Open Access

Novel measurement of the strong-phase difference between $D^{0} \to K^{-} π^{+}$ and ${\bar{D}}^{0} \to K^{-} π^{+}$ decays using $C$ -even and $C$ -odd quantum-correlated $D \bar{D}$ pairs

M. Ablikim¹, M. N. Achasov^4,c, P. Adlarson⁷⁷, X. C. Ai⁸², R. Aliberti³⁶, A. Amoroso^76a,76c, Q. An^73,59,a, Y. Bai⁵⁸, O. Bakina³⁷ et al. (BESIII Collaboration)

O. Bakina³⁷, Y. Ban^47,h, H.-R. Bao⁶⁵, V. Batozskaya^1,45, K. Begzsuren³³, N. Berger³⁶, M. Berlowski⁴⁵, M. Bertani^29a, D. Bettoni^30a, F. Bianchi^76a,76c, E. Bianco^76a,76c, A. Bortone^76a,76c, I. Boyko³⁷, R. A. Briere⁵, A. Brueggemann⁷⁰, H. Cai⁷⁸, M. H. Cai^39,k,l, X. Cai^1,59, A. Calcaterra^29a, G. F. Cao^1,65, N. Cao^1,65, S. A. Cetin^63a, X. Y. Chai^47,h, J. F. Chang^1,59, G. R. Che⁴⁴, Y. Z. Che^1,59,65, C. H. Chen⁹, Chao Chen⁵⁶, G. Chen¹, H. S. Chen^1,65, H. Y. Chen²¹, M. L. Chen^1,59,65, S. J. Chen⁴³, S. L. Chen⁴⁶, S. M. Chen⁶², T. Chen^1,65, X. R. Chen^32,65, X. T. Chen^1,65, X. Y. Chen^12,g, Y. B. Chen^1,59, Y. Q. Chen³⁵, Y. Q. Chen¹⁶, Z. Chen²⁵, Z. J. Chen^26,i, Z. K. Chen⁶⁰, S. K. Choi¹⁰, X. Chu^12,g, G. Cibinetto^30a, F. Cossio^76c, J. Cottee-Meldrum⁶⁴, J. J. Cui⁵¹, H. L. Dai^1,59, J. P. Dai⁸⁰, A. Dbeyssi¹⁹, R. E. de Boer³, D. Dedovich³⁷, C. Q. Deng⁷⁴, Z. Y. Deng¹, A. Denig³⁶, I. Denysenko³⁷, M. Destefanis^76a,76c, F. De Mori^76a,76c, B. Ding^68,1, X. X. Ding^47,h, Y. Ding³⁵, Y. Ding⁴¹, Y. X. Ding³¹, J. Dong^1,59, L. Y. Dong^1,65, M. Y. Dong^1,59,65, X. Dong⁷⁸, M. C. Du¹, S. X. Du⁸², S. X. Du^12,g, Y. Y. Duan⁵⁶, P. Egorov^37,b, G. F. Fan⁴³, J. J. Fan²⁰, Y. H. Fan⁴⁶, J. Fang^1,59, J. Fang⁶⁰, S. S. Fang^1,65, W. X. Fang¹, Y. Q. Fang^1,59, R. Farinelli^30a, L. Fava^76b,76c, F. Feldbauer³, G. Felici^29a, C. Q. Feng^73,59, J. H. Feng¹⁶, L. Feng^39,k,l, Q. X. Feng^39,k,l, Y. T. Feng^73,59, M. Fritsch³, C. D. Fu¹, J. L. Fu⁶⁵, Y. W. Fu^1,65, H. Gao⁶⁵, X. B. Gao⁴², Y. Gao^73,59, Y. N. Gao²⁰, Y. N. Gao^47,h, Y. Y. Gao³¹, S. Garbolino^76c, I. Garzia^30a,30b, L. Ge⁵⁸, P. T. Ge²⁰, Z. W. Ge⁴³, C. Geng⁶⁰, E. M. Gersabeck⁶⁹, A. Gilman⁷¹, K. Goetzen¹³, J. D. Gong³⁵, L. Gong⁴¹, W. X. Gong^1,59, W. Gradl³⁶, S. Gramigna^30a,30b, M. Greco^76a,76c, M. H. Gu^1,59, Y. T. Gu¹⁵, C. Y. Guan^1,65, A. Q. Guo³², L. B. Guo⁴², M. J. Guo⁵¹, R. P. Guo⁵⁰, Y. P. Guo^12,g, A. Guskov^37,b, J. Gutierrez²⁸, K. L. Han⁶⁵, T. T. Han¹, F. Hanisch³, K. D. Hao^73,59, X. Q. Hao²⁰, F. A. Harris⁶⁷, K. K. He⁵⁶, K. L. He^1,65, F. H. Heinsius³, C. H. Heinz³⁶, Y. K. Heng^1,59,65, C. Herold⁶¹, P. C. Hong³⁵, G. Y. Hou^1,65, X. T. Hou^1,65, Y. R. Hou⁶⁵, Z. L. Hou¹, H. M. Hu^1,65, J. F. Hu^57,j, Q. P. Hu^73,59, S. L. Hu^12,g, T. Hu^1,59,65, Y. Hu¹, Z. M. Hu⁶⁰, G. S. Huang^73,59, K. X. Huang⁶⁰, L. Q. Huang^32,65, P. Huang⁴³, X. T. Huang⁵¹, Y. P. Huang¹, Y. S. Huang⁶⁰, T. Hussain⁷⁵, N. Hüsken³⁶, N. in der Wiesche⁷⁰, J. Jackson²⁸, Q. Ji¹, Q. P. Ji²⁰, W. Ji^1,65, X. B. Ji^1,65, X. L. Ji^1,59, Y. Y. Ji⁵¹, Z. K. Jia^73,59, D. Jiang^1,65, H. B. Jiang⁷⁸, P. C. Jiang^47,h, S. J. Jiang⁹, T. J. Jiang¹⁷, X. S. Jiang^1,59,65, Y. Jiang⁶⁵, J. B. Jiao⁵¹, J. K. Jiao³⁵, Z. Jiao²⁴, S. Jin⁴³, Y. Jin⁶⁸, M. Q. Jing^1,65, X. M. Jing⁶⁵, T. Johansson⁷⁷, S. Kabana³⁴, N. Kalantar-Nayestanaki⁶⁶, X. L. Kang⁹, X. S. Kang⁴¹, M. Kavatsyuk⁶⁶, B. C. Ke⁸², V. Khachatryan²⁸, A. Khoukaz⁷⁰, R. Kiuchi¹, O. B. Kolcu^63a, B. Kopf³, M. Kuessner³, X. Kui^1,65, N. Kumar²⁷, A. Kupsc^45,77, W. Kühn³⁸, Q. Lan⁷⁴, W. N. Lan²⁰, T. T. Lei^73,59, M. Lellmann³⁶, T. Lenz³⁶, C. Li⁴⁴, C. Li⁴⁸, C. H. Li⁴⁰, C. K. Li²¹, D. M. Li⁸², F. Li^1,59, G. Li¹, H. B. Li^1,65, H. J. Li²⁰, H. N. Li^57,j, Hui Li⁴⁴, J. R. Li⁶², J. S. Li⁶⁰, K. Li¹, K. L. Li^39,k,l, K. L. Li²⁰, L. J. Li^1,65, Lei Li⁴⁹, M. H. Li⁴⁴, M. R. Li^1,65, P. L. Li⁶⁵, P. R. Li^39,k,l, Q. M. Li^1,65, Q. X. Li⁵¹, R. Li^18,32, S. X. Li¹², T. Li⁵¹, T. Y. Li⁴⁴, W. D. Li^1,65, W. G. Li^1,a, X. Li^1,65, X. H. Li^73,59, X. L. Li⁵¹, X. Y. Li^1,8, X. Z. Li⁶⁰, Y. Li²⁰, Y. G. Li^47,h, Y. P. Li³⁵, Z. J. Li⁶⁰, Z. Y. Li⁸⁰, H. Liang^73,59, Y. F. Liang⁵⁵, Y. T. Liang^32,65, G. R. Liao¹⁴, L. B. Liao⁶⁰, M. H. Liao⁶⁰, Y. P. Liao^1,65, J. Libby²⁷, A. Limphirat⁶¹, C. C. Lin⁵⁶, D. X. Lin^32,65, L. Q. Lin⁴⁰, T. Lin¹, B. J. Liu¹, B. X. Liu⁷⁸, C. Liu³⁵, C. X. Liu¹, F. Liu¹, F. H. Liu⁵⁴, Feng Liu⁶, G. M. Liu^57,j, H. Liu^39,k,l, H. B. Liu¹⁵, H. H. Liu¹, H. M. Liu^1,65, Huihui Liu²², J. B. Liu^73,59, J. J. Liu²¹, K. Liu⁷⁴, K. Liu^39,k,l, K. Y. Liu⁴¹, Ke Liu²³, L. C. Liu⁴⁴, Lu Liu⁴⁴, M. H. Liu^12,g, P. L. Liu¹, Q. Liu⁶⁵, S. B. Liu^73,59, T. Liu^12,g, W. K. Liu⁴⁴, W. M. Liu^73,59, W. T. Liu⁴⁰, X. Liu^39,k,l, X. Liu⁴⁰, X. K. Liu^39,k,l, X. L. Liu^12,g, X. Y. Liu⁷⁸, Y. Liu⁸², Y. Liu⁸², Y. Liu^39,k,l, Y. B. Liu⁴⁴, Z. A. Liu^1,59,65, Z. D. Liu⁹, Z. Q. Liu⁵¹, X. C. Lou^1,59,65, F. X. Lu⁶⁰, H. J. Lu²⁴, J. G. Lu^1,59, X. L. Lu¹⁶, Y. Lu⁷, Y. H. Lu^1,65, Y. P. Lu^1,59, Z. H. Lu^1,65, C. L. Luo⁴², J. R. Luo⁶⁰, J. S. Luo^1,65, M. X. Luo⁸¹, T. Luo^12,g, X. L. Luo^1,59, Z. Y. Lv²³, X. R. Lyu^65,p, Y. F. Lyu⁴⁴, Y. H. Lyu⁸², F. C. Ma⁴¹, H. L. Ma¹, J. L. Ma^1,65, L. L. Ma⁵¹, L. R. Ma⁶⁸, Q. M. Ma¹, R. Q. Ma^1,65, R. Y. Ma²⁰, T. Ma^73,59, X. T. Ma^1,65, X. Y. Ma^1,59, Y. M. Ma³², F. E. Maas¹⁹, I. MacKay⁷¹, M. Maggiora^76a,76c, S. Malde⁷¹, Q. A. Malik⁷⁵, H. X. Mao^39,k,l, Y. J. Mao^47,h, Z. P. Mao¹, S. Marcello^76a,76c, A. Marshall⁶⁴, F. M. Melendi^30a,30b, Y. H. Meng⁶⁵, Z. X. Meng⁶⁸, G. Mezzadri^30a, H. Miao^1,65, T. J. Min⁴³, R. E. Mitchell²⁸, X. H. Mo^1,59,65, B. Moses²⁸, N. Yu. Muchnoi^4,c, J. Muskalla³⁶, Y. Nefedov³⁷, F. Nerling^19,e, L. S. Nie²¹, I. B. Nikolaev^4,c, Z. Ning^1,59, S. Nisar^11,m, Q. L. Niu^39,k,l, W. D. Niu^12,g, C. Normand⁶⁴, S. L. Olsen^10,65, Q. Ouyang^1,59,65, S. Pacetti^29b,29c, X. Pan⁵⁶, Y. Pan⁵⁸, A. Pathak¹⁰, Y. P. Pei^73,59, M. Pelizaeus³, H. P. Peng^73,59, X. J. Peng^39,k,l, Y. Y. Peng^39,k,l, K. Peters^13,e, K. Petridis⁶⁴, J. L. Ping⁴², R. G. Ping^1,65, S. Plura³⁶, V. Prasad³⁵, F. Z. Qi¹, H. R. Qi⁶², M. Qi⁴³, S. Qian^1,59, W. B. Qian⁶⁵, C. F. Qiao⁶⁵, J. H. Qiao²⁰, J. J. Qin⁷⁴, J. L. Qin⁵⁶, L. Q. Qin¹⁴, L. Y. Qin^73,59, P. B. Qin⁷⁴, X. P. Qin^12,g, X. S. Qin⁵¹, Z. H. Qin^1,59, J. F. Qiu¹, Z. H. Qu⁷⁴, J. Rademacker⁶⁴, C. F. Redmer³⁶, A. Rivetti^76c, M. Rolo^76c, G. Rong^1,65, S. S. Rong^1,65, F. Rosini^29b,29c, Ch. Rosner¹⁹, M. Q. Ruan^1,59, N. Salone⁴⁵, A. Sarantsev^37,d, Y. Schelhaas³⁶, K. Schoenning⁷⁷, M. Scodeggio^30a, K. Y. Shan^12,g, W. Shan²⁵, X. Y. Shan^73,59, Z. J. Shang^39,k,l, J. F. Shangguan¹⁷, L. G. Shao^1,65, M. Shao^73,59, C. P. Shen^12,g, H. F. Shen^1,8, W. H. Shen⁶⁵, X. Y. Shen^1,65, B. A. Shi⁶⁵, H. Shi^73,59, J. L. Shi^12,g, J. Y. Shi¹, S. Y. Shi⁷⁴, X. Shi^1,59, H. L. Song^73,59, J. J. Song²⁰, T. Z. Song⁶⁰, W. M. Song³⁵, Y. J. Song^12,g, Y. X. Song^47,h,n, S. Sosio^76a,76c, S. Spataro^76a,76c, F. Stieler³⁶, S. S. Su⁴¹, Y. J. Su⁶⁵, G. B. Sun⁷⁸, G. X. Sun¹, H. Sun⁶⁵, H. K. Sun¹, J. F. Sun²⁰, K. Sun⁶², L. Sun⁷⁸, S. S. Sun^1,65, T. Sun^52,f, Y. C. Sun⁷⁸, Y. H. Sun³¹, Y. J. Sun^73,59, Y. Z. Sun¹, Z. Q. Sun^1,65, Z. T. Sun⁵¹, C. J. Tang⁵⁵, G. Y. Tang¹, J. Tang⁶⁰, J. J. Tang^73,59, L. F. Tang⁴⁰, Y. A. Tang⁷⁸, L. Y. Tao⁷⁴, M. Tat⁷¹, J. X. Teng^73,59, J. Y. Tian^73,59, W. H. Tian⁶⁰, Y. Tian³², Z. F. Tian⁷⁸, I. Uman^63b, B. Wang⁶⁰, B. Wang¹, Bo Wang^73,59, C. Wang^39,k,l, C. Wang²⁰, Cong Wang²³, D. Y. Wang^47,h, H. J. Wang^39,k,l, J. J. Wang⁷⁸, K. Wang^1,59, L. L. Wang¹, L. W. Wang³⁵, M. Wang^73,59, M. Wang⁵¹, N. Y. Wang⁶⁵, S. Wang^12,g, T. Wang^12,g, T. J. Wang⁴⁴, W. Wang⁶⁰, W. Wang⁷⁴, W. P. Wang^36,59,73,o, X. Wang^47,h, X. F. Wang^39,k,l, X. J. Wang⁴⁰, X. L. Wang^12,g, X. N. Wang^1,65, Y. Wang⁶², Y. D. Wang⁴⁶, Y. F. Wang^1,8,65, Y. H. Wang^39,k,l, Y. J. Wang^73,59, Y. L. Wang²⁰, Y. N. Wang⁷⁸, Y. Q. Wang¹, Yaqian Wang¹⁸, Yi Wang⁶², Yuan Wang^18,32, Z. Wang^1,59, Z. L. Wang⁷⁴, Z. L. Wang², Z. Q. Wang^12,g, Z. Y. Wang^1,65, D. H. Wei¹⁴, H. R. Wei⁴⁴, F. Weidner⁷⁰, S. P. Wen¹, Y. R. Wen⁴⁰, U. Wiedner³, G. Wilkinson⁷¹, M. Wolke⁷⁷, C. Wu⁴⁰, J. F. Wu^1,8, L. H. Wu¹, L. J. Wu²⁰, L. J. Wu^1,65, Lianjie Wu²⁰, S. G. Wu^1,65, S. M. Wu⁶⁵, X. Wu^12,g, X. H. Wu³⁵, Y. J. Wu³², Z. Wu^1,59, L. Xia^73,59, X. M. Xian⁴⁰, B. H. Xiang^1,65, D. Xiao^39,k,l, G. Y. Xiao⁴³, H. Xiao⁷⁴, Y. L. Xiao^12,g, Z. J. Xiao⁴², C. Xie⁴³, K. J. Xie^1,65, X. H. Xie^47,h, Y. Xie⁵¹, Y. G. Xie^1,59, Y. H. Xie⁶, Z. P. Xie^73,59, T. Y. Xing^1,65, C. F. Xu^1,65, C. J. Xu⁶⁰, G. F. Xu¹, H. Y. Xu², H. Y. Xu^68,2, M. Xu^73,59, Q. J. Xu¹⁷, Q. N. Xu³¹, T. D. Xu⁷⁴, W. Xu¹, W. L. Xu⁶⁸, X. P. Xu⁵⁶, Y. Xu⁴¹, Y. Xu^12,g, Y. C. Xu⁷⁹, Z. S. Xu⁶⁵, F. Yan^12,g, H. Y. Yan⁴⁰, L. Yan^12,g, W. B. Yan^73,59, W. C. Yan⁸², W. H. Yan⁶, W. P. Yan²⁰, X. Q. Yan^1,65, H. J. Yang^52,f, H. L. Yang³⁵, H. X. Yang¹, J. H. Yang⁴³, R. J. Yang²⁰, T. Yang¹, Y. Yang^12,g, Y. F. Yang⁴⁴, Y. H. Yang⁴³, Y. Q. Yang⁹, Y. X. Yang^1,65, Y. Z. Yang²⁰, M. Ye^1,59, M. H. Ye^8,a, Z. J. Ye^57,j, Junhao Yin⁴⁴, Z. Y. You⁶⁰, B. X. Yu^1,59,65, C. X. Yu⁴⁴, G. Yu¹³, J. S. Yu^26,i, L. Q. Yu^12,g, M. C. Yu⁴¹, T. Yu⁷⁴, X. D. Yu^47,h, Y. C. Yu⁸², C. Z. Yuan^1,65, H. Yuan^1,65, J. Yuan³⁵, J. Yuan⁴⁶, L. Yuan², S. C. Yuan^1,65, X. Q. Yuan¹, Y. Yuan^1,65, Z. Y. Yuan⁶⁰, C. X. Yue⁴⁰, Ying Yue²⁰, A. A. Zafar⁷⁵, S. H. Zeng⁶⁴, X. Zeng^12,g, Y. Zeng^26,i, Y. J. Zeng⁶⁰, Y. J. Zeng^1,65, X. Y. Zhai³⁵, Y. H. Zhan⁶⁰, A. Q. Zhang^1,65, B. L. Zhang^1,65, B. X. Zhang¹, D. H. Zhang⁴⁴, G. Y. Zhang^1,65, G. Y. Zhang²⁰, H. Zhang^73,59, H. Zhang⁸², H. C. Zhang^1,59,65, H. H. Zhang⁶⁰, H. Q. Zhang^1,59,65, H. R. Zhang^73,59, H. Y. Zhang^1,59, J. Zhang⁸², J. Zhang⁶⁰, J. J. Zhang⁵³, J. L. Zhang²¹, J. Q. Zhang⁴², J. S. Zhang^12,g, J. W. Zhang^1,59,65, J. X. Zhang^39,k,l, J. Y. Zhang¹, J. Z. Zhang^1,65, Jianyu Zhang⁶⁵, L. M. Zhang⁶², Lei Zhang⁴³, N. Zhang⁸², P. Zhang^1,8, Q. Zhang²⁰, Q. Y. Zhang³⁵, R. Y. Zhang^39,k,l, S. H. Zhang^1,65, Shulei Zhang^26,i, X. M. Zhang¹, X. Y. Zhang⁴¹, X. Y. Zhang⁵¹, Y. Zhang¹, Y. Zhang⁷⁴, Y. T. Zhang⁸², Y. H. Zhang^1,59, Y. M. Zhang⁴⁰, Y. P. Zhang^73,59, Z. D. Zhang¹, Z. H. Zhang¹, Z. L. Zhang⁵⁶, Z. L. Zhang³⁵, Z. X. Zhang²⁰, Z. Y. Zhang⁷⁸, Z. Y. Zhang⁴⁴, Z. Z. Zhang⁴⁶, Zh. Zh. Zhang²⁰, G. Zhao¹, J. Y. Zhao^1,65, J. Z. Zhao^1,59, L. Zhao¹, L. Zhao^73,59, M. G. Zhao⁴⁴, N. Zhao⁸⁰, R. P. Zhao⁶⁵, S. J. Zhao⁸², Y. B. Zhao^1,59, Y. L. Zhao⁵⁶, Y. X. Zhao^32,65, Z. G. Zhao^73,59, A. Zhemchugov^37,b, B. Zheng⁷⁴, B. M. Zheng³⁵, J. P. Zheng^1,59, W. J. Zheng^1,65, X. R. Zheng²⁰, Y. H. Zheng^65,p, B. Zhong⁴², C. Zhong²⁰, H. Zhou^36,51,o, J. Q. Zhou³⁵, J. Y. Zhou³⁵, S. Zhou⁶, X. Zhou⁷⁸, X. K. Zhou⁶, X. R. Zhou^73,59, X. Y. Zhou⁴⁰, Y. X. Zhou⁷⁹, Y. Z. Zhou^12,g, A. N. Zhu⁶⁵, J. Zhu⁴⁴, K. Zhu¹, K. J. Zhu^1,59,65, K. S. Zhu^12,g, L. Zhu³⁵, L. X. Zhu⁶⁵, S. H. Zhu⁷², T. J. Zhu^12,g, W. D. Zhu^12,g, W. D. Zhu⁴², W. J. Zhu¹, W. Z. Zhu²⁰, Y. C. Zhu^73,59, Z. A. Zhu^1,65, X. Y. Zhuang⁴⁴, J. H. Zou¹, and J. Zu^73,59 (BESIII Collaboration)

¹Institute of High Energy Physics, Beijing 100049, People’s Republic of China
²Beihang University, Beijing 100191, People’s Republic of China
³Bochum Ruhr-University, D-44780 Bochum, Germany
⁴Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
⁵Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
⁶Central China Normal University, Wuhan 430079, People’s Republic of China
⁷Central South University, Changsha 410083, People’s Republic of China
⁸China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
⁹China University of Geosciences, Wuhan 430074, People’s Republic of China
¹⁰Chung-Ang University, Seoul, 06974, Republic of Korea
¹¹COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
¹²Fudan University, Shanghai 200433, People’s Republic of China
¹³GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
¹⁴Guangxi Normal University, Guilin 541004, People’s Republic of China
¹⁵Guangxi University, Nanning 530004, People’s Republic of China
¹⁶Guangxi University of Science and Technology, Liuzhou 545006, People’s Republic of China
¹⁷Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
¹⁸Hebei University, Baoding 071002, People’s Republic of China
¹⁹Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
²⁰Henan Normal University, Xinxiang 453007, People’s Republic of China
²¹Henan University, Kaifeng 475004, People’s Republic of China
²²Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
²³Henan University of Technology, Zhengzhou 450001, People’s Republic of China
²⁴Huangshan College, Huangshan 245000, People’s Republic of China
²⁵Hunan Normal University, Changsha 410081, People’s Republic of China
²⁶Hunan University, Changsha 410082, People’s Republic of China
²⁷Indian Institute of Technology Madras, Chennai 600036, India
²⁸Indiana University, Bloomington, Indiana 47405, USA
^29aINFN Laboratori Nazionali di Frascati, INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy;
^29bINFN Sezione di Perugia, I-06100, Perugia, Italy;
^29cUniversity of Perugia, I-06100, Perugia, Italy
^30aINFN Sezione di Ferrara, INFN Sezione di Ferrara, I-44122, Ferrara, Italy;
^30bUniversity of Ferrara, I-44122, Ferrara, Italy
³¹Inner Mongolia University, Hohhot 010021, People’s Republic of China
³²Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
³³Institute of Physics and Technology, Mongolian Academy of Sciences, Peace Avenue 54B, Ulaanbaatar 13330, Mongolia
³⁴Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile
³⁵Jilin University, Changchun 130012, People’s Republic of China
³⁶Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
³⁷Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
³⁸Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
³⁹Lanzhou University, Lanzhou 730000, People’s Republic of China
⁴⁰Liaoning Normal University, Dalian 116029, People’s Republic of China
⁴¹Liaoning University, Shenyang 110036, People’s Republic of China
⁴²Nanjing Normal University, Nanjing 210023, People’s Republic of China
⁴³Nanjing University, Nanjing 210093, People’s Republic of China
⁴⁴Nankai University, Tianjin 300071, People’s Republic of China
⁴⁵National Centre for Nuclear Research, Warsaw 02-093, Poland
⁴⁶North China Electric Power University, Beijing 102206, People’s Republic of China
⁴⁷Peking University, Beijing 100871, People’s Republic of China
⁴⁸Qufu Normal University, Qufu 273165, People’s Republic of China
⁴⁹Renmin University of China, Beijing 100872, People’s Republic of China
⁵⁰Shandong Normal University, Jinan 250014, People’s Republic of China
⁵¹Shandong University, Jinan 250100, People’s Republic of China
⁵²Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
⁵³Shanxi Normal University, Linfen 041004, People’s Republic of China
⁵⁴Shanxi University, Taiyuan 030006, People’s Republic of China
⁵⁵Sichuan University, Chengdu 610064, People’s Republic of China
⁵⁶Soochow University, Suzhou 215006, People’s Republic of China
⁵⁷South China Normal University, Guangzhou 510006, People’s Republic of China
⁵⁸Southeast University, Nanjing 211100, People’s Republic of China
⁵⁹State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of China
⁶⁰Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
⁶¹Suranaree University of Technology, University Avenue 111, Nakhon Ratchasima 30000, Thailand
⁶²Tsinghua University, Beijing 100084, People’s Republic of China
^63aTurkish Accelerator Center Particle Factory Group, Istinye University, 34010, Istanbul, Turkey;
^63bNear East University, Nicosia, North Cyprus, 99138, Mersin 10, Turkey
⁶⁴University of Bristol, H H Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
⁶⁵University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
⁶⁶University of Groningen, NL-9747 AA Groningen, The Netherlands
⁶⁷University of Hawaii, Honolulu, Hawaii 96822, USA
⁶⁸University of Jinan, Jinan 250022, People’s Republic of China
⁶⁹University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
⁷⁰University of Muenster, Wilhelm-Klemm-Strasse 9, 48149 Muenster, Germany
⁷¹University of Oxford, Keble Road, Oxford OX13RH, United Kingdom
⁷²University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China
⁷³University of Science and Technology of China, Hefei 230026, People’s Republic of China
⁷⁴University of South China, Hengyang 421001, People’s Republic of China
⁷⁵University of the Punjab, Lahore-54590, Pakistan
^76aUniversity of Turin and INFN, University of Turin, I-10125, Turin, Italy;
^76bUniversity of Eastern Piedmont, I-15121, Alessandria, Italy;
^76cINFN, I-10125, Turin, Italy
⁷⁷Uppsala University, Box 516, SE-75120 Uppsala, Sweden
⁷⁸Wuhan University, Wuhan 430072, People’s Republic of China
⁷⁹Yantai University, Yantai 264005, People’s Republic of China
⁸⁰Yunnan University, Kunming 650500, People’s Republic of China
⁸¹Zhejiang University, Hangzhou 310027, People’s Republic of China
⁸²Zhengzhou University, Zhengzhou 450001, People’s Republic of China

^*Full author list given at the end of the article.
^aDeceased.
^bAlso at the Moscow Institute of Physics and Technology, Moscow 141700, Russia.
^cAlso at the Novosibirsk State University, Novosibirsk, 630090, Russia.
^dAlso at the NRC “Kurchatov Institute”, PNPI, 188300, Gatchina, Russia.
^eAlso at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany.
^fAlso 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.
^gAlso 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.
^hAlso at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’s Republic of China.
ⁱAlso at School of Physics and Electronics, Hunan University, Changsha 410082, People’s Republic of China.
^jAlso at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, People’s Republic of China.
^kAlso at MOE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, People’s Republic of China.
^lAlso at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, People’s Republic of China.
^mAlso at the Department of Mathematical Sciences, IBA, Karachi 75270, Pakistan.
ⁿAlso at Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
^oAlso at Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany.
^pAlso at Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, People’s Republic of China.

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Phys. Rev. D 112, 072006 – Published 20 October, 2025

DOI: https://doi.org/10.1103/q6qr-8csr

Abstract

A novel measurement technique of strong-phase differences between the decay amplitudes of $D^{0}$ and ${\bar{D}}^{0}$ mesons is introduced which exploits quantum-correlated $D \bar{D}$ pairs produced by $e^{+} e^{-}$ collisions at energies above the $ψ (3770)$ production threshold, where $D \bar{D}$ pairs are produced in both even and odd eigenstates of the charge-conjugation symmetry. Employing this technique, the first determination of a $D^{0} - {\bar{D}}^{0}$ relative strong phase is reported with such data samples. The strong-phase difference between $D^{0} \to K^{-} π^{+}$ and ${\bar{D}}^{0} \to K^{-} π^{+}$ decays, $δ_{K π}^{D}$ , is measured to be $δ_{K π}^{D} = {({192.8}_{- 12.4 - 2.4}^{+ 11.0 + 1.9})}^{\circ}$ , using a dataset corresponding to an integrated luminosity of $7.13 {fb}^{- 1}$ collected at center-of-mass energies between 4.13–4.23 GeV by the BESIII experiment.

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Phys. Rev. D 112, 072006– Published 20 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 10 June 2025
Accepted 22 August 2025

DOI: https://doi.org/10.1103/q6qr-8csr

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Novel measurement of the strong-phase difference between $D^{0} \to K^{-} π^{+}$ and ${\bar{D}}^{0} \to K^{-} π^{+}$ decays using $C$ -even and $C$ -odd quantum-correlated $D \bar{D}$ pairs

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First Observation of Quantum Correlations in $e^{+} e^{-} \to X D \bar{D}$ and $C$ -Even Constrained $D \bar{D}$ Pairs

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Novel measurement of the strong-phase difference between D0→K−π+ and D¯0→K−π+ decays using C-even and C-odd quantum-correlated DD¯ pairs

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First Observation of Quantum Correlations in e+e−→XDD¯ and C-Even Constrained DD¯ Pairs

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Supplemental Material

References (40)

Novel measurement of the strong-phase difference between $D^{0} \to K^{-} π^{+}$ and ${\bar{D}}^{0} \to K^{-} π^{+}$ decays using $C$ -even and $C$ -odd quantum-correlated $D \bar{D}$ pairs

First Observation of Quantum Correlations in $e^{+} e^{-} \to X D \bar{D}$ and $C$ -Even Constrained $D \bar{D}$ Pairs