Partial wave analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mo stretchy="false">→</

Based on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>12.0</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:msup> <a:mi>fb</a:mi> <a:mrow> <a:mo>−</a:mo> <a:mn>1</a:mn> </a:mrow> </a:msup> </a:mrow> </a:math> of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>e</c:mi> <c:mo>+</c:mo> </c:msup> <c:msup> <c:mi>e</c:mi> <c:mo>−</c:mo> </c:msup> </c:math> collision data samples collected by the BESIII detector at center-of-mass energies from 4.1271 to 4.3583 GeV, a partial wave analysis is performed for the process <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>e</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>e</e:mi> <e:mo>−</e:mo> </e:msup> <e:mo stretchy="false">→</e:mo> <e:msup> <e:mi>π</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>π</e:mi> <e:mo>−</e:mo> </e:msup> <e:mi>J</e:mi> <e:mo>/</e:mo> <e:mi>ψ</e:mi> </e:math> . The cross sections for the subprocesses <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>e</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>e</h:mi> <h:mo>−</h:mo> </h:msup> <h:mo stretchy="false">→</h:mo> <h:msup> <h:mi>π</h:mi> <h:mo>+</h:mo> </h:msup> <h:msub> <h:mi>Z</h:mi> <h:mi>c</h:mi> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mn>3900</h:mn> <h:msup> <h:mo stretchy="false">)</h:mo> <h:mo>−</h:mo> </h:msup> <h:mo>+</h:mo> <h:mi mathvariant="normal">c</h:mi> <h:mo>.</h:mo> <h:mi mathvariant="normal">c</h:mi> <h:mo>.</h:mo> <h:mo stretchy="false">→</h:mo> <h:msup> <h:mi>π</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>π</h:mi> <h:mo>−</h:mo> </h:msup> <h:mi>J</h:mi> <h:mo>/</h:mo> <h:mi>ψ</h:mi> </h:math> , <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>f</p:mi> <p:mn>0</p:mn> </p:msub> <p:mo stretchy="false">(</p:mo> <p:mn>980</p:mn> <p:mo stretchy="false">)</p:mo> <p:mo stretchy="false">(</p:mo> <p:mo stretchy="false">→</p:mo> <p:msup> <p:mi>π</p:mi> <p:mo>+</p:mo> </p:msup> <p:msup> <p:mi>π</p:mi> <p:mo>−</p:mo> </p:msup> <p:mo stretchy="false">)</p:mo> <p:mi>J</p:mi> <p:mo>/</p:mo> <p:mi>ψ</p:mi> </p:math> , and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mo stretchy="false">(</w:mo> <w:msup> <w:mi>π</w:mi> <w:mo>+</w:mo> </w:msup> <w:msup> <w:mi>π</w:mi> <w:mo>−</w:mo> </w:msup> <w:msub> <w:mo stretchy="false">)</w:mo> <w:mrow> <w:mi mathvariant="normal">S</w:mi> <w:mtext>−</w:mtext> <w:mrow> <w:mi>wave</w:mi> </w:mrow> </w:mrow> </w:msub> <w:mi>J</w:mi> <w:mo>/</w:mo> <w:mi>ψ</w:mi> </w:math> are measured for the first time. The mass and width of the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msub> <bb:mi>Z</bb:mi> <bb:mi>c</bb:mi> </bb:msub> <bb:mo stretchy="false">(</bb:mo> <bb:mn>3900</bb:mn> <bb:msup> <bb:mo stretchy="false">)</bb:mo> <bb:mo>±</bb:mo> </bb:msup> </bb:math> are determined to be <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mn>3884.6</fb:mn> <fb:mo>±</fb:mo> <fb:mn>0.7</fb:mn> <fb:mo>±</fb:mo> <fb:mn>3.3</fb:mn> <fb:mtext> </fb:mtext> <fb:mtext> </fb:mtext> <fb:mi>MeV</fb:mi> <fb:mo>/</fb:mo> <fb:msup> <fb:mi>c</fb:mi> <fb:mn>2</fb:mn> </fb:msup> </fb:math> and <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mn>37.2</hb:mn> <hb:mo>±</hb:mo> <hb:mn>1.3</hb:mn> <hb:mo>±</hb:mo> <hb:mn>6.6</hb:mn> <hb:mtext> </hb:mtext> <hb:mtext> </hb:mtext> <hb:mi>MeV</hb:mi> </hb:math> , respectively. The first errors are statistical and the second systematic. The final state <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mo stretchy="false">(</jb:mo> <jb:msup> <jb:mi>π</jb:mi> <jb:mo>+</jb:mo> </jb:msup> <jb:msup> <jb:mi>π</jb:mi> <jb:mo>−</jb:mo> </jb:msup> <jb:msub> <jb:mo stretchy="false">)</jb:mo> <jb:mrow> <jb:mi mathvariant="normal">S</jb:mi> <jb:mtext>−</jb:mtext> <jb:mrow> <jb:mi>wave</jb:mi> </jb:mrow> </jb:mrow> </jb:msub> <jb:mi>J</jb:mi> <jb:mo>/</jb:mo> <jb:mi>ψ</jb:mi> </jb:math> dominates the process <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msup> <ob:mi>e</ob:mi> <ob:mo>+</ob:mo> </ob:msup> <ob:msup> <ob:mi>e</ob:mi> <ob:mo>−</ob:mo> </ob:msup> <ob:mo stretchy="false">→</ob:mo> <ob:msup> <ob:mi>π</ob:mi> <ob:mo>+</ob:mo> </ob:msup> <ob:msup> <ob:mi>π</ob:mi> <ob:mo>−</ob:mo> </ob:msup> <ob:mi>J</ob:mi> <ob:mo>/</ob:mo> <ob:mi>ψ</ob:mi> </ob:math> . By analyzing the cross sections of <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:msup> <rb:mi>π</rb:mi> <rb:mo>±</rb:mo> </rb:msup> <rb:msub> <rb:mi>Z</rb:m

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Journal
Physical review. D/Physical review. D.
Published
2025-11-20
DOI
https://doi.org/10.1103/f94z-snbh
Primary Topic
Quantum Chromodynamics and Particle Interactions
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article
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article

Partial wave analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mo stretchy="false">→</

T. Xiang, J. Y. Zhou, S. L. Olsen, C. F. Qiao et al.
Physical review. D/Physical review. D.
Quantum Chromodynamics and Particle Interactions
article

Partial wave analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mo stretchy="false">→</

T. Xiang, J. Y. Zhou, S. L. Olsen, C. F. Qiao, J. J. Zhang, X. Dong, J. Yu, J. Jackson, T. Li, A. Kupść, F. Stieler, H. L., S. B. Liu, Z. Y. Wang, A. Amoroso, T. Y. Xing, Z. Q. Liu, T. T. Han, J. K. Jiao, X. Y. Zhang, X. H. Li, J. H. Jeong, Y. J. Zeng, T. Johansson, B. X. Zhang, J. Zhang, X. Y. Shan, N. Berger, T. J. Zhu, C. Z. Yuan, Y. Hu, H. Zhang, J. Zhu, Y. P. Pei, Q. Liu, L. Liu, T. J. Jiang, C. Z. Yuan, J. L. Shi, A. Guskov, H. Lu, I. B. Nikolaev, R. Q., P. C. Hong, Y. N. Wang, S. Y. Shi, J. Libby, H. Q. Zhang, B. L. Zhang, X. D. Zhang, F. Cossio, W. Gradl, L. J. Li, Y. T. Feng, X. R. Chen, F. Hanisch, Y. J. Song, Yaqian Wang, X. T. Huang, Y. T. Liang, S. L. Hu, Yi Wang, H. B. Jiang, C. P. Shen, J. B. Liu, W. Wang, A. Sarantsev, X. R. Lyu, A. Q. Zhang, Y. Schelhaas, L. Y. Tao, S. Kabana, Lei Zhao, B. A. Shi, S. Pacetti, W. G. Li, Z. L. Wang, X. F. Wang, X. M. Xian, M. Y. Dong, W. M. Song, H. L., W. P. Wang, Q. Y. Zhang, Z. L. Hou, Y. X. Zhao, Ye Ding, T. Holtmann, P. Egorov, J. 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An, Bo Wang
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Abstract

Based on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>12.0</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:msup> <a:mi>fb</a:mi> <a:mrow> <a:mo>−</a:mo> <a:mn>1</a:mn> </a:mrow> </a:msup> </a:mrow> </a:math> of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>e</c:mi> <c:mo>+</c:mo> </c:msup> <c:msup> <c:mi>e</c:mi> <c:mo>−</c:mo> </c:msup> </c:math> collision data samples collected by the BESIII detector at center-of-mass energies from 4.1271 to 4.3583 GeV, a partial wave analysis is performed for the process <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>e</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>e</e:mi> <e:mo>−</e:mo> </e:msup> <e:mo stretchy="false">→</e:mo> <e:msup> <e:mi>π</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>π</e:mi> <e:mo>−</e:mo> </e:msup> <e:mi>J</e:mi> <e:mo>/</e:mo> <e:mi>ψ</e:mi> </e:math> . The cross sections for the subprocesses <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>e</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>e</h:mi> <h:mo>−</h:mo> </h:msup> <h:mo stretchy="false">→</h:mo> <h:msup> <h:mi>π</h:mi> <h:mo>+</h:mo> </h:msup> <h:msub> <h:mi>Z</h:mi> <h:mi>c</h:mi> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mn>3900</h:mn> <h:msup> <h:mo stretchy="false">)</h:mo> <h:mo>−</h:mo> </h:msup> <h:mo>+</h:mo> <h:mi mathvariant="normal">c</h:mi> <h:mo>.</h:mo> <h:mi mathvariant="normal">c</h:mi> <h:mo>.</h:mo> <h:mo stretchy="false">→</h:mo> <h:msup> <h:mi>π</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>π</h:mi> <h:mo>−</h:mo> </h:msup> <h:mi>J</h:mi> <h:mo>/</h:mo> <h:mi>ψ</h:mi> </h:math> , <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>f</p:mi> <p:mn>0</p:mn> </p:msub> <p:mo stretchy="false">(</p:mo> <p:mn>980</p:mn> <p:mo stretchy="false">)</p:mo> <p:mo stretchy="false">(</p:mo> <p:mo stretchy="false">→</p:mo> <p:msup> <p:mi>π</p:mi> <p:mo>+</p:mo> </p:msup> <p:msup> <p:mi>π</p:mi> <p:mo>−</p:mo> </p:msup> <p:mo stretchy="false">)</p:mo> <p:mi>J</p:mi> <p:mo>/</p:mo> <p:mi>ψ</p:mi> </p:math> , and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mo stretchy="false">(</w:mo> <w:msup> <w:mi>π</w:mi> <w:mo>+</w:mo> </w:msup> <w:msup> <w:mi>π</w:mi> <w:mo>−</w:mo> </w:msup> <w:msub> <w:mo stretchy="false">)</w:mo> <w:mrow> <w:mi mathvariant="normal">S</w:mi> <w:mtext>−</w:mtext> <w:mrow> <w:mi>wave</w:mi> </w:mrow> </w:mrow> </w:msub> <w:mi>J</w:mi> <w:mo>/</w:mo> <w:mi>ψ</w:mi> </w:math> are measured for the first time. The mass and width of the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msub> <bb:mi>Z</bb:mi> <bb:mi>c</bb:mi> </bb:msub> <bb:mo stretchy="false">(</bb:mo> <bb:mn>3900</bb:mn> <bb:msup> <bb:mo stretchy="false">)</bb:mo> <bb:mo>±</bb:mo> </bb:msup> </bb:math> are determined to be <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mn>3884.6</fb:mn> <fb:mo>±</fb:mo> <fb:mn>0.7</fb:mn> <fb:mo>±</fb:mo> <fb:mn>3.3</fb:mn> <fb:mtext> </fb:mtext> <fb:mtext> </fb:mtext> <fb:mi>MeV</fb:mi> <fb:mo>/</fb:mo> <fb:msup> <fb:mi>c</fb:mi> <fb:mn>2</fb:mn> </fb:msup> </fb:math> and <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mn>37.2</hb:mn> <hb:mo>±</hb:mo> <hb:mn>1.3</hb:mn> <hb:mo>±</hb:mo> <hb:mn>6.6</hb:mn> <hb:mtext> </hb:mtext> <hb:mtext> </hb:mtext> <hb:mi>MeV</hb:mi> </hb:math> , respectively. The first errors are statistical and the second systematic. The final state <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mo stretchy="false">(</jb:mo> <jb:msup> <jb:mi>π</jb:mi> <jb:mo>+</jb:mo> </jb:msup> <jb:msup> <jb:mi>π</jb:mi> <jb:mo>−</jb:mo> </jb:msup> <jb:msub> <jb:mo stretchy="false">)</jb:mo> <jb:mrow> <jb:mi mathvariant="normal">S</jb:mi> <jb:mtext>−</jb:mtext> <jb:mrow> <jb:mi>wave</jb:mi> </jb:mrow> </jb:mrow> </jb:msub> <jb:mi>J</jb:mi> <jb:mo>/</jb:mo> <jb:mi>ψ</jb:mi> </jb:math> dominates the process <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msup> <ob:mi>e</ob:mi> <ob:mo>+</ob:mo> </ob:msup> <ob:msup> <ob:mi>e</ob:mi> <ob:mo>−</ob:mo> </ob:msup> <ob:mo stretchy="false">→</ob:mo> <ob:msup> <ob:mi>π</ob:mi> <ob:mo>+</ob:mo> </ob:msup> <ob:msup> <ob:mi>π</ob:mi> <ob:mo>−</ob:mo> </ob:msup> <ob:mi>J</ob:mi> <ob:mo>/</ob:mo> <ob:mi>ψ</ob:mi> </ob:math> . By analyzing the cross sections of <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:msup> <rb:mi>π</rb:mi> <rb:mo>±</rb:mo> </rb:msup> <rb:msub> <rb:mi>Z</rb:m

Physical review. D/Physical review. D.Vol. 112(9)
University of Science and Technology Liaoning (CN), University of Hawaiʻi at Mānoa (US), Liaoning University (CN), Università degli Studi del Piemonte Orientale “Amedeo Avogadro” (IT), Uppsala University (SE), University of Science and Technology of China (CN), University of Hawaii System (US), Central South University (CN), Guangxi University (CN), Nanjing Normal University (CN), Liaoning Normal University (CN), North China Electric Power University (CN), Shandong University (CN), Sun Yat-sen University (CN), COMSATS University Islamabad (PK), Hangzhou Normal University (CN), Hunan University (CN), Henan University of Science and Technology (CN), University of Groningen (NL), GSI Helmholtz Centre for Heavy Ion Research (DE), University of the Punjab (PK), Hunan Normal University (CN), Henan University (CN), Shanxi University (CN), Shanghai Jiao Tong University (CN), Yantai University (CN), University of Tarapacá (CL), South China Normal University (CN), Yunnan University (CN), Jilin University (CN), Johannes Gutenberg University Mainz (DE), Justus-Liebig-Universität Gießen (DE), University of Ferrara (IT), Qufu Normal University (CN), Peking University (CN), Nankai University (CN), University of Münster (DE), Sichuan University (CN), Indian Institute of Technology Madras (IN), Fudan University (CN), Inner Mongolia University (CN), University of Perugia (IT), Shandong Normal University (CN), University of Manchester (GB), Guangxi Normal University (CN), China University of Geosciences (CN), Huangshan University (CN), Joint Institute for Nuclear Research (RU), University of Jinan (CN), Henan University of Technology (CN), Wuhan University (CN), Zhengzhou University (CN), Soochow University (CN), University of Oxford (GB), Central China Normal University (CN), National Centre for Nuclear Research (PL), Institute of Physics and Technology (MN), Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara (IT), Helmholtz Institute Mainz (DE), Indiana University Bloomington (US), Istinye University (TR), Hubei University of Automotive Technology (CN), Siberian Branch of the Russian Academy of Sciences (RU), Institute of Modern Physics (CN), Jilin Medical University (CN), Institute of High Energy Physics (CN), Shanxi University of Traditional Chinese Medicine (CN), Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati (IT), Piedmont University (US), Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (IT), University of Chinese Academy of Sciences (CN), Hebei University (CN), Budker Institute of Nuclear Physics (RU), China Center of Advanced Science and Technology (CN), University of Turin (IT), Indiana University (US), Chung-Ang University (KR), Near East University (CY), Carnegie Mellon University (US), Henan Normal University (CN), Zhejiang University (CN), Lanzhou University (CN), Southeast University (CN), Renmin University of China (CN), Suranaree University of Technology (TH), Beihang University (CN), Nanjing University (CN), Ruhr University Bochum (DE), University of South China (CN), Shanxi Normal University (CN), Tsinghua University (CN)
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