Amplitude Analysis of the Decays D^0→π^+π^-π^+π^- and
π^+π^-π^0π^0
BESIII Collaboration,M. Ablikim,M. N. Achasov,P. Adlarson,O. Afedulidis,X. C. Ai,R. Aliberti,A. Amoroso,Q. An,Y. Bai,O. Bakina,I. Balossino,Y. Ban,H. -R. Bao,V. Batozskaya,K. Begzsuren,N. Berger,M. Berlowski,M. Bertani,D. Bettoni,F. Bianchi,E. Bianco,A. Bortone,I. Boyko,R. A. Briere,A. Brueggemann,H. Cai,X. Cai,A. Calcaterra,G. F. Cao,N. Cao,S. A. Cetin,J. F. Chang,W. L. Chang,G. R. Che,G. Chelkov,C. Chen,C. H. Chen,Chao Chen,G. Chen,H. S. Chen,M. L. Chen,S. J. Chen,S. L. Chen,S. M. Chen,T. Chen,X. R. Chen,X. T. Chen,Y. B. Chen,Y. Q. Chen,Z. J. Chen,Z. Y. Chen,S. K. Choi,X. Chu,G. Cibinetto,F. Cossio,J. J. Cui,H. L. Dai,J. P. Dai,A. Dbeyssi,R. E. de Boer,D. Dedovich,C. Q. Deng,Z. Y. Deng,A. Denig,I. Denysenko,M. Destefanis,F. De Mori,B. Ding,X. X. Ding,Y. Ding,Y. Ding,J. Dong,L. Y. Dong,M. Y. Dong,X. Dong,M. C. Du,S. X. Du,Z. H. Duan,P. Egorov,Y. H. Fan,J. Fang,J. Fang,S. S. Fang,W. X. Fang,Y. Fang,Y. Q. Fang,R. Farinelli,L. Fava,F. Feldbauer,G. Felici,C. Q. Feng,J. H. Feng,Y. T. Feng,K. Fischer,M. Fritsch,C. D. Fu,J. L. Fu,Y. W. Fu,H. Gao,Y. N. Gao,Yang Gao,S. Garbolino,I. Garzia,P. T. Ge,Z. W. Ge,C. Geng,E. M. Gersabeck,A. Gilman,K. Goetzen,L. Gong,W. X. Gong,W. Gradl,S. Gramigna,M. Greco,M. H. Gu,Y. T. Gu,C. Y. Guan,Z. L. Guan,A. Q. Guo,L. B. Guo,M. J. Guo,R. P. Guo,Y. P. Guo,A. Guskov,J. Gutierrez,K. L. Han,T. T. Han,X. Q. Hao,F. A. Harris,K. K. He,K. L. He,F. H. Heinsius,C. H. Heinz,Y. K. Heng,C. Herold,T. Holtmann,P. C. Hong,G. Y. Hou,X. T. Hou,Y. R. Hou,Z. L. Hou,B. Y. Hu,H. M. Hu,J. F. Hu,T. Hu,Y. Hu,G. S. Huang,K. X. Huang,L. Q. Huang,X. T. Huang,Y. P. Huang,T. Hussain,F. Hölzken,N Hüsken,N. in der Wiesche,M. Irshad,J. Jackson,S. Janchiv,J. H. Jeong,Q. Ji,Q. P. Ji,W. Ji,X. B. Ji,X. L. Ji,Y. Y. Ji,X. Q. Jia,Z. K. Jia,D. Jiang,H. B. Jiang,P. C. Jiang,S. S. Jiang,T. J. Jiang,X. S. Jiang,Y. Jiang,J. B. Jiao,J. K. Jiao,Z. Jiao,S. Jin,Y. Jin,M. Q. Jing,X. M. Jing,T. Johansson,S. Kabana,N. Kalantar-Nayestanaki,X. L. Kang,X. S. Kang,M. Kavatsyuk,B. C. Ke,V. Khachatryan,A. Khoukaz,R. Kiuchi,O. B. Kolcu,B. Kopf,M. Kuessner,X. Kui,A. Kupsc,W. Kühn,J. J. Lane,P. Larin,L. Lavezzi,T. T. Lei,Z. H. Lei,H. Leithoff,M. Lellmann,T. Lenz,C. Li,C. Li,C. H. Li,Cheng Li,D. M. Li,F. Li,G. Li,H. Li,H. B. Li,H. J. Li,H. N. Li,Hui Li,J. R. Li,J. S. Li,Ke Li,L. J Li,L. K. Li,Lei Li,M. H. Li,P. R. Li,Q. M. Li,Q. X. Li,R. Li,S. X. Li,T. Li,W. D. Li,W. G. Li,X. Li,X. H. Li,X. L. Li,Xiaoyu Li,Y. G. Li,Z. J. Li,Z. X. Li,C. Liang,H. Liang,H. Liang,Y. F. Liang,Y. T. Liang,G. R. Liao,L. Z. Liao,Y. P. Liao,J. Libby,A. Limphirat,D. X. Lin,T. Lin,B. J. Liu,B. X. Liu,C. Liu,C. X. Liu,F. H. Liu,Fang Liu,Feng Liu,G. M. Liu,H. Liu,H. B. Liu,H. M. Liu,Huanhuan Liu,Huihui Liu,J. B. Liu,J. Y. Liu,K. Liu,K. Y. Liu,Ke Liu,L. Liu,L. C. Liu,Lu Liu,M. H. Liu,P. L. Liu,Q. Liu,S. B. Liu,T. Liu,W. K. Liu,W. M. Liu,X. Liu,X. Liu,Y. Liu,Y. Liu,Y. B. Liu,Z. A. Liu,Z. D. Liu,Z. Q. Liu,X. C. Lou,F. X. Lu,H. J. Lu,J. G. Lu,X. L. Lu,Y. Lu,Y. P. Lu,Z. H. Lu,C. L. Luo,M. X. Luo,T. Luo,X. L. Luo,X. R. Lyu,Y. F. Lyu,F. C. Ma,H. Ma,H. L. Ma,J. L. Ma,L. L. Ma,M. M. Ma,Q. M. Ma,R. Q. Ma,X. T. Ma,X. Y. Ma,Y. Ma,Y. M. Ma,F. E. Maas,M. Maggiora,S. Malde,A. Mangoni,Y. J. Mao,Z. P. Mao,S. Marcello,Z. X. Meng,J. G. Messchendorp,G. Mezzadri,H. Miao,T. J. Min,R. E. Mitchell,X. H. Mo,B. Moses,N. Yu. Muchnoi,J. Muskalla,Y. Nefedov,F. Nerling,I. B. Nikolaev,Z. Ning,S. Nisar,Q. L. Niu,W. D. Niu,Y. Niu,S. L. Olsen,Q. Ouyang,S. Pacetti,X. Pan,Y. Pan,A. Pathak,P. Patteri,Y. P. Pei,M. Pelizaeus,H. P. Peng,Y. Y. Peng,K. Peters,J. L. Ping,R. G. Ping,S. Plura,V. Prasad,F. Z. Qi,H. Qi,H. R. Qi,M. Qi,T. Y. Qi,S. Qian,W. B. Qian,C. F. Qiao,J. J. Qin,L. Q. Qin,X. S. Qin,Z. H. Qin,J. F. Qiu,S. Q. Qu,Z. H. Qu,C. F. Redmer,K. J. Ren,A. Rivetti,M. Rolo,G. Rong,Ch. Rosner,S. N. Ruan,N. Salone,A. Sarantsev,Y. Schelhaas,K. Schoenning,M. Scodeggio,K. Y. Shan,W. Shan,X. Y. Shan,J. F. Shangguan,L. G. Shao,M. Shao,C. P. Shen,H. F. Shen,W. H. Shen,X. Y. Shen,B. A. Shi,H. C. Shi,J. L. Shi,J. Y. Shi,Q. Q. Shi,R. S. Shi,S. Y. Shi,X. Shi,X. D. Shi,J. J. Song,T. Z. Song,W. M. Song,Y. J. Song,Y. X. Song,S. Sosio,S. Spataro,F. Stieler,Y. J. Su,G. B. Sun,G. X. Sun,H. Sun,H. K. Sun,J. F. Sun,K. Sun,L. Sun,S. S. Sun,T. Sun,W. Y. Sun,Y. Sun,Y. J. Sun,Y. Z. Sun,Z. Q. Sun,Z. T. Sun,C. J. Tang,G. Y. Tang,J. Tang,Y. A. Tang,L. Y. Tao,Q. T. Tao,M. Tat,J. X. Teng,V. Thoren,W. H. Tian,Y. Tian,Z. F. Tian,I. Uman,Y. Wan,S. J. Wang,B. Wang,B. L. Wang,Bo Wang,D. Y. Wang,F. Wang,H. J. Wang,J. P. Wang,K. Wang,L. L. Wang,M. Wang,Meng Wang,N. Y. Wang,S. Wang,S. Wang,T. Wang,T. J. Wang,W. Wang,W. Wang,W. P. Wang,X. Wang,X. F. Wang,X. J. Wang,X. L. Wang,X. N. Wang,Y. Wang,Y. D. Wang,Y. F. Wang,Y. L. Wang,Y. N. Wang,Y. Q. Wang,Yaqian Wang,Yi Wang,Z. Wang,Z. L. Wang,Z. Y. Wang,Ziyi Wang,D. Wei,D. H. Wei,F. Weidner,S. P. Wen,Y. R. Wen,U. Wiedner,G. Wilkinson,M. Wolke,L. Wollenberg,C. Wu,J. F. Wu,L. H. Wu,L. J. Wu,X. Wu,X. H. Wu,Y. Wu,Y. H. Wu,Y. J. Wu,Z. Wu,L. Xia,X. M. Xian,B. H. Xiang,T. Xiang,D. Xiao,G. Y. Xiao,S. Y. Xiao,Y. L. Xiao,Z. J. Xiao,C. Xie,X. H. Xie,Y. Xie,Y. G. Xie,Y. H. Xie,Z. P. Xie,T. Y. Xing,C. F. Xu,C. J. Xu,G. F. Xu,H. Y. Xu,Q. J. Xu,Q. N. Xu,W. Xu,W. L. Xu,X. P. Xu,Y. C. Xu,Z. P. Xu,Z. S. Xu,F. Yan,L. Yan,W. B. Yan,W. C. Yan,X. Q. Yan,H. J. Yang,H. L. Yang,H. X. Yang,Tao Yang,Y. Yang,Y. F. Yang,Y. X. Yang,Yifan Yang,Z. W. Yang,Z. P. Yao,M. Ye,M. H. Ye,J. H. Yin,Z. Y. You,B. X. Yu,C. X. Yu,G. Yu,J. S. Yu,T. Yu,X. D. Yu,C. Z. Yuan,J. Yuan,L. Yuan,S. C. Yuan,Y. Yuan,Z. Y. Yuan,C. X. Yue,A. A. Zafar,F. R. Zeng,S. H. Zeng,X. Zeng,Y. Zeng,Y. J. Zeng,Y. J. Zeng,X. Y. Zhai,Y. C. Zhai,Y. H. Zhan,A. Q. Zhang,B. L. Zhang,B. X. Zhang,D. H. Zhang,G. Y. Zhang,H. Zhang,H. C. Zhang,H. H. Zhang,H. H. Zhang,H. Q. Zhang,H. Y. Zhang,J. Zhang,J. Zhang,J. J. Zhang,J. L. Zhang,J. Q. Zhang,J. W. Zhang,J. X. Zhang,J. Y. Zhang,J. Z. Zhang,Jianyu Zhang,L. M. Zhang,Lei Zhang,P. Zhang,Q. Y. Zhang,Shuihan Zhang,Shulei Zhang,X. D. Zhang,X. M. Zhang,X. Y. Zhang,Y. Zhang,Y. T. Zhang,Y. H. Zhang,Y. M. Zhang,Yan Zhang,Yao Zhang,Z. D. Zhang,Z. H. Zhang,Z. L. Zhang,Z. Y. Zhang,Z. Y. Zhang,G. Zhao,J. Y. Zhao,J. Z. Zhao,Lei Zhao,Ling Zhao,M. G. Zhao,R. P. Zhao,S. J. Zhao,Y. B. Zhao,Y. X. Zhao,Z. G. Zhao,A. Zhemchugov,B. Zheng,J. P. Zheng,W. J. Zheng,Y. H. Zheng,B. Zhong,X. Zhong,H. Zhou,J. Y. Zhou,L. P. Zhou,X. Zhou,X. K. Zhou,X. R. Zhou,X. Y. Zhou,Y. Z. Zhou,J. Zhu,K. Zhu,K. J. Zhu,L. Zhu,L. X. Zhu,S. H. Zhu,S. Q. Zhu,T. J. Zhu,W. J. Zhu,Y. C. Zhu,Z. A. Zhu,J. H. Zou,J. Zu
arxiv（2023）
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摘要
Using e^+e^- annihilation data corresponding to an integrated luminosity of
2.93 fb^-1 taken at the center-of-mass energy √(s)=3.773 GeV with
the BESIII detector, a joint amplitude analysis is performed on the decays
D^0→π^+π^-π^+π^- and D^0→π^+π^-π^0π^0(non-η). The
fit fractions of individual components are obtained, and large interferences
among the dominant components of D^0→ a_1(1260)π,
D^0→π(1300)π, D^0→ρ(770)ρ(770) and
D^0→2(ππ)_S are found in both channels. With the obtained amplitude
model, the CP-even fractions of D^0→π^+π^-π^+π^- and
D^0→π^+π^-π^0π^0(non-η) are determined to be (75.2±1.1_
stat.±1.5_ syst.)% and (68.9±1.5_ stat.± 2.4_
syst.)%, respectively. The branching fractions of D^0→π^+π^-π^+π^- and D^0→π^+π^-π^0π^0(non-η) are measured
to be (0.688±0.010_ stat.± 0.010_ syst.)% and
(0.951±0.025_ stat.± 0.021_ syst.)%, respectively. The
amplitude analysis provides an important model for binning strategy in the
measurements of the strong phase parameters of D^0 → 4π when used to
determine the CKM angle γ (ϕ_3) via the B^-→ D K^- decay.
