# Search for $e^{+}e^{-}\to K^{+}K^{-}\psi(3770)$ at center-of-mass energies
from 4.84 to 4.95 GeV

M. Ablikim1, M. N. Achasov4,b, P. Adlarson75, O. Afedulidis3, X. C. Ai80, R.
Aliberti35, A. Amoroso74A,74C, Q. An71,58, Y. Bai57, O. Bakina36, I.
Balossino29A, Y. Ban46,g, H.-R. Bao63, V. Batozskaya1,44, K. Begzsuren32, N.
Berger35, M. Berlowski44, M. Bertani28A, D. Bettoni29A, F. Bianchi74A,74C, E.
Bianco74A,74C, A. Bortone74A,74C, I. Boyko36, R. A. Briere5, A. Brueggemann68,
H. Cai76, X. Cai1,58, A. Calcaterra28A, G. F. Cao1,63, N. Cao1,63, S. A.
Cetin62A, J. F. Chang1,58, W. L. Chang1,63, G. R. Che43, G. Chelkov36,a, C.
Chen43, C. H. Chen9, Chao Chen55, G. Chen1, H. S. Chen1,63, M. L. Chen1,58,63,
S. J. Chen42, S. L. Chen45, S. M. Chen61, T. Chen1,63, X. R. Chen31,63, X. T.
Chen1,63, Y. B. Chen1,58, Y. Q. Chen34, Z. J. Chen25,h, Z. Y. Chen1,63, S. K.
Choi10A, X. Chu43, G. Cibinetto29A, F. Cossio74C, J. J. Cui50, H. L. Dai1,58,
J. P. Dai78, A. Dbeyssi18, R. E. de Boer3, D. Dedovich36, C. Q. Deng72, Z. Y.
Deng1, A. Denig35, I. Denysenko36, M. Destefanis74A,74C, F. De Mori74A,74C, B.
Ding66,1, X. X. Ding46,g, Y. Ding34, Y. Ding40, J. Dong1,58, L. Y. Dong1,63,
M. Y. Dong1,58,63, X. Dong76, M. C. Du1, S. X. Du80, Z. H. Duan42, P.
Egorov36,a, Y. H. Fan45, J. Fang1,58, J. Fang59, S. S. Fang1,63, W. X. Fang1,
Y. Fang1, Y. Q. Fang1,58, R. Farinelli29A, L. Fava74B,74C, F. Feldbauer3, G.
Felici28A, C. Q. Feng71,58, J. H. Feng59, Y. T. Feng71,58, K. Fischer69, M.
Fritsch3, C. D. Fu1, J. L. Fu63, Y. W. Fu1, H. Gao63, Y. N. Gao46,g, Yang
Gao71,58, S. Garbolino74C, I. Garzia29A,29B, L. Ge80, P. T. Ge76, Z. W. Ge42,
C. Geng59, E. M. Gersabeck67, A. Gilman69, K. Goetzen13, L. Gong40, W. X.
Gong1,58, W. Gradl35, S. Gramigna29A,29B, M. Greco74A,74C, M. H. Gu1,58, Y. T.
Gu15, C. Y. Guan1,63, Z. L. Guan22, A. Q. Guo31,63, L. B. Guo41, M. J. Guo50,
R. P. Guo49, Y. P. Guo12,f, A. Guskov36,a, J. Gutierrez27, K. L. Han63, T. T.
Han1, X. Q. Hao19, F. A. Harris65, K. K. He55, K. L. He1,63, F. H. Heinsius3,
C. H. Heinz35, Y. K. Heng1,58,63, C. Herold60, T. Holtmann3, P. C. Hong12,f,
G. Y. Hou1,63, X. T. Hou1,63, Y. R. Hou63, Z. L. Hou1, B. Y. Hu59, H. M.
Hu1,63, J. F. Hu56,i, T. Hu1,58,63, Y. Hu1, G. S. Huang71,58, K. X. Huang59,
L. Q. Huang31,63, X. T. Huang50, Y. P. Huang1, T. Hussain73, F. Hölzken3, N
Hüsken27,35, N. in der Wiesche68, M. Irshad71,58, J. Jackson27, S. Janchiv32,
J. H. Jeong10A, Q. Ji1, Q. P. Ji19, W. Ji1,63, X. B. Ji1,63, X. L. Ji1,58, Y.
Y. Ji50, X. Q. Jia50, Z. K. Jia71,58, D. Jiang1,63, H. B. Jiang76, P. C.
Jiang46,g, S. S. Jiang39, T. J. Jiang16, X. S. Jiang1,58,63, Y. Jiang63, J. B.
Jiao50, J. K. Jiao34, Z. Jiao23, S. Jin42, Y. Jin66, M. Q. Jing1,63, X. M.
Jing63, T. Johansson75, S. Kabana33, N. Kalantar-Nayestanaki64, X. L. Kang9,
X. S. Kang40, M. Kavatsyuk64, B. C. Ke80, V. Khachatryan27, A. Khoukaz68, R.
Kiuchi1, O. B. Kolcu62A, B. Kopf3, M. Kuessner3, X. Kui1,63, N. Kumar26, A.
Kupsc44,75, W. Kühn37, J. J. Lane67, P. Larin18, L. Lavezzi74A,74C, T. T.
Lei71,58, Z. H. Lei71,58, H. Leithoff35, M. Lellmann35, T. Lenz35, C. Li47, C.
Li43, C. H. Li39, Cheng Li71,58, D. M. Li80, F. Li1,58, G. Li1, H. Li71,58, H.
B. Li1,63, H. J. Li19, H. N. Li56,i, Hui Li43, J. R. Li61, J. S. Li59, Ke Li1,
L. J Li1,63, L. K. Li1, Lei Li48, M. H. Li43, P. R. Li38,k, Q. M. Li1,63, Q.
X. Li50, R. Li17,31, S. X. Li12, T. Li50, W. D. Li1,63, W. G. Li1, X. Li1,63,
X. H. Li71,58, X. L. Li50, Xiaoyu Li1,63, Y. G. Li46,g, Z. J. Li59, Z. X.
Li15, C. Liang42, H. Liang71,58, H. Liang1,63, Y. F. Liang54, Y. T.
Liang31,63, G. R. Liao14, L. Z. Liao50, Y. P. Liao1,63, J. Libby26, A.
Limphirat60, D. X. Lin31,63, T. Lin1, B. J. Liu1, B. X. Liu76, C. Liu34, C. X.
Liu1, F. H. Liu53, Fang Liu1, Feng Liu6, G. M. Liu56,i, H. Liu38,j,k, H. B.
Liu15, H. M. Liu1,63, Huanhuan Liu1, Huihui Liu21, J. B. Liu71,58, J. Y.
Liu1,63, K. Liu38,j,k, K. Y. Liu40, Ke Liu22, L. Liu71,58, L. C. Liu43, Lu
Liu43, M. H. Liu12,f, P. L. Liu1, Q. Liu63, S. B. Liu71,58, T. Liu12,f, W. K.
Liu43, W. M. Liu71,58, X. Liu38,j,k, X. Liu39, Y. Liu38,j,k, Y. Liu80, Y. B.
Liu43, Z. A. Liu1,58,63, Z. D. Liu9, Z. Q. Liu50, X. C. Lou1,58,63, F. X.
Lu59, H. J. Lu23, J. G. Lu1,58, X. L. Lu1, Y. Lu7, Y. P. Lu1,58, Z. H. Lu1,63,
C. L. Luo41, M. X. Luo79, T. Luo12,f, X. L. Luo1,58, X. R. Lyu63, Y. F. Lyu43,
F. C. Ma40, H. Ma78, H. L. Ma1, J. L. Ma1,63, L. L. Ma50, M. M. Ma1,63, Q. M.
Ma1, R. Q. Ma1,63, X. T. Ma1,63, X. Y. Ma1,58, Y. Ma46,g, Y. M. Ma31, F. E.
Maas18, M. Maggiora74A,74C, S. Malde69, A. Mangoni28B, Y. J. Mao46,g, Z. P.
Mao1, S. Marcello74A,74C, Z. X. Meng66, J. G. Messchendorp13,64, G.
Mezzadri29A, H. Miao1,63, T. J. Min42, R. E. Mitchell27, X. H. Mo1,58,63, B.
Moses27, N. Yu. Muchnoi4,b, J. Muskalla35, Y. Nefedov36, F. Nerling18,d, I. B.
Nikolaev4,b, Z. Ning1,58, S. Nisar11,l, Q. L. Niu38,j,k, W. D. Niu55, Y. Niu
50, S. L. Olsen63, Q. Ouyang1,58,63, S. Pacetti28B,28C, X. Pan55, Y. Pan57, A.
Pathak34, P. Patteri28A, Y. P. Pei71,58, M. Pelizaeus3, H. P. Peng71,58, Y. Y.
Peng38,j,k, K. Peters13,d, J. L. Ping41, R. G. Ping1,63, S. Plura35, V.
Prasad33, F. Z. Qi1, H. Qi71,58, H. R. Qi61, M. Qi42, T. Y. Qi12,f, S.
Qian1,58, W. B. Qian63, C. F. Qiao63, X. K. Qiao80, J. J. Qin72, L. Q. Qin14,
X. S. Qin50, Z. H. Qin1,58, J. F. Qiu1, S. Q. Qu61, Z. H. Qu72, C. F.
Redmer35, K. J. Ren39, A. Rivetti74C, M. Rolo74C, G. Rong1,63, Ch. Rosner18,
S. N. Ruan43, N. Salone44, A. Sarantsev36,c, Y. Schelhaas35, K. Schoenning75,
M. Scodeggio29A, K. Y. Shan12,f, W. Shan24, X. Y. Shan71,58, Z. J Shang38,j,k,
J. F. Shangguan16, L. G. Shao1,63, M. Shao71,58, C. P. Shen12,f, H. F.
Shen1,8, W. H. Shen63, X. Y. Shen1,63, B. A. Shi63, H. C. Shi71,58, J. L.
Shi12, J. Y. Shi1, Q. Q. Shi55, R. S. Shi1,63, S. Y. Shi72, X. Shi1,58, J. J.
Song19, T. Z. Song59, W. M. Song34,1, Y. J. Song12, Y. X. Song46,g,m, S.
Sosio74A,74C, S. Spataro74A,74C, F. Stieler35, Y. J. Su63, G. B. Sun76, G. X.
Sun1, H. Sun63, H. K. Sun1, J. F. Sun19, K. Sun61, L. Sun76, S. S. Sun1,63, T.
Sun51,e, W. Y. Sun34, Y. Sun9, Y. J. Sun71,58, Y. Z. Sun1, Z. Q. Sun1,63, Z.
T. Sun50, C. J. Tang54, G. Y. Tang1, J. Tang59, Y. A. Tang76, L. Y. Tao72, Q.
T. Tao25,h, M. Tat69, J. X. Teng71,58, V. Thoren75, W. H. Tian59, Y.
Tian31,63, Z. F. Tian76, I. Uman62B, Y. Wan55, S. J. Wang 50, B. Wang1, B. L.
Wang63, Bo Wang71,58, D. Y. Wang46,g, F. Wang72, H. J. Wang38,j,k, J. P. Wang
50, K. Wang1,58, L. L. Wang1, M. Wang50, Meng Wang1,63, N. Y. Wang63, S.
Wang38,j,k, S. Wang12,f, T. Wang12,f, T. J. Wang43, W. Wang59, W. Wang72, W.
P. Wang71,58, X. Wang46,g, X. F. Wang38,j,k, X. J. Wang39, X. L. Wang12,f, X.
N. Wang1, Y. Wang61, Y. D. Wang45, Y. F. Wang1,58,63, Y. L. Wang19, Y. N.
Wang45, Y. Q. Wang1, Yaqian Wang17, Yi Wang61, Z. Wang1,58, Z. L. Wang72, Z.
Y. Wang1,63, Ziyi Wang63, D. Wei70, D. H. Wei14, F. Weidner68, S. P. Wen1, Y.
R. Wen39, U. Wiedner3, G. Wilkinson69, M. Wolke75, L. Wollenberg3, C. Wu39, J.
F. Wu1,8, L. H. Wu1, L. J. Wu1,63, X. Wu12,f, X. H. Wu34, Y. Wu71, Y. H. Wu55,
Y. J. Wu31, Z. Wu1,58, L. Xia71,58, X. M. Xian39, B. H. Xiang1,63, T.
Xiang46,g, D. Xiao38,j,k, G. Y. Xiao42, S. Y. Xiao1, Y. L. Xiao12,f, Z. J.
Xiao41, C. Xie42, X. H. Xie46,g, Y. Xie50, Y. G. Xie1,58, Y. H. Xie6, Z. P.
Xie71,58, T. Y. Xing1,63, C. F. Xu1,63, C. J. Xu59, G. F. Xu1, H. Y. Xu66, Q.
J. Xu16, Q. N. Xu30, W. Xu1, W. L. Xu66, X. P. Xu55, Y. C. Xu77, Z. P. Xu42,
Z. S. Xu63, F. Yan12,f, L. Yan12,f, W. B. Yan71,58, W. C. Yan80, X. Q. Yan1,
H. J. Yang51,e, H. L. Yang34, H. X. Yang1, Tao Yang1, Y. Yang12,f, Y. F.
Yang43, Y. X. Yang1,63, Yifan Yang1,63, Z. W. Yang38,j,k, Z. P. Yao50, M.
Ye1,58, M. H. Ye8, J. H. Yin1, Z. Y. You59, B. X. Yu1,58,63, C. X. Yu43, G.
Yu1,63, J. S. Yu25,h, T. Yu72, X. D. Yu46,g, Y. C. Yu80, C. Z. Yuan1,63, J.
Yuan34, L. Yuan2, S. C. Yuan1, Y. Yuan1,63, Z. Y. Yuan59, C. X. Yue39, A. A.
Zafar73, F. R. Zeng50, S. H. Zeng72, X. Zeng12,f, Y. Zeng25,h, Y. J. Zeng59,
Y. J. Zeng1,63, X. Y. Zhai34, Y. C. Zhai50, Y. H. Zhan59, A. Q. Zhang1,63, B.
L. Zhang1,63, B. X. Zhang1, D. H. Zhang43, G. Y. Zhang19, H. Zhang71, H. C.
Zhang1,58,63, H. H. Zhang59, H. H. Zhang34, H. Q. Zhang1,58,63, H. Y.
Zhang1,58, J. Zhang80, J. Zhang59, J. J. Zhang52, J. L. Zhang20, J. Q.
Zhang41, J. W. Zhang1,58,63, J. X. Zhang38,j,k, J. Y. Zhang1, J. Z. Zhang1,63,
Jianyu Zhang63, L. M. Zhang61, Lei Zhang42, P. Zhang1,63, Q. Y. Zhang39,80, R.
Y Zhang38,j,k, Shuihan Zhang1,63, Shulei Zhang25,h, X. D. Zhang45, X. M.
Zhang1, X. Y. Zhang50, Y. Zhang72, Y. T. Zhang80, Y. H. Zhang1,58, Y. M.
Zhang39, Yan Zhang71,58, Yao Zhang1, Z. D. Zhang1, Z. H. Zhang1, Z. L.
Zhang34, Z. Y. Zhang76, Z. Y. Zhang43, G. Zhao1, J. Y. Zhao1,63, J. Z.
Zhao1,58, Lei Zhao71,58, Ling Zhao1, M. G. Zhao43, R. P. Zhao63, S. J. Zhao80,
Y. B. Zhao1,58, Y. X. Zhao31,63, Z. G. Zhao71,58, A. Zhemchugov36,a, B.
Zheng72, J. P. Zheng1,58, W. J. Zheng1,63, Y. H. Zheng63, B. Zhong41, X.
Zhong59, H. Zhou50, J. Y. Zhou34, L. P. Zhou1,63, X. Zhou76, X. K. Zhou6, X.
R. Zhou71,58, X. Y. Zhou39, Y. Z. Zhou12,f, J. Zhu43, K. Zhu1, K. J.
Zhu1,58,63, L. Zhu34, L. X. Zhu63, S. H. Zhu70, S. Q. Zhu42, T. J. Zhu12,f, W.
J. Zhu12,f, Y. C. Zhu71,58, Z. A. Zhu1,63, J. H. Zou1, J. Zu71,58
(BESIII Collaboration)
1 Institute of High Energy Physics, Beijing 100049, People’s Republic of China
2 Beihang University, Beijing 100191, People’s Republic of China
3 Bochum Ruhr-University, D-44780 Bochum, Germany
4 Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6 Central China Normal University, Wuhan 430079, People’s Republic of China
7 Central South University, Changsha 410083, People’s Republic of China
8 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
9 China University of Geosciences, Wuhan 430074, People’s Republic of China
10 Chung-Ang University, Seoul, 06974, Republic of Korea
11 COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind
Road, 54000 Lahore, Pakistan
12 Fudan University, Shanghai 200433, People’s Republic of China
13 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
14 Guangxi Normal University, Guilin 541004, People’s Republic of China
15 Guangxi University, Nanning 530004, People’s Republic of China
16 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
17 Hebei University, Baoding 071002, People’s Republic of China
18 Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
19 Henan Normal University, Xinxiang 453007, People’s Republic of China
20 Henan University, Kaifeng 475004, People’s Republic of China
21 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
22 Henan University of Technology, Zhengzhou 450001, People’s Republic of
China
23 Huangshan College, Huangshan 245000, People’s Republic of China
24 Hunan Normal University, Changsha 410081, People’s Republic of China
25 Hunan University, Changsha 410082, People’s Republic of China
26 Indian Institute of Technology Madras, Chennai 600036, India
27 Indiana University, Bloomington, Indiana 47405, USA
28 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
29 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara,
Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
30 Inner Mongolia University, Hohhot 010021, People’s Republic of China
31 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
32 Institute of Physics and Technology, Peace Avenue 54B, Ulaanbaatar 13330,
Mongolia
33 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica
1000000, Chile
34 Jilin University, Changchun 130012, People’s Republic of China
35 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
36 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
37 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
38 Lanzhou University, Lanzhou 730000, People’s Republic of China
39 Liaoning Normal University, Dalian 116029, People’s Republic of China
40 Liaoning University, Shenyang 110036, People’s Republic of China
41 Nanjing Normal University, Nanjing 210023, People’s Republic of China
42 Nanjing University, Nanjing 210093, People’s Republic of China
43 Nankai University, Tianjin 300071, People’s Republic of China
44 National Centre for Nuclear Research, Warsaw 02-093, Poland
45 North China Electric Power University, Beijing 102206, People’s Republic of
China
46 Peking University, Beijing 100871, People’s Republic of China
47 Qufu Normal University, Qufu 273165, People’s Republic of China
48 Renmin University of China, Beijing 100872, People’s Republic of China
49 Shandong Normal University, Jinan 250014, People’s Republic of China
50 Shandong University, Jinan 250100, People’s Republic of China
51 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
52 Shanxi Normal University, Linfen 041004, People’s Republic of China
53 Shanxi University, Taiyuan 030006, People’s Republic of China
54 Sichuan University, Chengdu 610064, People’s Republic of China
55 Soochow University, Suzhou 215006, People’s Republic of China
56 South China Normal University, Guangzhou 510006, People’s Republic of China
57 Southeast University, Nanjing 211100, People’s Republic of China
58 State Key Laboratory of Particle Detection and Electronics, Beijing 100049,
Hefei 230026, People’s Republic of China
59 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
60 Suranaree University of Technology, University Avenue 111, Nakhon
Ratchasima 30000, Thailand
61 Tsinghua University, Beijing 100084, People’s Republic of China
62 Turkish Accelerator Center Particle Factory Group, (A)Istinye University,
34010, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus,
99138, Mersin 10, Turkey
63 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
64 University of Groningen, NL-9747 AA Groningen, The Netherlands
65 University of Hawaii, Honolulu, Hawaii 96822, USA
66 University of Jinan, Jinan 250022, People’s Republic of China
67 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
68 University of Muenster, Wilhelm-Klemm-Strasse 9, 48149 Muenster, Germany
69 University of Oxford, Keble Road, Oxford OX13RH, United Kingdom
70 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
71 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
72 University of South China, Hengyang 421001, People’s Republic of China
73 University of the Punjab, Lahore-54590, Pakistan
74 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
75 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
76 Wuhan University, Wuhan 430072, People’s Republic of China
77 Yantai University, Yantai 264005, People’s Republic of China
78 Yunnan University, Kunming 650500, People’s Republic of China
79 Zhejiang University, Hangzhou 310027, People’s Republic of China
80 Zhengzhou University, Zhengzhou 450001, People’s Republic of 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,
People’s Republic of China
f Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and
Institute of Modern Physics, Fudan University, Shanghai 200443, People’s
Republic of China
g Also at State Key Laboratory of Nuclear Physics and Technology, Peking
University, Beijing 100871, People’s Republic of China
h Also at School of Physics and Electronics, Hunan University, Changsha
410082, China
i Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of
Quantum Matter, South China Normal University, Guangzhou 510006, China
j Also at MOE Frontiers Science Center for Rare Isotopes, Lanzhou University,
Lanzhou 730000, People’s Republic of China
k Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou
730000, People’s Republic of China
l Also at the Department of Mathematical Sciences, IBA, Karachi 75270,
Pakistan
m Also at Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne,
Switzerland

###### Abstract

Using $e^{+}e^{-}$ collision data, corresponding to an integrated luminosity
of $892\,\rm pb^{-1}$ collected at center-of-mass energies from 4.84 to 4.95
GeV with the BESIII detector, we search for the process $e^{+}e^{-}\to
K^{+}K^{-}\psi(3770)$ by reconstructing two charged kaons and one $D$ meson
from $\psi(3770)$. No significant signal of $e^{+}e^{-}\to
K^{+}K^{-}\psi(3770)$ is found and the upper limits of the Born cross sections
are reported at 90% confidence level.

##  I Introduction

The charmonium states ($c\bar{c}$) provide an excellent experimental
laboratory for understanding the non-perturbative mechanism of quantum
chromodynamics (QCD). The conventional charmonium states, like $J/\psi$,
$\psi(2S)$, and $\psi(3770)$, have played a significant role in studying the
behavior of quarks and gluons. In recent years, more vector states have been
observed in the charmonium energy region, which challenges the conventional
charmonium states predicted by the quark potential model quarkmodel . Some of
them, such as $\psi(4040)$, $\psi(4160)$ and $\psi(4415)$, have been observed
by analyzing the line shape of the cross sections of electron-positron
annihilating into inclusive hadron states BES:2007zwq  that are dominated by
open-charm processes; others, such as $Y(4230)$, $Y(4390)$, and $Y(4660)$,
have been discovered via hidden-charm final states paper2 ; paper3 ;
BESIII:2021njb ; Belle:2008xmh . According to the quark potential model
Kher:2018 , the masses of the 5S and 6S vector charmonium states are around
4.6 GeV and 5.2 GeV, respectively. In the mass region of $4.7$ GeV to $4.95$
GeV, there should be only one vector charmonium $4^{3}D_{1}$ state with mass
about 4.8 GeV. For the exotic states, there are different theoretical
predictions based on various hypotheses. For example, in Ref. Dong:2021juy , a
vector $\Xi_{c}\bar{\Xi}_{c}$ molecule is predicted, whereas lattice QCD does
not expect such a state Chiu:2005ey . To resolve this controversial situation,
further experimental and theoretical investigations are required.

Recently, BESIII reported a new structure around 4.79 GeV in the line shape of
the cross sections of the process $e^{+}e^{-}\to D^{*+}_{s}D^{*-}_{s}$
BESIII:2023wsc . This structure appears to be consistent with the structure
observed around 4.71 GeV in BESIII’s previous measurement of $e^{+}e^{-}\to
K^{+}K^{-}J/\psi$ Y4710  and is also evident in $e^{+}e^{-}\to
K_{S}^{0}K_{S}^{0}J/\psi$ BESIII:2022kcv , considering the large uncertainties
of both mass and width. These new observations inspire us to search for a new
process $e^{+}e^{-}\to K^{+}K^{-}\psi(3770)$. The process
$e^{+}e^{-}\to\pi^{+}\pi^{-}\psi(3770)$ has been studied in the BESIII
experiment pipi3770 ; pipi37701 ; PIPIDD . Searching for new high-mass vector
states involving both $\psi(3770)$ and kaons would provide valuable
information to determine the nature of these new structures. Although there is
no definite theoretical prediction for $e^{+}e^{-}\to K^{+}K^{-}\psi(3770)$
(Ref. Brambilla:2022hhi  only predicts the inclusive width of $Y(4710)$ decays
into $J/\psi$ or $\psi(3686)$), a naive presumption suggests that this process
would be suppressed in conventional charmonium Qian:2023taw  or
$[cs][\bar{c}\bar{s}]$ tetraquark assumptions Lu:2016cwr , while an
enhancement is expected in the $f_{0}(980)\psi(2S/1D)$ molecule model
Guo:2008zg .

In this paper, for the first time we search for the process $e^{+}e^{-}\to
K^{+}K^{-}\psi(3770)$ by using an integrated luminosity of $892\,\rm pb^{-1}$
$e^{+}e^{-}$ collision data collected at center-of-mass (CM) energies from
4.84 to 4.95 GeV with the BESIII detector lum_bes3 . The CM energy and
corresponding luminosities are listed in Table 1.

##  II BESIII detector and Monte Carlo

The BESIII detector BESIII  records symmetric $e^{+}e^{-}$ collisions provided
by the BEPCII storage ring Yu:IPAC2016-TUYA01  in the center-of-mass energy
range from 2.0 to 4.95 GeV, with a peak luminosity of $1\times
10^{33}\;\text{cm}^{-2}\text{s}^{-1}$ achieved at $\sqrt{s}=3.77\;\text{GeV}$.
The cylindrical core of the BESIII 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), which are all 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 identifier
modules interleaved with steel. The charged-particle momentum resolution at
$1~{}{\rm GeV}$ is $0.5\%$, and the specific energy loss ($dE/dx$) resolution
is $6\%$ for the 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 of the TOF barrel part is 68 ps, while the
end cap TOF system is upgraded in 2015 with multi-gap resistive plate chamber
technology, providing a time resolution of 60 ps update1 ; update2 .

Simulated samples produced with a Geant4-based geant4  Monte Carlo (MC)
package, which includes the geometric description detvis  of the BESIII
detector and the detector response, are used to determine the detection
efficiency and to estimate backgrounds. The simulation includes the beam
energy spread and initial state radiation (ISR) in the $e^{+}e^{-}$
annihilations modeled with the generator kkmc kkmc . The inclusive MC sample
includes the production of open charm processes, the ISR production of vector
charmonium(-like) states, and the continuum processes incorporated in kkmc
kkmc . All particle decays are modelled with evtgen evtgen  using branching
fractions either taken from the Particle Data Group PDG2022 , when available,
or otherwise estimated with lundcharm lundcharm . Final state radiation (FSR)
from charged final state particles is incorporated using the photos package
photos .

##  III EVENT SELECTION

The dominant decay channel of $\psi(3770)$ is $\psi(3770)\to D\bar{D}$. For
the signal process $e^{+}e^{-}\to K^{+}K^{-}\psi(3770)$, we only reconstruct
two charged kaons and one $\bar{D}$ meson, the presence of $D$ mesons is
inferred by the recoiling mass of $K^{+}K^{-}\bar{D}$. To reconstruct the
$\bar{D}$ mesons, we select nine decay modes with large BF and clean
backgrounds, including three modes $\bar{D}^{0}\to K^{+}\pi^{-}$,
$\bar{D}^{0}\to K^{+}\pi^{-}\pi^{0}$ and $\bar{D}^{0}\to
K^{+}\pi^{+}\pi^{-}\pi^{-}$ with a summed up to a total 26.6% branching
fraction of $\bar{D}^{0}$ decays; six modes $D^{-}\to K^{+}\pi^{-}\pi^{-}$,
$D^{-}\to K^{+}\pi^{-}\pi^{-}\pi^{0}$, $D^{-}\to K_{S}^{0}\pi^{-}$, $D^{-}\to
K_{S}^{0}\pi^{-}\pi^{0}$, $D^{-}\to K_{S}^{0}\pi^{-}\pi^{-}\pi^{+}$, and
$D^{-}\to K^{+}K^{-}\pi^{-}$ with a summed up to 27.2% branching fraction of
$D^{-}$ decays. Throughout the whole text, charge conjugated decays are always
implied.

Charged tracks detected in the MDC are required to be within a polar angle
($\theta$) range of $|\rm{cos\theta}|<0.93$, where $\theta$ is defined with
respect to the $z$-axis, which is the symmetry axis of the MDC. For charged
tracks not originating from $K_{S}^{0}$ decays, the distance of closest
approach to the interaction point (IP) must be less than 10 cm along the
$z$-axis, $|V_{z}|$, and less than 1 cm in the transverse plane, $|V_{xy}|$.
Particle identification (PID) for charged tracks combines measurements of the
energy deposited in the MDC (d$E$/d$x$) and the flight time in the TOF to form
likelihoods $\mathcal{L}(h)~{}(h=p,K,\pi)$ for each hadron $h$ hypothesis.
Charged kaons and pions are identified by comparing the likelihoods for the
kaon and pion hypotheses, $\mathcal{L}(K)>\mathcal{L}(\pi)$ and
$\mathcal{L}(\pi)>\mathcal{L}(K)$, respectively.

Each $K_{S}^{0}$ candidate is reconstructed from two oppositely charged tracks
satisfying $|V_{z}|<$ 20 cm. The two charged tracks are assigned as
$\pi^{+}\pi^{-}$ without imposing further PID criteria. They are constrained
to originate from a common vertex and are required to have an invariant mass
within $(0.486,0.510)~{}{\rm GeV}/c^{2}$. This mass window corresponds to
about three times the mass resolution. The decay length of the $K^{0}_{S}$
candidate is required to be greater than twice the vertex resolution away from
the IP.

The $\pi^{0}$ candidates are reconstructed via $\pi^{0}\to\gamma\gamma$. Here,
photon candidates are identified using showers in the EMC. The deposited
energy of each shower must be more than 25 MeV in the barrel region
($|\cos\theta|<0.80$) and more than 50 MeV in the end cap region
($0.86<|\cos\theta|<0.92$). To exclude showers that originate from charged
tracks, the angle subtended by the EMC shower and the position of the closest
charged track at the EMC must be greater than 10 degrees as measured from the
IP. To suppress electronic noise and showers unrelated to the event, the
difference between the EMC time and the event start time is required to be
within [0, 700] ns. A one-constraint (1C) kinematic fit is performed to
constrain the invariant mass of photon pair to the nominal mass of $\pi^{0}$
PDG2022 , and and a list of $\pi^{0}$ candidates is prepared for subsequent
event selection.

If there are multiple reconstructed $\bar{D}$ candidates, the one with the
closest mass to the nominal $\bar{D}$ mass PDG2022  is selected. A 1C
kinematic fit is then carried out with the $\bar{D}$ meson’s nominal mass
constraint to improve the resolution of the recoiling mass spectrum and to
reduce the background. The $\chi^{2}$ value of the 1C kinematic fit is set to
be less than 13. This selection criterion is optimized by maximizing the Punzi
figure of merit, $\frac{S}{\sqrt{B}+\alpha/2}$ opt , where $S$ is the number
of signal from the signal MC sample, $B$ is the estimated background yield
from the inclusive MC samples, and $\alpha$, set at 3, is the expected
significance. The $K^{\pm}$ candidates, which meet the particle identification
criteria and possess the lowest momentum among those not utilized in $\bar{D}$
reconstruction, are assumed to be the bachelor kaons unrelated to $D$ or
$\bar{D}$ decays.

Even though the process $e^{+}e^{-}\to\phi\psi(3770)$ is highly suppressed in
a electron-positron collision experiment due to C-parity violation, we require
the $|M_{K^{+}K^{-}}-M_{\phi}|>0.02~{}{\rm GeV}/c^{2}$ to reduce the
backgrounds including $\phi$ meson in the final states, in which the
$M_{K^{+}K^{-}}$ and $M_{\phi}$ denote the invariant mass of $K^{+}K^{-}$ and
$\phi$ nominal mass, respectively. After imposing all event selection
criteria, we compare the recoiling mass distributions, $R(K^{+}K^{-}\bar{D})$
and $R(K^{+}K^{-})$, between data and inclusive MC sample, as shown in Fig 1.
Here,
$R(K^{+}K^{-}\bar{D})=\sqrt{(P_{e^{+}e^{-}}-P_{K^{+}}-P_{K^{-}}-P_{\bar{D}})^{2}}$
and $R(K^{+}K^{-})=\sqrt{(P_{e^{+}e^{-}}-P_{K^{+}}-P_{K^{-}})^{2}}$ are the
recoil mass of the $K^{+}K^{-}\bar{D}$ and $K^{+}K^{-}$, respectively, where
$P_{e^{+}e^{-}}$, $P_{K^{\pm}}$ and $P_{\bar{D}}$ are the 4-momenta of the
initial $e^{+}e^{-}$ system, the $K^{\pm}$ and $\bar{D}$, respectively. In
general, the data can be well described by the inclusive MC sample.

##  IV DATA ANALYSIS

To extract the signal yields, a two-dimensional (2D) unbinned maximum
likelihood fit is performed to the recoiling mass distributions
$RM(K^{+}K^{-}\bar{D})$ versus $RM(K^{+}K^{-})$. The 2D probability density
function (PDF) for the signal is taken from the signal MC simulation. The PDFs
of background contributions are extracted from the inclusive MC samples. The
dominant backgrounds come from $K^{+}K^{-}D\bar{D}\pi^{0}$ and
$K^{+}K^{-}D\bar{D}\pi^{0}\pi^{0}$ processes. Neither unexpected structure nor
peaking background is found from the inclusive MC in the fitting region. To
further test the reliability of background shape, we compare the
$RM(K^{+}K^{-}\bar{D})$ and $RM(K^{+}K^{-})$ distributions (include signal
region and non-signal region) between data and MC simulation without any
requirement on the $\chi^{2}$ of $D$ kinematic fit. No significant difference
between data and inclusive MC sample is found. Since no significant signal of
$e^{+}e^{-}\to K^{+}K^{-}D\bar{D}$ is observed and the $D\bar{D}$ invariant
mass distribution of $e^{+}e^{-}\to K^{+}K^{-}D\bar{D}$ is similar with that
of $\psi(3770)$ because of the limited phase space, this component is ignored
in the fits. Figure 1 shows the $RM(K^{+}K^{-}\bar{D})$ versus
$RM(K^{+}K^{-})$ fitting results at CM energies $\sqrt{s}=4.84$, $4.91$, and
$4.95$ GeV.

Fig. 1: The recoiling mass distributions of $K^{+}K^{-}\bar{D}$ (left panel)
and $K^{+}K^{-}$ (middle panel), and their 2D scatter plot (right panel) at
$\sqrt{s}=4.84$, $4.91$, and $4.95$ GeV. In the left two columns, the dots
with error bars are data, the blue solid lines represent the fitted curve, the
green dotted lines represent signal shapes, the pink dashed lines present
backgrounds. Notice at $\sqrt{s}=4.84$, the signals are too tiny to be
visible.

In the fits at each energy points, the cross sections of $e^{+}e^{-}\to
K^{+}K^{-}\psi(3770)$ with $\psi(3770)\to D^{0}\bar{D}^{0}$ and $\psi(3770)\to
D^{+}D^{-}$ are constrained to be the same. Therefore, after considering the
detection efficiency and BF of $\bar{D}$ decays, the ratios of the signal
yields in the charged mode relative to the neutral modes are fixed to
$f_{4.84}=0.46$, $f_{4.91}=0.53$, and $f_{4.95}=0.54$ for the three energy
points, respectively.

The Born cross section is calculated as,

$\small\sigma^{B}(e^{+}e^{-}\to K^{+}K^{-}\psi(3770))=\frac{N_{\rm
sig}}{2\mathcal{L}_{\rm int}(1+\delta(s))\frac{1}{|1-\Pi|^{2}}\epsilon_{\rm
sig}B_{\rm sub}},$ (1)

where $N_{\rm sig}$ is the number of signal events in the data,
$\mathcal{L}_{\rm int}$ is the integrated luminosity of data measured by
Bhabha events lum_bes3 , $\epsilon_{\rm sig}$ is the detection efficiency,
$B_{\rm sub}$ is aggregate of the BFs of $\psi(3770)\to D\bar{D}$ and
subsequent $D$ decays across the nine tag modes, $\frac{1}{|1-\Pi|^{2}}$ is
the vacuum polarization factor EPJC , and $1+\delta(s)$ is the radiative
correction factor defined as

$1+\delta(s)=\frac{\int\sigma(s(1-x))F(x,s)dx}{\sigma(s)},$ (2)

where $F(x,s)$ is radiator function calculated by QED with accuracy 0.1% QED .
$\sigma$ is the cross section.

No obvious signal is found for the process $e^{+}e^{-}\to
K^{+}K^{-}\psi(3770)$. Utilizing the Bayesian approach li  and incorporating
the systematic uncertainties, that will be discussed in Sec. V, we estimate
the upper limits on the Born cross sections for $e^{+}e^{-}\to
K^{+}K^{-}\psi(3770)$ at 90% confidence level at these three energy points.
The corresponding likelihood distributions are shown in Fig. 2, and the upper
limit results are listed in Table 1.

Fig. 2: Normalized likelihood ($L/L_{max}$) as a function of the number of signal events. The red and blue solid curves are the likelihood distributions before and after involving the multiplicative systematic uncertainties, respectively. The black arrow shows the upper limit of the number of events at 90% confidence level after considering the systematic uncertainties. Table 1: Related quantities at each energy point. Here $\sqrt{s}$ is the CM energy, $\mathcal{L}_{\rm int}$ is the integrated luminosity, $N_{\rm sig}$ is the number of signal events by the best fit, $\epsilon_{\rm sig}$ is the efficiency including the BFs of $\psi(3770)$ and $\bar{D}$ decays, $(1+\delta(s))$ is the radiative correction factor, $\frac{1}{|1-\Pi|^{2}}$ is the vacuum polarization, and $\sigma^{B}$ is the upper limit of the Born cross section, and $N^{\rm upper}$ is the upper limit of the signal yield after considering systematic uncertainties. $\sqrt{s}~{}{\rm(GeV)}$ | $\mathcal{L}_{\rm int}(\rm{pb}^{-1})$ | $N_{\rm sig}$ | $N^{\rm upper}$ | $\epsilon_{\rm sig}(\%)$ | $(1+\delta(s))$ | $\frac{1}{|1-\Pi|^{2}}$ |  $\sigma^{B}$(pb)
---|---|---|---|---|---|---|---
4.84 | 525.16$\pm$2.78 | $0.00^{+0.56}_{-0.54}$ |  $<$4.7 | 0.487$\pm$0.015 | 0.727 | 1.056 |  $<$1.2
4.91 | 207.82$\pm$1.10 | $3.0^{+4.2}_{-5.2}$ |  $<$14.6 | 1.473$\pm$0.027 | 0.757 | 1.056 |  $<$3.0
4.95 | 159.28$\pm$0.84 | $0.8^{+6.1}_{-5.0}$ |  $<$14.2 | 1.736$\pm$0.028 | 0.772 | 1.056 |  $<$3.1

##  V SYSTEMATIC UNCRTAINTY

In the measurements of the Born cross sections, the systematic uncertainties
are categorized into additive and multiplicative uncertainties. The additive
uncertainties originate from the fit to the $RM(K^{+}K^{-}\bar{D})$ versus
$RM(K^{+}K^{-})$, that directly affects the fitting results. The
multiplicative uncertainties are associated with the efficiencies, and will
affect the cross section calculation.

The additive uncertainties originate from the 2D fits, which are primarily
influenced by the uncertainty in the signal and background shapes. The
uncertainty associated with the signal shape is negligible. In the nominal
determination of the upper limits, the background shape is derived from the
inclusive MC simulation. To assess the corresponding systematic uncertainty, a
2D polynomial function is utilized as an alternate option. The 2D polynomial
function is formed by the product of two polynomial functions corresponding to
$RM(K^{+}K^{-}\bar{D})$ and $RM(K^{+}K^{-})$. For the $RM(K^{+}K^{-}\bar{D})$
dimension, we have experimented with a constant and a 1st-order polynomial
function, whereas for the $RM(K^{+}K^{-})$ dimension, we have explored 2nd and
3rd-order polynomial functions. The resulting upper limits based on these two
background shapes are detailed in Table 1, and the larger values are selected
for conservation.

The multiplicative uncertainties include luminosity ($\mathcal{L}_{\rm int}$),
$K^{\pm}$ and $\pi^{\pm}$ tracking and PID, $\pi^{0}$ reconstruction,
radiative correction factor ($1+\delta(s)$), $K_{S}^{0}$ reconstruction, 1C
kinematic fit, MC statistics, and quoted BFs. The integrated luminosity is
measured using Bhabha events, the uncertainty is about 0.6% lum_bes3 . The
$K^{\pm}$ tracking and PID efficiencies are estimated by double tag hadronic
$D\bar{D}$ events kev . The data/MC efficiency differences are weighted by the
corresponding momentum spectra from signal MC events. The $K^{\pm}$ tracking
and PID systematic uncertainties are determined to be 8.5% and 2.9%,
respectively. The systematic uncertainties of $\pi^{\pm}$ tracking and PID are
cited from previous work, the systematic uncertainty is 1.6% for both tracking
and PID PI . In this work, the $\pi^{0}$ selection criteria are the same as
those used in Ref. epjc76 . We assign 1.0% as the systematic uncertainty per
$\pi^{0}$ reconstruction, which includes the effect of photon selection, mass
window and 1C kinematic fit. The systematic uncertainty of radiative
correction factor is estimated by comparing the difference between factors
obtained by the phase space line shape and flat line shape, and is determined
to be 10.0%, 10.5%, and 11.0% for $\sqrt{s}=4.84$, $4.91$, and $4.95$ GeV,
respectively. The systematic uncertainty of quoted BFs is 10%, including the
$\psi(3770)\to D\bar{D}$ and $\bar{D}$ subsequent decays PDG2022 . The
systematic uncertainty of $K_{S}^{0}$ reconstruction is 0.2%, quoting from
Ref. kev . For the uncertainty of kinematic fit, we try to correct the track
helix parameters in the MC simulation so as to describe the data better. The
correction factors are obtained by using control sample $J/\psi\to\phi
f_{0}(980)$ paper980 . The efficiency difference before and after the
correction, 1%, is taken as the systematic uncertainty of the kinematic fit.
The uncertainties of MC statistics are 3.1%, 1.8%, and 1.6% for
$\sqrt{s}=4.84$, $4.91$, and $4.95$ GeV, respectively. The uncertainties
associated with the physics model are estimated by comparing the detection
efficiencies with those of phase space and $e^{+}e^{-}\to
f_{0}(980)\psi(3770)\to K^{+}K^{-}\psi(3770)$. The relative differences, which
are $15.6\%$, $17.6\%$, and $20.0\%$ for $\sqrt{s}=4.84$, $4.91$, and $4.95$
GeV, respectively, are reported as the corresponding systematic uncertainties.
Adding each systematic uncertainty in quadrature, we obtain the total
systematic uncertainties for each energy point. All the multiplicative
systematic uncertainties are summarized in Table 2. The blue and red lines in
Fig. 2 show with and without considering the systematic uncertainty likelihood
distribution.

Table 2:  Multiplicative systematic uncertainties (%) in the measurements of the Born cross sections. Uncertainty | 4.84 GeV | 4.91 GeV | 4.95 GeV
---|---|---|---
Luminosity | 0.6 | 0.6 | 0.6
$K^{\pm}$ tracking | 8.5 | 8.5 | 8.5
$K^{\pm}$ PID | 2.9 | 2.9 | 2.9
$\pi^{\pm}$ tracking | 1.6 | 1.6 | 1.6
$\pi^{\pm}$ PID | 1.6 | 1.6 | 1.6
Radiative correction factor | 10.0 | 10.5 | 11.0
Quoted $\mathcal{B}$ | 10.0 | 10.0 | 10.0
$K_{S}^{0}$ reconstruction | 0.2 | 0.2 | 0.2
Kinematic fit | 1.0 | 1.0 | 1.0
MC statistics | 3.1 | 1.8 | 1.6
Physics model | 15.6 | 17.6 | 20.0
Total | 23.2 | 24.7 | 26.7

##  VI SUMMARY

In this paper, we search for the process $e^{+}e^{-}\to K^{+}K^{-}\psi(3770)$
using 896 $\rm{pb}^{-1}$ of $e^{+}e^{-}$ annihilation data taken at CM
energies from 4.84 to 4.95 GeV. No significant signal for $e^{+}e^{-}\to
K^{+}K^{-}\psi(3770)$ is observed. Therefore, we determine the upper limits of
the Born cross sections at 90% confidence level to be $1\sim 3$ pb. We also
notice that the upper limits reported in this paper are obviously smaller than
the cross sections measured in the process
$e^{+}e^{-}\to\pi^{+}\pi^{-}D^{+}D^{-}$ PIPIDD , which could be attributed to
a combination of factors, including the suppressed phase space and strange
quark production in $e^{+}e^{-}\to K^{+}K^{-}\psi(3770)$. But we don’t know
which factor is dominant at present. Further measurements based on additional
data samples within and beyond this energy region, that will be collected at
BESIII in the future, may help to clarify this matter.

##  VII ACKNOWLEDGMENTS

The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing
center for their strong support. This work is supported in part by National
Key R&D Program of China under Contracts Nos. 2020YFA0406300, 2020YFA0406400;
National Natural Science Foundation of China (NSFC) under Contracts Nos.
11635010, 11735014, 11835012, 11935015, 11935016, 11935018, 11961141012,
12025502, 12035009, 12035013, 12061131003, 12192260, 12192261, 12192262,
12192263, 12192264, 12192265, 12221005, 12225509, 12235017; the Chinese
Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS
Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale
Scientific Facility Funds of the NSFC and CAS under Contract No. U1832207; CAS
Key Research Program of Frontier Sciences under Contracts Nos. QYZDJ-SSW-
SLH003, QYZDJ-SSW-SLH040; 100 Talents Program of CAS; The Institute of Nuclear
and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics
and Cosmology; European Union’s Horizon 2020 research and innovation programme
under Marie Sklodowska-Curie grant agreement under Contract No. 894790; German
Research Foundation DFG under Contracts Nos. 455635585, Collaborative Research
Center CRC 1044, FOR5327, GRK 2149; Istituto Nazionale di Fisica Nucleare,
Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470;
National Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335;
National Science and Technology fund of Mongolia; National Science Research
and Innovation Fund (NSRF) via the Program Management Unit for Human Resources
& Institutional Development, Research and Innovation of Thailand under
Contract No. B16F640076; Polish National Science Centre under Contract No.
2019/35/O/ST2/02907; The Swedish Research Council; U. S. Department of Energy
under Contract No. DE-FG02-05ER41374.

## References

  * (1) S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985).
  * (2) M. Ablikim et al. (BES Collaboration), Phys. Lett. B 660, 315 (2008).
  * (3) B. Aubert et al. (BaBar Collaboration), Phys. Rev. Lett. 95, 142001 (2005).
  * (4) B. Aubert et al. (BaBar Collaboration), Phys. Rev. Lett. 98, 212001 (2007).
  * (5) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 104, 052012 (2021).
  * (6) G. Pakhlova et al. (Belle Collaboration), Phys. Rev. Lett. 101, 172001 (2008).
  * (7) V. Kher and A. K. Rai, Chin. Phys. C 42, no.8, 083101 (2018)
  * (8) X. K. Dong, F. K. Guo and B. S. Zou, Progr. Phys. 41, 65-93 (2021).
  * (9) T. W. Chiu et al. (TWQCD Collaboration), Phys. Rev. D 73, 094510 (2006).
  * (10) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 131, 151903 (2023)
  * (11) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 131, 211902 (2023).
  * (12) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 107, 092005 (2023)
  * (13) C. P. Shen et al. (Belle Collaboration), Phys. Rev. Lett. 104, 112004 (2010).
  * (14) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 100, 032005 (2019).
  * (15) M. Ablikim et al. (BESIII Collaboration), Phys. Lett. B 804, 135395 (2020).
  * (16) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 106, 052012 (2022).
  * (17) N. Brambilla, W. K. Lai, A. Mohapatra and A. Vairo, Phys. Rev. D 107, 054034 (2023).
  * (18) R. Q. Qian and X. Liu, Phys. Rev. D 108, 094046 (2023).
  * (19) Q. F. Lü and Y. B. Dong, Phys. Rev. D 94, 074007 (2016).
  * (20) F. K. Guo, C. Hanhart and U. G. Meissner, Phys. Lett. B 665, 26-29 (2008).
  * (21) M. Ablikim et al. (BESIII Collaboration), Chin. Phys. C 46, 113003 (2022);
  * (22) M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum. Meth. A 614, 345 (2010).
  * (23) C. H. Yu et al., Proceedings of IPAC2016, Busan, Korea, 2016.
  * (24) X. Li et et al., Radiat. Detect. Technol. Methods 1, 13 (2017).
  * (25) Y. X. Guo et al., Radiat. Detect. Technol. Methods 1, 15 (2017).
  * (26) S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum. Meth. A 506, 250 (2003).
  * (27) K. X. Huang, et al., Nucl. Sci. Tech. 33, 142 (2022).
  * (28) S. Jadach, B. F. L. Ward, and Z. Was, Phys. Rev. D 63, 113009 (2001); Comput. Phys. Commun. 130, 260 (2000).
  * (29) D. J. Lange, Nucl. Instrum. Meth. A 462, 152 (2001); R. G. Ping, Chin. Phys. C 32, 599 (2008).
  * (30) R. L. Workman et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  * (31) J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang, and Y. S. Zhu, Phys. Rev. D 62, 034003 (2000).
  * (32) E. Richter-Was, Phys. Lett. B 303, 163 (1993).
  * (33) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 104, 052008 (2021).
  * (34) M. Ablikim et al. (BESIII Collaboration), JHEP 09, 107 (2022).
  * (35) Giovanni Punzi, arXiv:physics/0308063
  * (36) S. Actis et al. (Working Group on Radiative Corrections and Monte Carlo Generators for Low Energies), Eur. Phys. J. C 66, 585-686 (2010).
  * (37) E. A. Kuraev and V. S. Fadin, Sov. J. Nucl. Phys. 41, 466 (1985).
  * (38) K. Stenson, arXiv:physics/0605236.
  * (39) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 97, 072004 (2018).
  * (40) M. Ablikim et al. (BESIII Collaboration),  Eur. Phys. J. C 76, 369 (2016).
  * (41) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 87, 012002 (2013).