\pm0.26 $ $ 4217.31\pm0.05 $ $ 4218.93\pm0.06\pm0.32 $
4237$ ^1 $ 49788-50254 $ 530.30\pm2.39 $ $ 3097.36\pm0.24 $ $ 4233.99\pm0.04 $ $ 4235.77\pm0.04\pm0.30 $
4246$ ^1 $ 50255-50793 $ 538.10\pm2.69 $ $ 3097.35\pm0.24 $ $ 4242.18\pm0.04 $ $ 4243.97\pm0.04\pm0.30 $
4270$ ^1 $ 50796-51302 $ 531.10\pm3.13 $ $ 3098.09\pm0.26 $ $ 4265.74\pm0.04 $ $ 4266.81\pm0.04\pm0.32 $
4280$ ^1 $ 51305-51498 $ 175.70\pm0.97 $ $ 3097.55\pm0.48 $ $ 4277.73\pm0.04 $ $ 4277.78\pm0.11\pm0.52 $
4290$ ^2 $ 59902-60363 500 $ 3100.07\pm0.28 $ $ 4289.33\pm0.06 $ $ 4288.43\pm0.06\pm0.34 $
4315$ ^2 $ 60364-60805 500 $ 3099.97\pm0.30 $ $ 4313.46\pm0.06 $ $ 4312.68\pm0.06\pm0.35 $
4340$ ^2 $ 60808-61242 500 $ 3099.71\pm0.29 $ $ 4338.45\pm0.06 $ $ 4337.93\pm0.06\pm0.35 $
4380$ ^2 $ 61249-61762 500 $ 3099.68\pm0.30 $ $ 4378.35\pm0.06 $ $ 4377.88\pm0.06\pm0.35 $
4400$ ^2 $ 61763-62285 500 $ 3100.61\pm0.31 $ $ 4398.21\pm0.06 $ $ 4396.83\pm0.06\pm0.36 $
4440$ ^2 $ 62286-62823 570 $ 3099.73\pm0.29 $ $ 4437.59\pm0.06 $ $ 4437.10\pm0.06\pm0.35 $


Table1.Summary of the data samples, including run numbers, integrated luminosity $ {\cal L} $ [10], the measured $ J/\psi $ mass after FSR correction $ M^{\rm cor}( J/\psi) $ (in MeV/$ c^2 $), $ M_{\rm p}( \mu^+\mu^-) $ (in MeV/$ c^2 $), and $ E_{{\rm{cm}}} $. Superscripts represent data from different periods: "1" denotes 2017XYZ data, and "2" denotes 2019XYZ data. The first uncertainties are statistical and the second systematic.

A GEANT4 [11] based detector simulation package is developed to model the detector response for MC events. In our analysis, the di-muon sample is generated with BABAYAGA3.5 [12], and the $ e^+e^-\to \gamma_{\rm ISR}J/\psi $ sample is generated with KKMC [13, 14]. One million events are generated for each process at each CM energy.
III.EVENT SELECTION AND MEASUREMENT OF $ M_{p}( \mu^+\mu^-) $
The di-muon process $ e^+e^-\to (\gamma_{\rm ISR/FSR}) \mu^+\mu^- $ is selected by requiring two oppositely charged tracks in the detector, each positively identified as a muon. Both charged tracks are reconstructed from hits in the MDC within the polar angle range $ |\cos\theta|<0.8 $ and their extrapolations to the interaction point (IP) within 10 cm along the beam direction and 1 cm in the plane perpendicular to the beam. The energy deposition in the EMC for each charged track is required to be less than 0.4 GeV to suppress backgrounds from radiative Bhabha events.
The sample after these selections includes di-muon events with no photon emission or with very low-energy radiative photons, ISR $ J/\psi $ with $ J/\psi\to \mu^+\mu^- $, and ISR $ \mu^+\mu^- $ events with a smooth $ \mu^+\mu^- $ invariant mass ($ M( \mu^+\mu^-) $) distribution. The events in the $ J/\psi $ mass region are used for track momentum calibration and those with high invariant mass are used to measure the $ E_{{\rm{cm}}} $ after additional selection criteria are applied, as described below.
To suppress di-muon events with high energy radiative photons, a requirement on the cosine of the opening angle between the two tracks, $ \cos\theta_{ \mu^+\mu^-} < -0.9997 $ is applied. To further remove cosmic ray events, the TOF time difference between the two tracks is required to be $ |\Delta t| < 2 $ ns. The background contribution after these selection criteria is less than 0.1% compared with the signal and is therefore neglected in the following analysis.
The $ M( \mu^+\mu^-) $ distribution for the 4190 data sample is shown in Fig. 1 as an example. The distributions of the other samples are very similar. The distribution is a Gaussian due to the momentum resolution of the $ \mu^+\mu^- $, though it is distorted by ISR and FSR effects, producing a tail on the left side of the peak. The central part of the distribution can be approximated with a Gaussian function. We measure the peak position of the distribution ($ M_{\rm p}( \mu^+\mu^-) $) by fitting it with a Gaussian function in the range of $ (-1\sigma,\; +1.5\sigma) $ around the peak, where $ \sigma $ is the standard deviation of the Gaussian. If the goodness of the fit, $ \chi^2/ndf>2.0 $ ($ ndf $ is the number of degrees of freedom of the fit), the fit range is slightly reduced until $ \chi^2/ndf<2.0 $, guaranteeing a good fit quality. The fit result for the 4190 data sample is shown in Fig. 1. The values of $ M_{\rm p}( \mu^+\mu^-) $ for the other data samples are obtained using a similar method and are listed in Table 1.
Figure1. (color?online)?The $ \mu^+\mu^- $ invariant mass distribution and the fit result of the 4190 sample. Dots with error bars are data, and the solid red curve is the fit.

To examine the stability of the $ E_{{\rm{cm}}} $ over the data-taking period for each data sample, the fit procedure is repeated for each run of the data sample. The measured peak values of the $ \mu^+\mu^- $ invariant mass distribution versus run number for all 16 samples are shown in Fig. 2. There are small jumps of less than 1 MeV in the 4130, 4200, 4210, 4246, 4380, and 4400 samples. Before and after the jumps, the energy is stable. We fit each stable part of the distribution with a linear function and Table 2 summarizes the average, $ M^{\rm ave}( \mu^+\mu^-) $, for each period of time. The deviation of $ M^{\rm ave}( \mu^+\mu^-) $ from the peak position obtained in the full data sample is considered as one source of systematic uncertainty.
Figure2. (color?online)?Measured run-by-run values for the $ M_{\rm p}( \mu^+\mu^-) $ of di-muon events in each data sample. The red solid lines show the fit results for the data samples of each stable period of time. The green dotted lines are the fit results of the entire sample when there is an energy jump.

Sample Run Number $ M^{\rm ave}( \mu^+\mu^-) $ Run Number $ M^{\rm ave}( \mu^+\mu^-) $
4130 59163-59190 $ 4131.44\pm0.36 $ 59191-59573 $ 4130.02\pm0.05 $
4160 59574-59896 $ 4158.49\pm0.05 $
4190 47543-48170 $ 4187.52\pm0.06 $
4200 48172-48290 $ 4197.14\pm0.12 $ 48291-48713 $ 4198.07\pm0.06 $
4210 48174-49065 $ 4206.75\pm0.06 $ 49066-49239 $ 4207.49\pm0.09 $
4220 49270-49787 $ 4216.33\pm0.05 $
4237 49788-50254 $ 4233.21\pm0.04 $
4246 50255-50520 $ 4241.01\pm0.08 $ 50521-50793 $ 4241.55\pm0.05 $
4270 50796-51302 $ 4265.20\pm0.06 $
4280 51305-51498 $ 4275.34\pm0.09 $
4290 59902-60363 $ 4288.91\pm0.05 $
4315 60364-60805 $ 4312.79\pm0.04 $
4340 60808-61242 $ 4337.93\pm0.05 $
4380 61249-61400 $ 4378.23\pm0.09 $ 61401-61762 $ 4377.61\pm0.06 $
4400 61763-61980 $ 4397.51\pm0.08 $ 61981-62285 $ 4398.06\pm0.07 $
4440 62286-62823 $ 4437.01\pm0.05 $


Table2.Average value $ M^{\rm ave}( \mu^+\mu^-) $ (in MeV/$ c^{2} $) for each stable data-taking period within each data sample.

IV.MOMENTUM CALIBRATION WITH ISR $\boldsymbol{J/\psi}$ SIGNAL
The momentum measurement of the muon tracks is validated with $ J/\psi \to \mu^+\mu^- $ candidates produced via the process $ e^+e^-\to \gamma_{\rm ISR} J/\psi $ selected in the previous section. The distribution of $ M( \mu^+\mu^-) $ for each sample is fitted with a crystal-ball function [15] for the $ J/\psi $ signal and a linear function to model the background from continuum production of $ e^+e^-\to \gamma \mu^+\mu^- $. Figure 3(a) shows the fit result for the 4190 data sample as an example. The peak position of the $ J/\psi $ signal, $ M^{\rm obs}(J/\psi) $, is used to calibrate the momentum measurement of the muon tracks.
Figure3. (color online) (a) Fit to the $ M(\mu^{+}\mu^{-}) $ distribution in the $ J/\psi $ signal region for the 4190 data sample. Black dots with error bars are data, the red curve shows the fit result, the blue curve indicates the signal, and the green dashed line indicates the background. (b) The difference between $ M^{\rm cor}(J/\psi) $ and the world average mass of $ J/\psi $ [16], $ \Delta M^{\rm cor}(J/\psi) $ for each data sample.

Due to FSR, $ J/\psi\to \mu^+\mu^-\gamma_{\rm FSR} $, the measured $ M^{\rm obs}(J/\psi) $ is slightly lower than the world average $ J/\psi $ mass ($ m_{ J/\psi} $) given by the PDG [16]. The mass shift due to the FSR photon(s) $ \Delta M^{\gamma J/\psi}_{\rm FSR} $ of the process $ e^+e^-\to \gamma_{\rm ISR}J/\psi $ at each $ E_{{\rm{cm}}} $ is obtained by using the generator PHOTOS [17] with FSR turned on or off. The shift is around 0.3 MeV/$ c^2 $ with minimal dependence on the CM energy of the data sample.
Comparing the $ M^{\rm cor}(J/\psi) = M^{\rm obs}(J/\psi)+\Delta M^{\gamma J/\psi}_{\rm FSR} $ (as shown in Table 1) with the world-average $ J/\psi $ mass value $ m_{ J/\psi} $ in the Particle Data Book (PDG), we measure the bias in the $ J/\psi $ mass measurement ($ \Delta M^{\rm cor}(J/\psi) $) due to the muon track momentum calibration, as shown in Fig. 3(b). It can be seen that the bias in the $ J/\psi $ invariant mass is stable throughout one running year, but is quite different in the 2017XYZ and 2019XYZ samples. This may indicate that the calibrations in these two periods of time have significant differences.
Through MC simulation we find that the bias in the $ M_{\rm p}( \mu^+\mu^-) $ measurement depends linearly on $ M( \mu^+\mu^-) $ (see Fig. 4), and there exists $ E_{{\rm{cm}}} = M( \mu^+\mu^-) $ with no radiation, so the correction to the $ M_{\rm p}( \mu^+\mu^-) $ due to calibration is expressed as
Figure4. (color?online)?(a) The distribution of $ \Delta M^{\rm cal}(J/\psi) $ of different $ E_{\rm cm} $ for the MC simulation of $ \gamma_{\rm ISR}J\psi $ process without FSR. The average value is $ 1.67\pm0.01 $ MeV/$ c^{2} $. (b) $ \Delta M $ is the difference between the reconstructed and generated center-of-mass energy ($ E_{\rm cm} $) reported as a function of $ M( \mu^+\mu^-) $ ($ M( \mu^+\mu^-) $ is equal to$ E_{\rm cm} $ for events without radiation). The di-muon events are generated without radiation emission. The bias at $ J/\psi $ mass given from (b) is $ 1.67\pm0.24 $ MeV/$ c^{2} $, which is consistent with the result provided in (a). The linear fit to the points provides the dependence of the bias on $ M_{\rm p}( \mu^+\mu^-) $ (slope $ k $) due to track momentum calibration, which is assumed to be the same for data and simulation.

$ \Delta M_{\rm cal} = -(k \times ( E_{{\rm{cm}}} - m_{ J/\psi}) + \Delta M^{\rm cor}(J/\psi)) (\rm{MeV}), $
(2)
where the slopes $ k = (7.11\pm 0.50)\times $$ 10^{-4} $ and $(7.04\pm $$ 0.57)\times 10^{-4}$ correspond to the 2017XYZ and 2019XYZ samples, respectively. They agree within the statistical uncertainties of the MC samples, which indicates that the momentum dependence of the calibration constants is very similar in the 2017XYZ and 2019XYZ samples.
V.THE MASS SHIFT $ \Delta M_{\rm ISR/FSR} $
$ E_{{\rm{cm}}} $ of the initial $ e^+e^- $ pair is measured via the di-muon process $ e^+e^-\to (\gamma_{\rm ISR/FSR}) \mu^+\mu^- $. However, due to the emission of radiative photons, the invariant mass of the $ \mu^+\mu^- $ pair is smaller than $ E_{{\rm{cm}}} $ by $ \Delta M_{\rm ISR/FSR} $. This correction is estimated with MC simulation using BABAYAGA3.5 [12].
We generate one million di-muon events for each sample with ISR/FSR turned on or off, apply the same event selection criteria to the di-muon events as in the data (described in Sec. III), and fit the distributions of $ M( \mu^+\mu^-) $ from the samples with ISR/FSR on and off with a Gaussian function in the range around the peak (same as in Sec. III). The difference in $ M_{\rm p}( \mu^+\mu^-) $ is taken as the mass shift $ \Delta M_{\rm ISR/FSR} $ caused by ISR or FSR. $ \Delta M_{\rm ISR/FSR} $ versus $ E_{{\rm{cm}}} $ shown in Fig. 5 indicates that the ISR/FSR effect depends linearly on $ E_{{\rm{cm}}} $. The data are fitted with a linear function to provide an improved precision measurement of the correction. From the fit,
Figure5. (color online) Mass shift $ \Delta M_{\rm ISR/FSR} $ versus CM energy for $ e^+e^-\to (\gamma_{\rm ISR/FSR}) \mu^+\mu^- $ MC samples. The solid red line is the linear fit.

$ \Delta M_{\rm ISR/FSR} = ( 1.17\pm 0.05)\times 10^{-3}\times E_{{\rm{cm}}} + (-1.91\pm 0.20) (\rm{MeV}) $
(3)
with a correlation factor of $ -0.99 $ between the slope and the intercept, and the goodness of the fit is $ \chi^2/ndf = $$ 6.2/12 $.
VI.SYSTEMATIC UNCERTAINTIES
The systematic uncertainty in $ E_{{\rm{cm}}} $ is from the momentum calibration of $ \mu^{\pm} $, the estimation of the mass shift $ \Delta M_{\rm ISR/FSR} $ due to ISR/FSR, the open angle cut of $ \cos\theta_{ \mu^+\mu^-} $, the corresponding fit procedure, and the generator. The bias of the momentum measurement of $ \mu^{\pm} $ and the estimation of the mass shift $ \Delta M_{\rm ISR/FSR} $ due to ISR/FSR both have a linear relationship with $ E_{{\rm{cm}}} $, and the uncertainty produced by the uncertainty of the parameters is regarded as the systematic uncertainties.
To reduce the influence of the events with high radiation, we required $ \cos\theta_{ \mu^+\mu^-}<-0.9997 $. Different cut values will give different $ M_{\rm p}( \mu^+\mu^-) $ and corresponding radiation correction values $ \Delta M_{\rm ISR/FSR} $. The changes in these two parts cancel each other out. The largest difference comes from the data between $ -0.9997 $ and $ -0.99975 $, and is $ 0.12\pm 0.02 $ MeV. We take 0.14 MeV as the uncertainty due to this requirement.
$ M_{\rm p}( \mu^+\mu^-) $ is measured by fitting with a Gaussian function in the range of $ (-1\sigma,\; +1.5\sigma) $ around the peak with fit quality $ \chi^2/ndf < 2.0 $. If the fit range is smaller than the standard range, the difference in the fit results is less than 0.1 MeV. We take this as the uncertainty due to the fit method.
The contribution to the systematic uncertainty of the ISR/FSR correction from the generator is negligibly small, as claimed in Ref. [12]. The uncertainties from other sources, such as background and other event selection criteria, are negligible.
Assuming all sources of systematic uncertainty are independent, the total systematic uncertainty is obtained by adding all the items in quadrature, which is listed in Table 1. The uncertainty is smaller than 0.6 MeV for all data samples.
VII.SUMMARY
The center-of-mass energies, $ E_{{\rm{cm}}} $, of the data samples are obtained using Eq. (1), with the correction factors in Eqs. (2) and (3). The final results are listed in Table 1, including the statistical and systematic uncertainties. The corresponding statistical uncertainty is very small, and the systematic uncertainty is less than 0.36 MeV everywhere, with the exception of the point at 4280 MeV, where the error on $ \Delta M^{\rm cor} $ is much larger than the rest. The stability of $ E_{{\rm{cm}}} $ over time for the data samples is also examined.
The results presented in this work are essential for the discovery of new states and the investigation of the transitions of charmonium and charmoniumlike states [18] using the BESIII data. Some of the analyses have been presented in Refs. [19-24].
ACKNOWLEDGEMENTS
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support.
相关话题/Measurements center energies