Observation of D^0\to K_1(1270)^- e^+ν_e
BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, M. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, Z. J Chen, W. S. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. DeMori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, S. X. Du, Y. L. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, M. Fritsch, C. D. Fu, Y. Gao, Y. Gao, Y. Gao, Y. G. Gao, I. Garzia, P. T. Ge, C. Geng, E. M. Gersabeck, A Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, S. Gu, Y. T. Gu, C. Y Guan, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov, T. T. Han, et al. (422 additional authors not shown)
aa r X i v : . [ h e p - e x ] F e b Observation of D → K (1270) − e + ν e M. Ablikim , M. N. Achasov ,c , P. Adlarson , S. Ahmed , M. Albrecht , R. Aliberti , A. Amoroso A, C ,M. R. An , Q. An , , X. H. Bai , Y. Bai , O. Bakina , R. Baldini Ferroli A , I. Balossino A , Y. Ban ,k ,K. Begzsuren , N. Berger , M. Bertani A , D. Bettoni A , F. Bianchi A, C , J. Bloms , A. Bortone A, C ,I. Boyko , R. A. Briere , H. Cai , X. Cai , , A. Calcaterra A , G. F. Cao , , N. Cao , , S. A. Cetin A ,J. F. Chang , , W. L. Chang , , G. Chelkov ,b , D. Y. Chen , G. Chen , H. S. Chen , , M. L. Chen , ,S. J. Chen , X. R. Chen , Y. B. Chen , , Z. J Chen ,l , W. S. Cheng C , G. Cibinetto A , F. Cossio C ,X. F. Cui , H. L. Dai , , X. C. Dai , , A. Dbeyssi , R. E. de Boer , D. Dedovich , Z. Y. Deng , A. Denig ,I. Denysenko , M. Destefanis A, C , F. De Mori A, C , Y. Ding , C. Dong , J. Dong , , L. Y. Dong , ,M. Y. Dong , , , X. Dong , S. X. Du , Y. L. Fan , J. Fang , , S. S. Fang , , Y. Fang , R. Farinelli A ,L. Fava B, C , F. Feldbauer , G. Felici A , C. Q. Feng , , J. H. Feng , M. Fritsch , C. D. Fu , Y. Gao ,Y. Gao ,k , Y. Gao , , Y. G. Gao , I. Garzia A, B , P. T. Ge , C. Geng , E. M. Gersabeck , A Gilman ,K. Goetzen , L. Gong , W. X. Gong , , W. Gradl , M. Greco A, C , L. M. Gu , M. H. Gu , , S. Gu ,Y. T. Gu , C. Y Guan , , A. Q. Guo , L. B. Guo , R. P. Guo , Y. P. Guo ,h , A. Guskov , T. T. Han ,W. Y. Han , X. Q. Hao , F. A. Harris , N H¨usken , , K. L. He , , F. H. Heinsius , C. H. Heinz , T. Held ,Y. K. Heng , , , C. Herold , M. Himmelreich ,f , T. Holtmann , Y. R. Hou , Z. L. Hou , H. M. Hu , ,J. F. Hu ,m , T. Hu , , , Y. Hu , G. S. Huang , , L. Q. Huang , X. T. Huang , Y. P. Huang , Z. Huang ,k ,T. Hussain , W. Ikegami Andersson , W. Imoehl , M. Irshad , , S. Jaeger , S. Janchiv ,j , Q. Ji , Q. P. Ji ,X. B. Ji , , X. L. Ji , , Y. Y. Ji , H. B. Jiang , X. S. Jiang , , , J. B. Jiao , Z. Jiao , S. Jin , Y. Jin ,T. Johansson , N. Kalantar-Nayestanaki , X. S. Kang , R. Kappert , M. Kavatsyuk , B. C. Ke , ,I. K. Keshk , A. Khoukaz , P. Kiese , R. Kiuchi , R. Kliemt , L. Koch , O. B. Kolcu A,e , B. Kopf ,M. Kuemmel , M. Kuessner , A. Kupsc , M. G. Kurth , , W. K¨uhn , J. J. Lane , J. S. Lange , P. Larin ,A. Lavania , L. Lavezzi A, C , Z. H. Lei , , H. Leithoff , M. Lellmann , T. Lenz , C. Li , C. H. Li ,Cheng Li , , D. M. Li , F. Li , , G. Li , H. Li , H. Li , , H. B. Li , , H. J. Li , J. L. Li , J. Q. Li ,J. S. Li , Ke Li , L. K. Li , Lei Li , P. R. Li , S. Y. Li , W. D. Li , , W. G. Li , X. H. Li , , X. L. Li ,Xiaoyu Li , , Z. Y. Li , H. Liang , , H. Liang , , H. Liang , Y. F. Liang , Y. T. Liang , G. R. Liao ,L. Z. Liao , , J. Libby , C. X. Lin , B. J. Liu , C. X. Liu , D. Liu , , F. H. Liu , Fang Liu , Feng Liu ,H. B. Liu , H. M. Liu , , Huanhuan Liu , Huihui Liu , J. B. Liu , , J. L. Liu , J. Y. Liu , , K. Liu ,K. Y. Liu , Ke Liu , L. Liu , , M. H. Liu ,h , P. L. Liu , Q. Liu , Q. Liu , S. B. Liu , , Shuai Liu ,T. Liu , , W. M. Liu , , X. Liu , Y. Liu , Y. B. Liu , Z. A. Liu , , , Z. Q. Liu , X. C. Lou , , ,F. X. Lu , F. X. Lu , H. J. Lu , J. D. Lu , , J. G. Lu , , X. L. Lu , Y. Lu , Y. P. Lu , , C. L. Luo ,M. X. Luo , P. W. Luo , T. Luo ,h , X. L. Luo , , S. Lusso C , X. R. Lyu , F. C. Ma , H. L. Ma , L. L.Ma , M. M. Ma , , Q. M. Ma , R. Q. Ma , , R. T. Ma , X. X. Ma , , X. Y. Ma , , F. E. Maas ,M. Maggiora A, C , S. Maldaner , S. Malde , Q. A. Malik , A. Mangoni B , Y. J. Mao ,k , Z. P. Mao ,S. Marcello A, C , Z. X. Meng , J. G. Messchendorp , G. Mezzadri A , T. J. Min , R. E. Mitchell ,X. H. Mo , , , Y. J. Mo , N. Yu. Muchnoi ,c , H. Muramatsu , S. Nakhoul ,f , Y. Nefedov , F. Nerling ,f ,I. B. Nikolaev ,c , Z. Ning , , S. Nisar ,i , S. L. Olsen , Q. Ouyang , , , S. Pacetti B, C , X. Pan ,h ,Y. Pan , A. Pathak , P. Patteri A , M. Pelizaeus , H. P. Peng , , K. Peters ,f , J. Pettersson , J. L. Ping ,R. G. Ping , , R. Poling , V. Prasad , , H. Qi , , H. R. Qi , K. H. Qi , M. Qi , T. Y. Qi , T. Y. Qi ,S. Qian , , W. B. Qian , Z. Qian , C. F. Qiao , L. Q. Qin , X. P. Qin , X. S. Qin , Z. H. Qin , , J. F. Qiu ,S. Q. Qu , K. H. Rashid , K. Ravindran , C. F. Redmer , A. Rivetti C , V. Rodin , M. Rolo C , G. Rong , ,Ch. Rosner , M. Rump , H. S. Sang , A. Sarantsev ,d , Y. Schelhaas , C. Schnier , K. Schoenning ,M. Scodeggio A, B , D. C. Shan , W. Shan , X. Y. Shan , , J. F. Shangguan , M. Shao , , C. P. Shen ,P. X. Shen , X. Y. Shen , , H. C. Shi , , R. S. Shi , , X. Shi , , X. D Shi , , J. J. Song , W. M. Song , ,Y. X. Song ,k , S. Sosio A, C , S. Spataro A, C , K. X. Su , P. P. Su , F. F. Sui , G. X. Sun , H. K. Sun ,J. F. Sun , L. Sun , S. S. Sun , , T. Sun , , W. Y. Sun , W. Y. Sun , X Sun ,l , Y. J. Sun , , Y. K. Sun , ,Y. Z. Sun , Z. T. Sun , Y. H. Tan , Y. X. Tan , , C. J. Tang , G. Y. Tang , J. Tang , J. X. Teng , ,V. Thoren , W. H. Tian , Y. T. Tian , I. Uman B , B. Wang , C. W. Wang , D. Y. Wang ,k , H. J. Wang ,H. P. Wang , , K. Wang , , L. L. Wang , M. Wang , M. Z. Wang ,k , Meng Wang , , W. Wang ,W. H. Wang , W. P. Wang , , X. Wang ,k , X. F. Wang , X. L. Wang ,h , Y. Wang , Y. Wang , ,Y. D. Wang , Y. F. Wang , , , Y. Q. Wang , Y. Y. Wang , Z. Wang , , Z. Y. Wang , Ziyi Wang ,Zongyuan Wang , , D. H. Wei , P. Weidenkaff , F. Weidner , S. P. Wen , D. J. White , U. Wiedner ,G. Wilkinson , M. Wolke , L. Wollenberg , J. F. Wu , , L. H. Wu , L. J. Wu , , X. Wu ,h , Z. Wu , ,L. Xia , , H. Xiao ,h , S. Y. Xiao , Z. J. Xiao , X. H. Xie ,k , Y. G. Xie , , Y. H. Xie , T. Y. Xing , , G. F. Xu ,Q. J. Xu , W. Xu , , X. P. Xu , Y. C. Xu , F. Yan ,h , L. Yan ,h , W. B. Yan , , W. C. Yan , Xu Yan ,H. J. Yang ,g , H. X. Yang , L. Yang , S. L. Yang , Y. X. Yang , Yifan Yang , , Zhi Yang , M. Ye , ,M. H. Ye , J. H. Yin , Z. Y. You , B. X. Yu , , , C. X. Yu , G. Yu , , J. S. Yu ,l , T. Yu , C. Z. Yuan , ,L. Yuan , X. Q. Yuan ,k , Y. Yuan , Z. Y. Yuan , C. X. Yue , A. Yuncu A,a , A. A. Zafar , Y. Zeng ,l ,B. X. Zhang , Guangyi Zhang , H. Zhang , H. H. Zhang , H. H. Zhang , H. Y. Zhang , , J. J. Zhang ,J. L. Zhang , J. Q. Zhang , J. W. Zhang , , , J. Y. Zhang , J. Z. Zhang , , Jianyu Zhang , , Jiawei Zhang , ,L. M. Zhang , L. Q. Zhang , Lei Zhang , S. Zhang , S. F. Zhang , Shulei Zhang ,l , X. D. Zhang ,X. Y. Zhang , Y. Zhang , Y. H. Zhang , , Y. T. Zhang , , Yan Zhang , , Yao Zhang , Yi Zhang ,h ,Z. H. Zhang , Z. Y. Zhang , G. Zhao , J. Zhao , J. Y. Zhao , , J. Z. Zhao , , Lei Zhao , , Ling Zhao ,M. G. Zhao , Q. Zhao , S. J. Zhao , Y. B. Zhao , , Y. X. Zhao , Z. G. Zhao , , A. Zhemchugov ,b ,B. Zheng , J. P. Zheng , , Y. Zheng ,k , Y. H. Zheng , B. Zhong , C. Zhong , L. P. Zhou , , Q. Zhou , ,X. Zhou , X. K. Zhou , X. R. Zhou , , X. Y. Zhou , A. N. Zhu , , J. Zhu , K. Zhu , K. J. Zhu , , ,S. H. Zhu , T. J. Zhu , W. J. Zhu ,h , W. J. Zhu , Y. C. Zhu , , Z. A. Zhu , , B. S. Zou , J. H. Zou (BESIII Collaboration) Institute of High Energy Physics, Beijing 100049, People’s Republic of China Beihang University, Beijing 100191, People’s Republic of China Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China Bochum Ruhr-University, D-44780 Bochum, Germany Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA Central China Normal University, Wuhan 430079, People’s Republic of China China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan Fudan University, Shanghai 200443, People’s Republic of China G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany Guangxi Normal University, Guilin 541004, People’s Republic of China Guangxi University, Nanning 530004, People’s Republic of China Hangzhou Normal University, Hangzhou 310036, People’s Republic of China Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany Henan Normal University, Xinxiang 453007, People’s Republic of China Henan University of Science and Technology, Luoyang 471003, People’s Republic of China Huangshan College, Huangshan 245000, People’s Republic of China Hunan Normal University, Changsha 410081, People’s Republic of China Hunan University, Changsha 410082, People’s Republic of China Indian Institute of Technology Madras, Chennai 600036, India Indiana University, Bloomington, Indiana 47405, USA 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 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122,Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy Institute of Modern Physics, Lanzhou 730000, People’s Republic of China Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia Jilin University, Changchun 130012, People’s Republic of China Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany Lanzhou University, Lanzhou 730000, People’s Republic of China Liaoning Normal University, Dalian 116029, People’s Republic of China Liaoning University, Shenyang 110036, People’s Republic of China Nanjing Normal University, Nanjing 210023, People’s Republic of China Nanjing University, Nanjing 210093, People’s Republic of China Nankai University, Tianjin 300071, People’s Republic of China North China Electric Power University, Beijing 102206, People’s Republic of China Peking University, Beijing 100871, People’s Republic of China Qufu Normal University, Qufu 273165, People’s Republic of China Shandong Normal University, Jinan 250014, People’s Republic of China Shandong University, Jinan 250100, People’s Republic of China Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China Shanxi Normal University, Linfen 041004, People’s Republic of China Shanxi University, Taiyuan 030006, People’s Republic of China Sichuan University, Chengdu 610064, People’s Republic of China Soochow University, Suzhou 215006, People’s Republic of China South China Normal University, Guangzhou 510006, People’s Republic of China Southeast University, Nanjing 211100, People’s Republic of China State Key Laboratory of Particle Detection and Electronics,Beijing 100049, Hefei 230026, People’s Republic of China Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China Suranaree University of Technology, University Avenue 111, Nakhon Ratchasima 30000, Thailand Tsinghua University, Beijing 100084, People’s Republic of China Turkish Accelerator Center Particle Factory Group, (A)Istanbul Bilgi University, 34060Eyup, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China University of Groningen, NL-9747 AA Groningen, The Netherlands University of Hawaii, Honolulu, Hawaii 96822, USA University of Jinan, Jinan 250022, People’s Republic of China University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom University of Minnesota, Minneapolis, Minnesota 55455, USA University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany University of Oxford, Keble Rd, Oxford, UK OX13RH University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China University of Science and Technology of China, Hefei 230026, People’s Republic of China University of South China, Hengyang 421001, People’s Republic of China University of the Punjab, Lahore-54590, Pakistan University of Turin and INFN, (A)University of Turin, I-10125, Turin, Italy; (B)Universityof Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy Uppsala University, Box 516, SE-75120 Uppsala, Sweden Wuhan University, Wuhan 430072, People’s Republic of China Xinyang Normal University, Xinyang 464000, People’s Republic of China Zhejiang University, Hangzhou 310027, People’s Republic of China Zhengzhou University, Zhengzhou 450001, People’s Republic of China a Also at Bogazici University, 34342 Istanbul, Turkey b Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia c Also at the Novosibirsk State University, Novosibirsk, 630090, Russia d Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia e Also at Istanbul Arel University, 34295 Istanbul, Turkey f Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany g Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministryof Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Instituteof Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China h Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Instituteof Modern Physics, Fudan University, Shanghai 200443, People’s Republic of China i Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA j Currently at: Institute of Physics and Technology, Peace Ave.54B, Ulaanbaatar 13330, Mongolia k Also at State Key Laboratory of Nuclear Physics and Technology,Peking University, Beijing 100871, People’s Republic of China l School of Physics and Electronics, Hunan University, Changsha 410082, China m Also at Guangdong Provincial Key Laboratory of Nuclear Science, Instituteof Quantum Matter, South China Normal University, Guangzhou 510006, China
Using 2.93 fb − of e + e − collision data taken with the BESIII detector at a center-of-mass energyof 3.773 GeV, the observation of the D → K (1270) − e + ν e semileptonic decay is presented. Thestatistical significance of the decay D → K (1270) − e + ν e is greater than 10 σ . The branchingfraction of D → K (1270) − e + ν e is measured to be (1 . ± . +0 . − . ± . × − . Here, thefirst uncertainty is statistical, the second is systematic, and the third originates from the assumedbranching fraction of K (1270) − → K − π + π − . PACS numbers: 13.20.Fc, 12.15.Hh
Semileptonic (SL) D decays offer a good testbed tounderstand nonperturbative strong-interaction dynamicsin weak decays [1, 2]. Studies of the SL D decays intothe strange axial-vector mesons K (1270) or K (1400)are especially appealing. Reference [3] points out thatthe combined measurements of D → ¯ K (1270) ℓ + ν ℓ and B → K (1270) γ provide a possible way to determinethe photon polarization in b → sγ transitions withoutconsiderable theoretical ambiguity. Knowledge of the b → sγ photon polarization plays a unique role inprobing right-handed couplings in new physics [3–5].Throughout this Letter, charged conjugated modes arealways implied.To date, the K (1270) and K (1400) mesons have beenextensively investigated in τ , D , B , and charmoniumdecays [6–15]. In theory, the physical mass eigenstatesof K (1270) and K (1400) mesons are decomposed asmixtures of the P and P states with a mixing angle θ K . Various approaches were proposed to extract θ K ,but with very different results [16–23]. Experimentalmeasurements of D → ¯ K (1270) e + ν e offer deeperinsight into the mixing angle θ K , which is essential forreliable calculations describing the τ [16], B [18, 24], and D [25, 26] decays involving K , and for investigations inthe field of hadron spectroscopy [27].The branching fractions (BFs) of D → ¯ K (1270) e + ν e have been computed with differentmodels: the Isgur-Scora-Grinstein-Wise (ISGW) quarkmodel [1] and its update, ISGW2 [2], three-point QCDsum rules (3PSR) [28], covariant light-front quarkmodel (CLFQM) [29], and the light-cone QCD sumrules (LCSR) [30, 31]. The predicted BFs, whichare sensitive to θ K and its sign, vary from 10 − to10 − [28, 29, 31]. Measurements of these decay BFs arethe key to testing different theoretical calculations andunderstanding the weak-decay mechanisms of D mesons.For example, assuming isospin symmetry, the ratio of the partial decay widths for the SL D decays, whichare both mediated via c → se + ν e , is expected to beunity [32]. Measuring the BFs thus allows a test ofisospin invariance in D → ¯ K (1270) e + ν e . Large D → ¯ K (1270) ℓ + ν ℓ samples also supply a cleanenvironment, with no additional hadrons in the finalstate, to accurately determine the mass and width of K (1270) meson, and to explore the relative strengthsand phases of K (1270) decays into various final states,which currently all suffer large uncertainties.An observation of D + → ¯ K (1270) e + ν e waspreviously reported by BESIII [33]. However, theonly evidence for D → K (1270) − e + ν e was reportedby CLEO [34]. This Letter presents an observationof D → K (1270) − e + ν e by using an e + e − datasample corresponding to an integrated luminosity of2.93 fb − [35] recorded at a center-of-mass energy of3.773 GeV with the BESIII detector [36].Details about the design and performance of theBESIII detector are given in Ref. [36]. Simulated samplesproduced with a geant4 -based [37] Monte Carlo (MC)package, which includes the geometric description of theBESIII detector and the detector response, are used todetermine the detection efficiency and to estimate thebackgrounds. The simulation includes the beam-energyspread and initial-state radiation (ISR) in the e + e − annihilations modeled with the generator kkmc [38].The inclusive MC samples consist of the production ofthe D ¯ D pairs, the non- D ¯ D decays of the ψ (3770), theISR production of the J/ψ and ψ (3686) states, and thecontinuum processes incorporated in kkmc [38]. Theknown decay modes are modeled with evtgen [39] usingBFs taken from the Particle Data Group [40], and theremaining unknown decays from the charmonium stateswith lundcharm [41]. Final-state radiation (FSR)from charged final-state particles is incorporated withthe photos package [42]. The D → K (1270) − e + ν e decay is simulated with the ISGW2 model [43] andthe K (1270) − meson is allowed to decay into allintermediate processes that result in a K − π + π − finalstate. The resonance shape of the K (1270) − mesonis parameterized by a relativistic Breit-Wigner function,and the mass and width of K (1270) − meson are fixedat the world-average values (1 . ± . c and(90 ±
20) MeV, respectively [40]. The BFs of K (1270)meson subdecays measured by Belle [44] are input togenerate the signal MC events, since they give betterconsistency between data and MC simulation than thosereported in Ref. [40].The measurement employs the e + e − → ψ (3770) → D ¯ D decay chain. The ¯ D mesons are reconstructedby their hadronic decays to ¯ D → K + π − , K + π − π ,and K + π − π − π + . These inclusively selected eventsare referred to as single-tag (ST) ¯ D mesons. In thepresence of the ST ¯ D mesons, candidates for D → K (1270) − e + ν e are selected to form double-tag (DT)events. For a given tag mode, the BF of D → K (1270) − e + ν e , B SL , is obtained by B SL = N DT / ( N ST · ε SL · B sub ) , (1)where N ST and N DT are the ST and DT yields in thedata sample, ε SL = ε DT /ε ST is the efficiency of detectingthe SL decay in the presence of the ST ¯ D meson, and B sub is the BF of K (1270) − → K − π + π − . ε ST and ε DT are the ST and DT efficiencies of selecting the ST andDT candidates, respectively.All charged tracks must originate from the interactionpoint with a distance of closest approach less than1 cm in the transverse plane and less than 10 cmalong the axis of the multilayer drift chamber (MDC).Their polar angles ( θ ) are required to satisfy | cos θ | < .
93. Charged particle identification (PID) of chargedkaons and pions is performed by combining the time-of-flight (TOF) information and the specific ionizationenergy loss ( dE/dx ) measured in the MDC. Positron PIDuses the combined information from the dE/dx , TOF,and electromagnetic calorimeter (EMC). The combinedconfidence levels under the positron, pion, and kaonhypotheses ( CL e , CL π and CL K , respectively) arecalculated. Kaon (pion) candidates are required tosatisfy CL K > CL π ( CL π > CL K ). Positron candidatesare required to satisfy CL e / ( CL e + CL π + CL K ) > . π meson is reconstructed via π → γγ decay. The energy deposited in the EMC of each photonis required to be greater than 25 MeV in the barrel( | cos θ | < .
80) region or 50 MeV in the end caps(0 . < | cos θ | < .
92) region, and the shower time hasto be within 700 ns of the event start time. Pairings withboth photons from the end caps are rejected because of poor resolution. The γγ combination with an invariantmass in the range (0 . , . /c are regarded as a π candidates, and a kinematic fit by constraining the γγ invariant mass to the π nominal mass [40] is performedto improve the mass resolution. For ¯ D → K + π − , thebackgrounds from cosmic ray events, radiative Bhabhascattering, and dimuon events are suppressed with thesame requirements as used in Ref. [45].The ST ¯ D mesons are identified by the energydifference ∆ E ≡ E ¯ D − E beam and the beam-constrainedmass M BC ≡ p E − | ~p ¯ D | , where E beam is thebeam energy, and E ¯ D and ~p ¯ D are the total energy andmomentum of the ST ¯ D in the e + e − rest frame. If thereare multiple combinations in an event, the combinationwith the smallest | ∆ E | is chosen for each tag mode. Thecombinatorial backgrounds in the M BC distributions aresuppressed by requiring ∆ E within ( − , − , − ,
28) MeV for ¯ D → K + π − , K + π − π , and K + π − π − π + , respectively, which correspond to about3 . σ away from the fitted peak.The M BC distributions of the accepted ST candidatesin the data sample for the three tag modes are shownin Fig. 1. To extract the ST yield for each tag mode,an unbinned maximum-likelihood fit is performed to thecorresponding M BC distribution. The signal is describedby the MC-simulated shape convolved with a double-Gaussian function accounting for the resolution differencebetween data and MC simulation, and the background ismodeled by an ARGUS function [46]. Fit results areshown in Fig. 1. Events within M BC ∈ (1 . , . c are kept for further analysis. The ST yieldsfor the ¯ D → K + π − , K + π − π , and K + π − π − π + tagmodes are 542153 ± stat , 1080690 ± stat , and737036 ± stat , respectively.Particles recoiling against the ST ¯ D meson candi-datess are used to reconstruct candidates for D → K (1270) − e + ν e decay. It is required that there areonly four good unused charged tracks available for thisselection. The K (1270) − meson is reconstructed usingits dominant decay K (1270) − → K − π + π − . The chargeof the lepton candidate is required to be the same as thatof the charged kaon of tag side. The other three chargedtracks are identified as a kaon and two pions, based on thesame PID criteria used for the ST. The kaon candidatemust have charge opposite to that of the positron.Additional criteria that have been optimized byanalyzing the inclusive MC sample are further introducedto suppress backgrounds. To distinguish positrons frombackgrounds related to hadrons, the positron candidatesare required to satisfy the requirement of E/p − . > . × χ edE/dx , where E , p , and χ edE/dx are the energydeposited in the EMC, the momentum measured by theMDC, and the standard deviation between the measuredand expected dE/dx with the positron hypothesis,respectively. To suppress the background from D → K − π + π − π + , we require M K − π + π − π + e → π < . /c , ) × ) ( c E v e n t s / ( . M e V / ) × ) ( c E v e n t s / ( . M e V / ) × ) ( c E v e n t s / ( . M e V / ) c (GeV/ BC M ) c (GeV/ BC M ) c (GeV/ BC M - π + K → D π - π + K → D0204060 1.84 1.86 1.88 + π - π - π + K → D Fig. 1. Fits to the M BC distributions of the ST candidates in data. Points with error bars are data. Blue solid curves are thefit results and red dashed curves represent the background contributions of the fit. The pair of red arrows in each subfigureindicate the M BC window. where π + e → π is the positron candidate reconstructed withthe pion mass hypothesis. To suppress the backgroundfrom D → K − π + π ( π ), with π → e + e − γ (andmissing another π ), the opening angle between e + and π − ( θ a ) is required to satisfy cos θ a < .
94. To suppressthe background from D → K − π + π − π + π , we require M K − π + π − π + e → π π < . /c when there is at leastone reconstructed π among the photons recoiling againstthe ST ¯ D meson in an event. Furthermore, the openingangle between the missing momentum (defined below)and the most energetic unused shower ( θ b ) is requiredto satisfy cos θ b < .
81. To suppress the backgroundfrom D → K − π e + ν e with π → e + e − γ , we require M π + π − > .
31 GeV /c . Background involving K S decayis suppressed by requiring M π + π − outside the interval(0 . , . c . For the ¯ D → K + π − π tagmode, combinatorial background from D − → K + π − π − vs. D + → K − π + X is suppressed by requiring thedifference between the beam-energy and the energy of the( K + π − ) tag π − sig combination to be greater than 8 MeV.Information concerning the undetectable neutrino isinferred by the kinematic quantity M ≡ E −| ~p miss | , where E miss and ~p miss are the missing energy andmomentum of the SL candidate, respectively, calculatedby E miss ≡ E beam − Σ j E j and ~p miss ≡ − ~p ¯ D − Σ j ~p j in the e + e − center-of-mass frame. The index j sumsover the K − , π + , π − and e + of the signal candidate,and E j and ~p j are the energy and momentum of the j -th particle, respectively. To partially recover the energylost to FSR and bremsstrahlung, the four-momenta ofphoton(s) within 5 ◦ of the initial positron direction areadded to the positron four-momentum measured by theMDC. To improve the M resolution, all the candidatetracks plus the missing neutrino are subjected to a 4-constraint kinematic fit requiring energy and momentumconservation, as well as the invariant masses of the ¯ D and D candidate particles being constrained to thenominal D mass. The momenta from the kinematic fit are used to calculate M .Figure 2(a) shows the distribution of M K − π + π − vs. M of the accepted D → K − π + π − e + ν e candidateevents in the data sample after combining all tagmodes. A clear signal, which concentrates around the K (1270) − nominal mass in the M K − π + π − distributionand around zero in the M distribution, can be seen.The DT yield is obtained from a two-dimensional (2D)unbinned extended maximum-likelihood simultaneous fitto the data for the three tags. Due to the limiteddata set, the components of D → K (1400) − e + ν e , D → K ∗ (1410) − e + ν e , D → K ∗ (1430) − e + ν e , and D → ( K − π + π − ) non-resonance e + ν e are all ignored in thisanalysis. In the fit, the 2D signal shape is describedby the MC-simulated shape extracted from the signalMC events of D → K (1270) − e + ν e . The 2D shapesof the peaking background of D → K − π + π + π − andthe other backgrounds are modeled by those derivedfrom the inclusive MC sample. The number of peakingbackground events from D → K − π + π + π − is fixedat the simulated value, and the number of the otherbackgrounds is a free parameter. The smooth 2Dprobability density functions of signal and backgroundare modeled by using RooNDKeysPdf [47, 48]. Thesignal efficiencies with the ST modes ¯ D → K + π − , K + π − π , and K + π − π − π + are (14 . ± . stat )%,(13 . ± . stat )%, and (11 . ± . stat )%, respectively.The BFs given by the three tags are constrained tohave the same value in the fit. The 2D fit projectionsto the M and M K − π + π − distributions are shownin Figs. 2(b) and 2(c), respectively. From the fit, weobtain the DT yield of N DT = 109 . ± . stat . Thestatistical significance of the signal is estimated to begreater than 10 σ , by comparing the likelihoods with andwithout the signal component, and taking the changein the number of degrees of freedom into account. Thefitted product of the BFs for D → K (1270) − e + ν e and ) c ( G e V / - π + π - K M ) c / E v e n t s / ( M e V ) c E v e n t s / ( M e V / ) c / (GeV M ) c / (GeV M ) c (GeV/ - π + π - K M (a) (b) (c) Fig. 2. (a) Distribution of M K − π + π − vs. M of the DT candidate events. Projections of the 2D fit to (b) M and(c) M K − π + π − . The distributions are summed over all three tags. In (b) and (c), points with error bars are data; blue solid,red dotted, green dashed, and black dashed curves are total fit, signal, peaking background of D → K − π + π + π − , and otherbackground, respectively. In (b), the peaking background concentrating around 0.033 GeV /c is from D → K − π + π + π − π . K (1270) − → K − π + π − is B SL · B sub = (3 . ± . +0 . − . ) × − , where the first and second uncertainties are statisticaland systematic, respectively. The reliability of the MCsimulation is verified since the data distributions ofmomenta and cos θ of K − , π + , π − and e + as well asinvariant masses of K − π + and π + π − are consistent withthose of MC simulations.The systematic uncertainties relative to the measuredBF are discussed below. The DT method ensures thatmost uncertainties arising from the ST selection cancel.The uncertainty from the ST yield is assigned to be 0.5%,by examining the relative change in the yield betweendata and MC simulation after varying the signal shapeand the endpoint of the ARGUS function in the yield fits.The systematic uncertainties originating from e + tracking and PID efficiencies are studied by using thecontrol samples of e + e − → γe + e − events and those for K − and π ± are investigated with the DT D ¯ D hadronicevents. The e + efficiencies for tracking and PID arealso re-weighted in 2D (momentum and cos θ ) to matchthose of the D → K (1270) − e + ν e data. For K − and π + , similar weighting is performed on momentum onlysince the data and MC angular distributions alreadyagree well. Small differences between the data and MCefficiencies for K − tracking, e + tracking, and e + PIDare found, which are +(2 . ± . . ± . − (1 . ± . e + , K − , π + , and π − are assigned as 0.2% (0.2%),0.4% (0.3%), 0.2% (0.2%), and 0.2% (0.2%), respectively.Any systematic effects related to the require-ments on M K − π + π − π + e → π , M K − π + π − π + e → π π , M π + π − ,∆ E [( K − π + ) tag π +sig ], cos θ a , cos θ b , are examined by varying individual requirements by ± .
05 GeV/ c , ± . c , ± .
01 GeV/ c , ± .
004 GeV, ± .
02, and ± . K (1270) − meson subdecays on the signal efficienciesis estimated by varying each of the subdecay BFs ofBelle [44] by ± σ and by comparing our nominal signalefficiency to the one based on the world average BFs of K (1270) − meson decays. The quadratic sum of the twovariations in the detection efficiency, 3.0%, is assigned asthe related systematic uncertainty.The systematic uncertainty of the 2D fit is estimated tobe +6 . − . by examining the BF changes with alternativesignal and background shapes. The uncertainty from thesignal shape is mainly caused by varying the K (1270)width by ± σ . The uncertainty of background shape ismainly due to non- K (1270) − sources of K − π + π − . Itis assigned to be the change of the fitted DT yield afterfixing a non-resonant component by referring to the non-resonant fraction in B → J/ψ ¯ Kππ [44]. The uncertaintydue to the MC samples’ limited size, 1.0%, is consideredas a source of systematic uncertainty.The uncertainty from FSR recovery is assigned tobe 0.3% based on studies of a large sample of D → K − e + ν e [50]. The uncertainty due to the kinematic fitis ignored since it is only used to improve the M resolution. The total systematic uncertainty is estimatedto be +8 . − . by adding all the individual contributions inquadrature.Using the world average of B sub = (32 . ± . B SL = B D → K (1270) − e + ν e = (1 . ± . +0 . − . ± . × − , where the third uncertainty is from the externaluncertainty of the assumed BF B sub .In summary, using an e + e − collision data sampleof 2.93 fb − taken at a center-of-mass energy of3.773 GeV, we report the first observation of D → K (1270) − e + ν e . The obtained product of the BFs for D → K (1270) − e + ν e and K (1270) − → K − π + π − isconsistent with the CLEO’s result but with precisionimproved by about threefold [34]. Our BF of D → K (1270) − e + ν e contributes (1 . ± . D [40], which lies between theISGW prediction (1%) and the ISGW2 prediction(2%), consistent with the BESIII results for the D + counterpart [33]. Our BF of D → K (1270) − e + ν e agrees with the CLFQM and LCSR predictions when θ K ≈ ◦ or 57 ◦ [29, 30] and clearly disfavors theprediction reported in Ref. [31]. Using the BF of D + → ¯ K (1270) e + ν e measured by BESIII [33] and the world-average lifetimes of D and D + [40], we determine theratio of the partial decay widths of the two decays to beΓ D → K (1270) − e + ν e / Γ D + → ¯ K (1270) e + ν e = 1 . ± . ± . ± .
04, where the systematic uncertainties from thebackground shape, the tracking and PID efficiencies of K − , π + , and e + as well as FSR recovery are canceled, theuncertainties of the lifetimes of D and D + are included;the uncertainties of the quoted BFs for K (1270) mesondecays are largely canceled. This result agrees with unityas predicted by isospin symmetry.Observation of ¯ K (1270) mesons in the clean envi-ronment of SL D decays opens up the opportunityto further determine the nature of these axial-vectormesons. Studies of the Kππ hadronic system withlarger D → ¯ K (1270) e + ν e samples anticipated atBESIII [52] in the near future will allow for deeperexplorations of the production, mass, width, and mixingangle of the ¯ K (1270) meson, as well as provide accessto hadronic-transition form factors. Moreover, jointanalyses with high statistics samples of D → ¯ K (1270) ℓ + ν ℓ at the future super τ -charm factories [53,54] and B → K (1270) γ samples at Belle II [55]and LHCb [56] will be able to determine the photonpolarization in b → sγ transitions with high accuracy,and thereby over-constrain the right-handed couplings innew physics models.The BESIII collaboration thanks the staff of BEPCIIand the IHEP computing center for their strong support.This work is supported in part by National KeyResearch and Development Program of China underContracts Nos. 2020YFA0406300, 2020YFA0406400;National Natural Science Foundation of China (NSFC)under Contracts Nos. 11775230, 11605124, 11625523,11635010, 11735014, 11822506, 11835012, 11935015,11935016, 11935018, 11961141012; the Chinese Academyof Sciences (CAS) Large-Scale Scientific Facility Pro-gram; Joint Large-Scale Scientific Facility Funds ofthe NSFC and CAS under Contracts Nos. U1732263,U1832207, U1932108; CAS Key Research Program of Frontier Sciences under Contracts Nos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100 Talents Programof CAS; INPAC and Shanghai Key Laboratory forParticle Physics and Cosmology; ERC under ContractNo. 758462; European Union Horizon 2020 researchand innovation programme under Contract No. MarieSklodowska-Curie grant agreement No 894790; Ger-man Research Foundation DFG under Contracts Nos.443159800, Collaborative Research Center CRC 1044,FOR 2359, FOR 2359, GRK 214; Istituto Nazionaledi Fisica Nucleare, Italy; Ministry of Development ofTurkey under Contract No. DPT2006K-120470; NationalScience and Technology fund; Olle Engkvist Foundationunder Contract No. 200-0605; STFC (United Kingdom);The Knut and Alice Wallenberg Foundation (Sweden)under Contract No. 2016.0157; The Royal Society,UK under Contracts Nos. DH140054, DH160214; TheSwedish Research Council; U. S. Department of Energyunder Contracts Nos. DE-FG02-05ER41374, DE-SC-0012069. 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