Eur. Phys. J. C (2022) 82: 1009
https://doi.org/10.1140/epjc/s10052-022-10872-2

Regular Article - Experimental Physics

Improved measurement of the strong-phase difference ${\delta }_D^{K\pi }$ in quantum-correlated $D\overline{D}$ decays

¹ Institute of High Energy Physics, 100049, Beijing, People’s Republic of China
² Beihang University, 100191, Beijing, People’s Republic of China
³ Beijing Institute of Petrochemical Technology, 102617, Beijing, People’s Republic of China
⁴ Bochum Ruhr-University, 44780, Bochum, Germany
⁵ Carnegie Mellon University, 15213, Pittsburgh, PA, USA
⁶ Central China Normal University, 430079, Wuhan, People’s Republic of China
⁷ Central South University, 410083, Changsha, People’s Republic of China
⁸ China Center of Advanced Science and Technology, 100190, Beijing, People’s Republic of China
⁹ COMSATS University Islamabad, Lahore Campus, Defence Road Off, Raiwind Road, 54000, Lahore, Pakistan
¹⁰ Fudan University, 200433, Shanghai, People’s Republic of China
¹¹ G.I. Budker Institute of Nuclear Physics SB RAS (BINP), 630090, Novosibirsk, Russia
¹² Guangxi Normal University, 541004, Guilin, People’s Republic of China
¹³ Guangxi University, 530004, Nanning, People’s Republic of China
¹⁴ Hangzhou Normal University, 310036, Hangzhou, People’s Republic of China
¹⁵ Hebei University, 071002, Baoding, People’s Republic of China
¹⁶ Helmholtz Institute Mainz, Staudinger Weg 18, Mainz, 55099, Germany
¹⁷ Henan Normal University, 453007, Xinxiang, People’s Republic of China
¹⁸ Henan University of Science and Technology, 471003, Luoyang, People’s Republic of China
¹⁹ Henan University of Technology, 450001, Zhengzhou, People’s Republic of China
²⁰ Huangshan College, 245000, Huangshan, People’s Republic of China
²¹ Hunan Normal University, 410081, Changsha, People’s Republic of China
²² Hunan University, 410082, Changsha, People’s Republic of China
²³ Indian Institute of Technology Madras, 600036, Chennai, India
²⁴ Indiana University, 47405, Bloomington, IN, USA
²⁵ INFN Laboratori Nazionali di Frascati, INFN Laboratori Nazionali di Frascati, 00044, Frascati, Italy
²⁶ INFN Laboratori Nazionali di Frascati, INFN Sezione di Perugia, 06100, Perugia, Italy
²⁷ University of Perugia, 06100, Perugia, Italy
²⁸ INFN Sezione di Ferrara, 44122, Ferrara, Italy
²⁹ INFN Sezione di Ferrara, University of Ferrara, 44122, Ferrara, Italy
³⁰ Institute of Modern Physics, 730000, Lanzhou, People’s Republic of China
³¹ Institute of Physics and Technology, Peace Ave. 54B, 13330, Ulaanbaatar, Mongolia
³² Jilin University, 130012, Changchun, People’s Republic of China
³³ Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, 55099, Mainz, Germany
³⁴ Joint Institute for Nuclear Research, 141980, Dubna, Moscow region, Russia
³⁵ Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, Giessen, 35392, Germany
³⁶ Lanzhou University, 730000, Lanzhou, People’s Republic of China
³⁷ Liaoning Normal University, 116029, Dalian, People’s Republic of China
³⁸ Liaoning University, 110036, Shenyang, People’s Republic of China
³⁹ Nanjing Normal University, 210023, Nanjing, People’s Republic of China
⁴⁰ Nanjing University, 210093, Nanjing, People’s Republic of China
⁴¹ Nankai University, 300071, Tianjin, People’s Republic of China
⁴² National Centre for Nuclear Research, 02-093, Warsaw, Poland
⁴³ North China Electric Power University, 102206, Beijing, People’s Republic of China
⁴⁴ Peking University, 100871, Beijing, People’s Republic of China
⁴⁵ Qufu Normal University, 273165, Qufu, People’s Republic of China
⁴⁶ Shandong Normal University, 250014, Jinan, People’s Republic of China
⁴⁷ Shandong University, 250100, Jinan, People’s Republic of China
⁴⁸ Shanghai Jiao Tong University, 200240, Shanghai, People’s Republic of China
⁴⁹ Shanxi Normal University, 041004, Linfen, People’s Republic of China
⁵⁰ Shanxi University, 030006, Taiyuan, People’s Republic of China
⁵¹ Sichuan University, 610064, Chengdu, People’s Republic of China
⁵² Soochow University, 215006, Suzhou, People’s Republic of China
⁵³ South China Normal University, 510006, Guangzhou, People’s Republic of China
⁵⁴ Southeast University, 211100, Nanjing, People’s Republic of China
⁵⁵ State Key Laboratory of Particle Detection and Electronics, 100049, Beijing, Hefei, People’s Republic of China
⁵⁶ Sun Yat-Sen University, 510275, Guangzhou, People’s Republic of China
⁵⁷ Suranaree University of Technology, University Avenue 111, 30000, Nakhon Ratchasima, Thailand
⁵⁸ Tsinghua University, 100084, Beijing, People’s Republic of China
⁵⁹ Turkish Accelerator Center Particle Factory Group, Istinye University, 34010, Istanbul, Turkey
⁶⁰ Turkish Accelerator Center Particle Factory Group, Near East University, Nicosia North Cyprus, Mersin 10, Turkey
⁶¹ University of Chinese Academy of Sciences, 100049, Beijing, People’s Republic of China
⁶² University of Groningen, 9747 AA, Groningen, The Netherlands
⁶³ University of Hawaii, 96822, Honolulu, HI, USA
⁶⁴ University of Jinan, 250022, Jinan, People’s Republic of China
⁶⁵ University of Manchester, Oxford Road, M13 9PL, Manchester, UK
⁶⁶ University of Muenster, Wilhelm-Klemm-Str. 9, 48149, Muenster, Germany
⁶⁷ University of Oxford, Keble Rd, OX13RH, Oxford, UK
⁶⁸ University of Science and Technology Liaoning, 114051, Anshan, People’s Republic of China
⁶⁹ University of Science and Technology of China, 230026, Hefei, People’s Republic of China
⁷⁰ University of South China, 421001, Hengyang, People’s Republic of China
⁷¹ University of the Punjab, 54590, Lahore, Pakistan
⁷² University of Turin, 10125, Turin, Italy
⁷³ University of Turin and INFN, University of Eastern Piedmont, 15121, Alessandria, Italy
⁷⁴ University of Turin and INFN, INFN, 10125, Turin, Italy
⁷⁵ Uppsala University, Box 516, Uppsala, 75120, Sweden
⁷⁶ Wuhan University, 430072, Wuhan, People’s Republic of China
⁷⁷ Xinyang Normal University, 464000, Xinyang, People’s Republic of China
⁷⁸ Yunnan University, 650500, Kunming, People’s Republic of China
⁷⁹ Zhejiang University, 310027, Hangzhou, People’s Republic of China
⁸⁰ Zhengzhou University, 450001, Zhengzhou, People’s Republic of China
⁸¹ the Moscow Institute of Physics and Technology, 141700, Moscow, Russia
⁸² the Novosibirsk State University, 630090, Novosibirsk, Russia
⁸³ the NRC “Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
⁸⁴ Goethe University Frankfurt, 60323, Frankfurt am Main, Germany
⁸⁵ 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, 200240, Shanghai, People’s Republic of China
⁸⁶ Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, 200443, Shanghai, People’s Republic of China
⁸⁷ State Key Laboratory of Nuclear Physics and Technology, Peking University, 100871, Beijing, People’s Republic of China
⁸⁸ School of Physics and Electronics, Hunan University, 410082, Changsha, China
⁸⁹ Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, 510006, Guangzhou, China
⁹⁰ Frontiers Science Center for Rare Isotopes, Lanzhou University, 730000, Lanzhou, People’s Republic of China
⁹¹ Lanzhou Center for Theoretical Physics, Lanzhou University, 730000, Lanzhou, People’s Republic of China
⁹² the Department of Mathematical Sciences, IBA, Karachi, Pakistan

^zb besiii-publications@ihep.ac.cn

Received: 21 August 2022
Accepted: 29 September 2022
Published online: 9 November 2022

Abstract

The decay $D\to K^{-}{\pi }^{+}$ is studied in a sample of quantum-correlated $D\overline{D}$ pairs, based on a data set corresponding to an integrated luminosity of 2.93 fb${}^{-1}$ collected at the $\psi (3770)$ resonance by the BESIII experiment. The asymmetry between $CP$-odd and $CP$-even eigenstate decays into $K^{-}{\pi }^{+}$ is determined to be ${\mathcal{A}}_{K\pi }=0.132\pm 0.011\pm 0.007$, where the first uncertainty is statistical and the second is systematic. This measurement is an update of an earlier study exploiting additional tagging modes, including several decay modes involving a $K_L^0$ meson. The branching fractions of the $K_L^0$ modes are determined as input to the analysis in a manner that is independent of any strong phase uncertainty. Using the predominantly $CP$-even tag $D\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and the ensemble of $CP$-odd eigenstate tags, the observable ${\mathcal{A}}_{K\pi }^{\pi \pi {\pi }^0}$ is measured to be $0.130\pm 0.012\pm 0.008$. The two asymmetries are sensitive to $r_D^{K\pi }cos{\delta }_D^{K\pi }$, where $r_D^{K\pi }$ and ${\delta }_D^{K\pi }$ are the ratio of amplitudes and phase difference, respectively, between the doubly Cabibbo-suppressed and Cabibbo-favoured decays. In addition, events containing $D\to K^{-}{\pi }^{+}$ tagged by $D\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ are studied in bins of phase space of the three-body decays. This analysis has sensitivity to both $r_D^{K\pi }cos{\delta }_D^{K\pi }$ and $r_D^{K\pi }sin{\delta }_D^{K\pi }$. A fit to ${\mathcal{A}}_{K\pi }$, ${\mathcal{A}}_{K\pi }^{\pi \pi {\pi }^0}$ and the phase-space distribution of the $D\to K_{S,L}^0{\pi }^{+}{\pi }^{-}$ tags yields ${\delta }_D^{K\pi }={\left(187.6{}_{-9.7}^{+8.9}{}_{-6.4}^{+5.4}\right)}^{\circ }$, where external constraints are applied for $r_D^{K\pi }$ and other relevant parameters. This is the most precise measurement of ${\delta }_D^{K\pi }$ in quantum-correlated $D\overline{D}$ decays.