Observation of e + e − → D + s D ¯ ¯ ¯ ¯ (∗)0 K − and study of the P -wave D s mesons
BESIII Collaboration, M. Ablikim, M. N. Achasov, S. Ahmed, M. Albrecht, M. Alekseev, A. Amoroso, F. F. An, Q. An, J. Z. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, Y. Ban, K. Begzsuren, D. W. Bennett, J. V. Bennett, N. Berger, M. Bertani, D. Bettoni, J. M. Bian, F. Bianchi, E. Boger, I. Boyko, R. A. Briere, H. Cai, X. Cai, O. Cakir, A. Calcaterra, G. F. Cao, S. A. Cetin, J. Chai, J. F. Chang, G. Chelkov, G. Chen, H. S. Chen, J. C. Chen, M. L. Chen, P. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, X. K. Chu, G. Cibinetto, F. Cossio, H. L. Dai, J. P. Dai, A. Dbeyssi, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, Z. L. Dou, S. X. Du, P. F. Duan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, S. Fegan, F. Feldbauer, G. Felici, C. Q. Feng, E. Fioravanti, M. Fritsch, C. D. Fu, Q. Gao, X. L. Gao, Y. Gao, Y. G. Gao, Z. Gao, B. Garillon, I. Garzia, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, M. H. Gu, Y. T. Gu, A. Q. Guo, R. P. Guo, Y. P. Guo, A. Guskov, Z. Haddadi, S. Han, X. Q. Hao, F. A. Harris, K. L. He, X. Q. He, F. H. Heinsius, et al. (357 additional authors not shown)
aa r X i v : . [ h e p - e x ] D ec Chinese Physics C Vol. **, No. * (20**) ******
Observation of e + e − → D + s D ( ∗ )0 K − and study of the P -wave D s mesons M. Ablikim( 麦 迪 娜 ) , M. N. Achasov ,d , S. Ahmed , M. Albrecht , M. Alekseev A, C , A. Amoroso A, C , F. F. An( 安 芬芬 ) ,Q. An( 安 琪 ) , , Y. Bai( 白 羽 ) , O. Bakina , R. Baldini Ferroli A , Y. Ban( 班 勇 ) , K. Begzsuren , D. W. Bennett , J. V. Bennett ,N. Berger , M. Bertani A , D. Bettoni A , F. Bianchi A, C , I. Boyko , R. A. Briere , H. Cai( 蔡 浩 ) , X. Cai( 蔡 啸 ) , ,A. Calcaterra A , G. F. Cao( 曹 国 富 ) , , S. A. Cetin B , J. Chai C , J. F. Chang( 常 劲 帆 ) , , W. L. Chang , , G. Chelkov ,b,c ,G. Chen( 陈 刚 ) , H. S. Chen( 陈 和 生 ) , , J. C. Chen( 陈 江 川 ) , M. L. Chen( 陈 玛 丽 ) , , S. J. Chen( 陈 申 见 ) , Y. B. Chen( 陈 元 柏 ) , ,W. S. Cheng( 成 伟 帅 ) C , G. Cibinetto A , F. Cossio C , H. L. Dai( 代 洪 亮 ) , , J. P. Dai( 代 建平 ) ,h , A. Dbeyssi , D. Dedovich ,Z. Y. Deng( 邓 子 艳 ) , A. Denig , I. Denysenko , M. Destefanis A, C , F. De Mori A, C , Y. Ding( 丁 勇 ) , C. Dong( 董 超 ) ,J. Dong( 董 静 ) , , L. Y. Dong( 董 燎 原 ) , , M. Y. Dong( 董 明 义 ) , Z. L. Dou( 豆 正 磊 ) , S. X. Du( 杜 书 先 ) , J. Z. Fan( 范荆 州 ) ,J. Fang( 方 建 ) , , S. S. Fang( 房 双 世 ) , , Y. Fang( 方 易 ) , R. Farinelli A, B , L. Fava B, C , F. Feldbauer , G. Felici A , C. Q. Feng( 封 常 青 ) , , M. Fritsch , C. D. Fu( 傅 成 栋 ) , Y. Fu( 付 颖 ) , Q. Gao( 高 清 ) , X. L. Gao( 高 鑫 磊 ) , , Y. N. Gao( 高 原 宁 ) , Y. G. Gao( 高 勇 贵 ) , Z. Gao( 高 榛 ) , , B. Garillon , I. Garzia A , A. Gilman , K. Goetzen , L. Gong( 龚 丽 ) , W. X. Gong( 龚 文 煊 ) , , W. Gradl ,M. Greco A, C , L. M. Gu( 谷 立 民 ) , M. H. Gu( 顾 皓 ) , , S. Gu( 顾 珊 ) , Y. T. Gu( 顾 运 厅 ) , A. Q. Guo( 郭 爱 强 ) , L. B. Guo( 郭 立 波 ) , R. P. Guo( 郭 如 盼 ) , , Y. P. Guo( 郭 玉 萍 ) , A. Guskov , Z. Haddadi , S. Han( 韩 爽 ) , X. Q. Hao( 郝 喜 庆 ) , F. A. Harris ,K. L. He( 何 康 林 ) , , F. H. Heinsius , T. Held , Y. K. Heng( 衡 月 昆 ) , Z. L. Hou( 侯 治 龙 ) , H. M. Hu( 胡 海 明 ) , , J. F. Hu( 胡 继 峰 ) ,h ,T. Hu( 胡 涛 ) , Y. Hu( 胡 誉 ) , G. S. Huang( 黄 光 顺 ) , , J. S. Huang( 黄 金 书 ) , X. T. Huang( 黄 性 涛 ) , X. Z. Huang( 黄 晓 忠 ) ,Z. L. Huang( 黄 智 玲 ) , N. Huesken , T. Hussain , W. Ikegami Andersson , W. Imoehl , M. Irshad , , Q. Ji( 纪 全 ) , Q. P. Ji( 姬 清 平 ) , X. B. Ji( 季 晓 斌 ) , , X. L. Ji( 季 筱 璐 ) , , H. L. Jiang( 姜 侯 兵 ) , X. S. Jiang( 江 晓 山 ) , X. Y. Jiang( 蒋 兴 雨 ) , J. B. Jiao( 焦 健 斌 ) , Z. Jiao( 焦 铮 ) , D. P. Jin( 金 大 鹏 ) , S. Jin( 金 山 ) , Y. Jin( 金 毅 ) , T. Johansson , N. Kalantar-Nayestanaki , X. S. Kang( 康 晓 珅 ) , M. Kavatsyuk , B. C. Ke( 柯 百 谦 ) , I. K. Keshk , T. Khan , , A. Khoukaz , P. Kiese , R. Kiuchi , R. Kliemt , L. Koch ,O. B. Kolcu B,f , B. Kopf , M. Kuemmel , M. Kuessner , A. Kupsc , M. Kurth , W. Kühn , J. S. Lange , P. Larin , L. Lavezzi C, ,H. Leithoff , C. Li( 李 翠 ) , Cheng Li( 李 澄 ) , , D. M. Li( 李 德 民 ) , F. Li( 李 飞 ) , , F. Y. Li( 李 峰 云 ) , G. Li( 李 刚 ) , H. B. Li( 李 海 波 ) , , H. J. Li( 李 惠 静 ) ,j , J. C. Li( 李 家 才 ) , J. W. Li( 李 井 文 ) , Ke Li( 李 科 ) , L. K. Li( 李 龙 科 ) , Lei Li( 李 蕾 ) , P. L. Li( 李 佩 莲 ) , ,P. R. Li( 李 培 荣 ) , Q. Y. Li( 李 启 云 ) , W. D. Li( 李 卫 东 ) , , W. G. Li( 李 卫 国 ) , X. L. Li( 李 晓 玲 ) , X. N. Li( 李 小 男 ) , , X. Q. Li( 李 学 潜 ) , Z. B. Li( 李 志 兵 ) , H. Liang( 梁 昊 ) , , Y. F. Liang( 梁 勇 飞 ) , Y. T. Liang( 梁 羽 铁 ) , G. R. Liao( 廖广 睿 ) , L. Z. Liao( 廖 龙 洲 ) , , J. Libby , C. X. Lin( 林 创 新 ) , D. X. Lin( 林 德 旭 ) , B. Liu( 刘 冰 ) ,h , B. J. Liu( 刘 北 江 ) , C. X. Liu( 刘 春 秀 ) , D. Liu( 刘 栋 ) , , D. Y. Liu( 刘 殿 宇 ) ,h , F. H. Liu( 刘 福 虎 ) , Fang Liu( 刘 芳 ) , Feng Liu( 刘 峰 ) , H. B. Liu( 刘 宏 邦 ) , H. L Liu( 刘 恒 君 ) ,H. M. Liu( 刘 怀 民 ) , , Huanhuan Liu( 刘 欢欢 ) , Huihui Liu( 刘 汇 慧 ) , J. B. Liu( 刘 建 北 ) , , J. Y. Liu( 刘 晶 译 ) , , K. Y. Liu( 刘 魁 勇 ) , Kai Liu( 刘 凯 ) , , Ke Liu( 刘 珂 ) , Q. Liu( 刘 倩 ) , S. B. Liu( 刘 树 彬 ) , , X. Liu( 刘 翔 ) , Y. B. Liu( 刘 玉 斌 ) , Z. A. Liu( 刘 振 安 ) , Zhiqing Liu( 刘 智 青 ) , Y. F. Long( 龙 云 飞 ) , X. C. Lou( 娄 辛 丑 ) , H. J. Lu( 吕 海 江 ) , J. D. Lu( 陆 嘉 达 ) , , J. G. Lu( 吕 军光 ) , ,Y. Lu( 卢 宇 ) , Y. P. Lu( 卢 云 鹏 ) , , C. L. Luo( 罗 成 林 ) , M. X. Luo( 罗 民 兴 ) , P. W. Luo( 罗 朋 威 ) , T. Luo( 罗 涛 ) ,j , X. L. Luo( 罗 小 兰 ) , , S. Lusso C , X. R. Lyu( 吕 晓 睿 ) , F. C. Ma( 马 凤 才 ) , H. L. Ma( 马 海 龙 ) , L. L. Ma( 马 连 良 ) , M. M. Ma( 马 明明 ) , ,Q. M. Ma( 马 秋 梅 ) , X. N. Ma( 马 旭 宁 ) , X. X. Ma( 马 新 鑫 ) , , X. Y. Ma( 马骁 妍 ) , , Y. M. Ma( 马 玉 明 ) , F. E. Maas ,M. Maggiora A, C , S. Maldaner , Q. A. Malik , A. Mangoni B , Y. J. Mao( 冒 亚 军 ) , Z. P. Mao( 毛 泽 普 ) , S. Marcello A, C ,Z. X. Meng( 孟 召 霞 ) , J. G. Messchendorp , G. Mezzadri A , J. Min( 闵 建 ) , , T. J. Min( 闵 天 觉 ) , R. E. Mitchell , X. H. Mo( 莫 晓 虎 ) , Y. J. Mo( 莫 玉 俊 ) , C. Morales Morales , N. Yu. Muchnoi ,d , H. Muramatsu , A. Mustafa , S. Nakhoul ,g , Y. Nefedov ,F. Nerling ,g , I. B. Nikolaev ,d , Z. Ning( 宁 哲 ) , , S. Nisar ,k , S. L. Niu( 牛 顺 利 ) , , S. L. Olsen , Q. Ouyang( 欧 阳 群 ) , S. Pacetti B ,Y. Pan( 潘 越 ) , , M. Papenbrock , P. Patteri A , M. Pelizaeus , H. P. Peng( 彭 海 平 ) , , K. Peters ,g , J. Pettersson , J. L. Ping( 平 加 伦 ) , R. G. Ping( 平 荣 刚 ) , , A. Pitka , R. Poling , V. Prasad , , M. Qi( 祁 鸣 ) , T. Y. Qi( 齐 天 钰 ) , S. Qian( 钱 森 ) , , C. F. Qiao( 乔从丰 ) , N. Qin( 覃 拈 ) , X. S. Qin , Z. H. Qin( 秦 中 华 ) , , J. F. Qiu( 邱 进 发 ) , S. Q. Qu( 屈 三 强 ) , K. H. Rashid ,i , C. F. Redmer ,M. Richter , M. Ripka , A. Rivetti C , M. Rolo C , G. Rong( 荣 刚 ) , , Ch. Rosner , M. Rump , A. Sarantsev ,e , M. Savrié B ,K. Schoenning , W. Shan( 单 葳 ) , X. Y. Shan( 单 心 钰 ) , , M. Shao( 邵 明 ) , , C. P. Shen( 沈 成 平 ) , P. X. Shen( 沈 培 迅 ) ,X. Y. Shen( 沈 肖 雁 ) , , H. Y. Sheng( 盛 华 义 ) , X. Shi( 史 欣 ) , , J. J. Song( 宋 娇娇 ) , X. Y. Song( 宋 欣 颖 ) , S. Sosio A, C , C. Sowa ,S. Spataro A, C , F. F. Sui( 隋 风飞 ) , G. X. Sun( 孙 功 星 ) , J. F. Sun( 孙 俊 峰 ) , L. Sun( 孙 亮 ) , S. S. Sun( 孙 胜 森 ) , , X. H. Sun( 孙 新 华 ) , Y. J. Sun( 孙 勇 杰 ) , , Y. K Sun( 孙 艳 坤 ) , , Y. Z. Sun( 孙 永 昭 ) , Z. J. Sun( 孙 志 嘉 ) , , Z. T. Sun( 孙 振 田 ) , Y. T Tan( 谭 雅 星 ) , , C. J. Tang( 唐 昌 建 ) , G. Y. Tang( 唐 光 毅 ) , X. Tang( 唐 晓 ) , M. Tiemens , B. Tsednee , I. Uman D , B. Wang( 王 斌 ) ,B. L. Wang( 王 滨 龙 ) , C. W. Wang( 王 成 伟 ) , D. Y. Wang( 王 大 勇 ) , H. H. Wang( 王 豪豪 ) , K. Wang( 王 科 ) , , L. L. Wang( 王 亮亮 ) ,L. S. Wang( 王 灵 淑 ) , M. Wang( 王 萌 ) , Meng Wang( 王 蒙 ) , , P. Wang( 王 平 ) , P. L. Wang( 王 佩 良 ) , R. M. Wang( 王 茹 敏 ) ,W. P. Wang( 王 维 平 ) , , X. F. Wang( 王 雄 飞 ) , Y. Wang( 王 越 ) , , Y. F. Wang( 王 贻 芳 ) , Z. Wang( 王 铮 ) , , Z. G. Wang( 王 志 刚 ) , ,Z. Y. Wang( 王 至 勇 ) , Zongyuan Wang( 王 宗 源 ) , , T. Weber , D. H. Wei( 魏 代 会 ) , P. Weidenkaff , S. P. Wen( 文 硕 频 ) , U. Wiedner ,M. Wolke , L. H. Wu( 伍 灵 慧 ) , L. J. Wu( 吴 连近 ) , , Z. Wu( 吴 智 ) , , L. Xia( 夏 磊 ) , , Y. Xia( 夏 宇 ) , Y. J. Xiao( 肖 言 佳 ) , ,Z. J. Xiao( 肖 振 军 ) , Y. G. Xie( 谢 宇 广 ) , , Y. H. Xie( 谢 跃 红 ) , X. A. Xiong( 熊 习 安 ) , , Q. L. Xiu( 修 青 磊 ) , , G. F. Xu( 许 国 发 ) ,L. Xu( 徐 雷 ) , Q. J. Xu( 徐 庆 君 ) , W. Xu( 许 威 ) , , X. P. Xu( 徐 新 平 ) , F. Yan( 严 芳 ) , L. Yan( 严亮 ) A, C , W. B. Yan( 鄢 文 标 ) , , Received *** 20** 闫 文 成 ) , Y. H. Yan( 颜 永 红 ) , H. J. Yang( 杨 海 军 ) ,h , H. X. Yang( 杨 洪 勋 ) , L. Yang( 杨柳 ) , R. X. Yang , , S. L. Yang( 杨 双 莉 ) , , Y. H. Yang( 杨 友华 ) , Y. X. Yang( 杨 永 栩 ) , Yifan Yang( 杨 翊 凡 ) , , Z. Q. Yang( 杨 子 倩 ) , M. Ye( 叶 梅 ) , , M. H. Ye( 叶 铭 汉 ) , J. H. Yin( 殷 俊 昊 ) , Z. Y. You( 尤 郑 昀 ) , B. X. Yu( 俞伯 祥 ) , C. X. Yu( 喻 纯 旭 ) , J. S. Yu( 俞 洁 晟 ) , C. Z. Yuan( 苑 长 征 ) , ,Y. Yuan( 袁 野 ) , A. Yuncu B,a , A. A. Zafar , Y. Zeng( 曾 云 ) , B. X. Zhang( 张 丙 新 ) , B. Y. Zhang( 张 炳 云 ) , , C. C. Zhang( 张 长 春 ) ,D. H. Zhang( 张 达 华 ) , H. H. Zhang( 张 宏 浩 ) , H. Y. Zhang( 章 红 宇 ) , , J. Zhang( 张 晋 ) , , J. L. Zhang( 张 杰 磊 ) , J. Q. Zhang ,J. W. Zhang( 张 家 文 ) , J. Y. Zhang( 张 建 勇 ) , J. Z. Zhang( 张 景 芝 ) , , K. Zhang( 张 坤 ) , , L. Zhang( 张 磊 ) , S. F. Zhang( 张 思 凡 ) ,T. J. Zhang( 张 天 骄 ) ,h , X. Y. Zhang( 张 学 尧 ) , Y. Zhang( 张 言 ) , , Y. H. Zhang( 张 银 鸿 ) , , Y. T. Zhang( 张 亚 腾 ) , ,Yang Zhang( 张 洋 ) , Yao Zhang( 张 瑶 ) , Yu Zhang( 张 宇 ) , Z. H. Zhang( 张 正 好 ) , Z. P. Zhang( 张 子 平 ) , Z. Y. Zhang( 张 振 宇 ) ,G. Zhao( 赵 光 ) , J. W. Zhao( 赵 京 伟 ) , , J. Y. Zhao( 赵 静 宜 ) , , J. Z. Zhao( 赵 京 周 ) , , Lei Zhao( 赵 雷 ) , , Ling Zhao( 赵 玲 ) ,M. G. Zhao( 赵 明 刚 ) , Q. Zhao( 赵 强 ) , S. J. Zhao( 赵 书 俊 ) , T. C. Zhao( 赵 天 池 ) , Y. B. Zhao( 赵 豫 斌 ) , , Z. G. Zhao( 赵 政 国 ) , ,A. Zhemchugov ,b , B. Zheng( 郑 波 ) , J. P. Zheng( 郑 建平 ) , , Y. H. Zheng( 郑 阳 恒 ) , B. Zhong( 钟 彬 ) , L. Zhou( 周 莉 ) , ,Q. Zhou( 周 巧 ) , , X. Zhou( 周 详 ) , X. K. Zhou( 周 晓 康 ) , , X. R. Zhou( 周 小 蓉 ) , , Xiaoyu Zhou( 周 晓 宇 ) , Xu Zhou( 周 旭 ) ,A. N. Zhu( 朱 傲 男 ) , , J. Zhu( 朱 江 ) , J. Zhu( 朱 江 ) , K. Zhu( 朱 凯 ) , K. J. Zhu( 朱 科 军 ) , S. H. Zhu( 朱 世 海 ) , X. L. Zhu( 朱 相 雷 ) ,Y. C. Zhu( 朱 莹 春 ) , , Y. S. Zhu( 朱 永 生 ) , , Z. A. Zhu( 朱 自 安 ) , , J. Zhuang( 庄建 ) , , B. S. Zou( 邹 冰 松 ) , J. H. Zou( 邹 佳 恒 ) (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 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia 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 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands Lanzhou University, Lanzhou 730000, 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 Peking University, Beijing 100871, 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 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 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 Tsinghua University, Beijing 100084, People’s Republic of China (A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey; (C)UludagUniversity, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China University of Hawaii, Honolulu, Hawaii 96822, USA University of Jinan, Jinan 250022, People’s Republic of China University of Minnesota, Minneapolis, Minnesota 55455, USA University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany 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 (A)University of Turin, I-10125, Turin, Italy; (B)University of 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 Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia d Also at the Novosibirsk State University, Novosibirsk, 630090, Russia e Also at the NRC "Kurchatov Institute", PNPI, 188300, Gatchina, Russia f Also at Istanbul Arel University, 34295 Istanbul, Turkey g Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany h Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for ParticlePhysics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China i Also at Government College Women University, Sialkot - 51310. Punjab, Pakistan. j Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai200443, People’s Republic of China k Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA
Abstract:
Studies of e + e − → D + s D ( ∗ )0 K − and the P -wave charmed-strange mesons are performed based on an e + e − collisiondata sample corresponding to an integrated luminosity of 567 pb − collected with the BESIII detector at √ s = 4 .
600 GeV . Theprocesses of e + e − → D + s D ∗ K − and D + s D K − are observed for the first time and are found to be dominated by the modes D + s D s (2536) − and D + s D ∗ s (2573) − , respectively. The Born cross sections are measured to be σ B ( e + e − → D + s D ∗ K − ) =(10 . ± . ± .
8) pb and σ B ( e + e − → D + s D K − ) = (19 . ± . ± .
6) pb , and the products of Born cross section and the decaybranching fraction are measured to be σ B ( e + e − → D + s D s (2536) − + c.c. ) ·B ( D s (2536) − → D ∗ K − ) = (7 . ± . ± .
7) pb and σ B ( e + e − → D + s D ∗ s (2573) − + c.c. ) ·B ( D ∗ s (2573) − → D K − ) = (19 . ± . ± .
0) pb . For the D s (2536) − and D ∗ s (2573) − mesons, the masses and widths are measured to be M ( D s (2536) − ) = (2537 . ± . ± .
1) MeV /c , Γ( D s (2536) − ) = (1 . ± . ± .
6) MeV , and M ( D ∗ s (2573) − ) = (2570 . ± . ± .
7) MeV /c , Γ( D ∗ s (2573) − ) = (17 . ± . ± .
1) MeV . The spin-parity of the D ∗ s (2573) − meson is determined to be J P = 2 + . In addition, the process e + e − → D + s D ( ∗ )0 K − are searched forusing the data samples taken at four (two) center-of-mass energies between 4.416 (4.527) and 4.575 GeV, and upper limits at the confidence level on the cross sections are determined. Key words: cross section, P -wave D s mesons, resonance parameters, spin-parity, BESIII PACS:
Although the Heavy Quark Effective Theory (HQET) [1–4] has achieved great success in the past decades in ex-plaining and predicting the spectrum of charmed-strangemesons ( D s ), there still exist discrepancies between the the- oretical predictions and experimental measurements, espe-cially for the P -wave excited states. The unexpectedly lowmasses of D ∗ s (2317) − and D s (2460) − stimulated theoreti-cal and experimental interest not only in them, but also in theother two P -wave charmed-strange states, D s (2536) − and D s (2573) − . The resonance parameters of the D s (2536) − and D ∗ s (2573) − mesons need more experimentally indepen-dent measurements [5]. In particular, the latest result on the D ∗ s (2573) − mass from LHCb [6, 7] deviates from the othermeasurements [8–10] significantly, and therefore, the worldaverage fit gives a bad quality χ /ndf = 17 . / [5], where ndf is the number of degrees of freedom. In addition, thequantum numbers spin and parity ( J P ) of the D ∗ s (2573) − meson have been determined to be J P = 2 + only recentlywith a partial wave analysis carried out by LHCb [11], andmore confirmation is needed.In recent years, measurements of the exclusive cross sec-tions for e + e − annihilation into charmed or charmed-strangemesons above the open charm threshold have attracted greatinterest. First, the charmonium states above the open charmthreshold ( ψ states) still lack of adequate experimental mea-surements and theoretical explanations. The latest parametervalues of these ψ resonances are given by BES [12] from a fitto the total cross section of hadron production in e + e − anni-hilation. However, model predictions for ψ decays into two-body final states were used, hence the values of the resonanceparameters remain model-dependent. Studies of the exclusive e + e − cross sections would help to measure the parameters ofthe ψ states model-independently. Second, many additional Y states with J P = 1 −− lying above the open charm thresh-old have been discovered recently [13–17]. Exclusive crosssection measurements will provide important information inexplaining these states. Measurements of e + e − cross sectionsfor the D ( ∗ )( s ) D ( ∗ )( s ) final states were performed by Belle [18–23], BABAR [24–26], and CLEO [27], only with low-lyingcharmed or charmed-strange mesons in the final states. Upto now, only the DD ∗ (2460) final states in e + e − annihilationhave been observed by Belle [32], others with higher excitedcharmed or charmed-strange mesons have not yet been ob-served. In addition, the cross sections of e + e − → DD ( ∗ ) π have also been measured by CLEO [27] and BESIII [28–31]. However, a search for final states with strange flavor, e + e − → D + s D ( ∗ )0 K − , has not been performed before.Using e + e − collision data corresponding to an integratedluminosity of 567 pb − [33] collected at a center-of-mass en-ergy of √ s = 4 . GeV with the BESIII detector operating atthe Beijing Electron-Positron Collider (BEPCII), we observethe processes e + e − → D + s D ∗ K − and e + e − → D + s D K − ,which are found to be dominated by D + s D s (2536) − and D + s D ∗ s (2573) − , respectively. For the observed D s (2536) − and D ∗ s (2573) − mesons, we present the resonance parame-ters and determine the spin and parity of D ∗ s (2573) − . In ad-dition, the processes e + e − → D + s D ( ∗ )0 K − are searched forusing the data samples taken at four (two) center-of-mass en-ergies between 4.416 (4.527) and 4.575 GeV, and upper limitsat confidence level on the cross sections are determined.Throughout the paper, the charge conjugate processes are im-plied to be included, unless explicitly stated otherwise. The BESIII detector is a magnetic spectrometer [35] lo-cated at the Beijing Electron Positron Collider (BEPCII) [36].The cylindrical core of the BESIII detector consists of ahelium-based multilayer drift chamber (MDC), a plastic scin-tillator time-of-flight system (TOF), and a CsI(Tl) electro-magnetic calorimeter (EMC), which are all enclosed in a su-perconducting solenoidal magnet providing a 1.0 T magneticfield. The solenoid is supported by an octagonal flux-returnyoke with resistive plate counter muon identifier modules in-terleaved with steel. The acceptance for charged particles andphotons is 93% over π solid angle. The charged-particle mo-mentum resolution at /c is . , and the specific en-ergy loss ( dE/dx ) resolution is for electrons from Bhabhascattering. The EMC measures photon energies with a reso-lution of . ( ) at GeV in the barrel (end cap) region.The time resolution of the TOF barrel part is 68 ps, while thatof the end cap part is 110 ps.Simulated data samples are produced with the
GEANT e + e − annihilations modeled with thegenerator KKMC [38]. The inclusive MC samples consist ofthe production of open charm processes, the ISR productionof vector charmonium(-like) states, and the continuum pro-cesses incorporated in
KKMC [38]. The known decay modesare model-led with
EVTGEN [39] using branching fractionstaken from the Particle Data Group [5], and the remainingunknown decays from the charmonium states with
LUND - CHARM [40]. Final state radiation (FSR) from charged finalstate particles is simulated with the
PHOTOS package [41].The intermediate states in the D + s → K + K − π + decay areconsidered in the simulation [42]. In the measurements of D s (2536) − and D ∗ s (2573) − resonance parameters, the an-gular distributions are taken into account in the generationof signal MC samples. For the signal process of e + e − → D + s D s (2536) − , D s (2536) − → D ∗ K − , the spin-parity ofthe D s (2536) − meson is assumed to be + . To determine thespin-parity of D ∗ s (2573) − , efficiencies were obtained fromthe two MC samples, which assume the spin-parity as − or + . The MC sample with spin-parity + is used in the mea-surement of the D ∗ s (2573) − resonance parameters. To identify the final state D + s D ( ∗ )0 K − , a partial recon-struction method is adopted, in which we detect the K − andreconstruct D + s candidates through the D + s → K + K − π + de-cay. The remaining D ( ∗ )0 meson is identified with the mass recoiling against the reconstructed K − D + s system.For each of the four reconstructed charged tracks, the po-lar angle in the MDC must satisfy | cos θ | < . , and the dis-tance of the closest approach from the e + e − interaction pointto the reconstructed track is required to be within cm inthe beam direction and within cm in the plane perpendicu-lar to the beam direction. The ionization energy loss dE/dx measured in the MDC and the time of flight measured bythe TOF are used to perform the particle identification (PID).Pion candidates are required to satisfy prob( π ) > prob(K) ,where prob( π ) and prob(K) are the PID confidence levels fora track to be a pion and kaon, respectively. Kaon candidatesare identified by requiring prob(K) > prob( π ) .The D + s meson candidates are reconstructed from twokaons with opposite charge and one charged pion. To sat-isfy strangeness and charge conservation, each D + s candi-date must be accompanied by a negatively charged kaon.For the D + s candidates, the distributions of the reconstructedmasses M ( K + K − ) versus M ( K − π + ) and M ( K − K + π + ) are shown in Figs. 1(a) and (b), respectively. The two dom-inant sub-resonant decays, i . e . , a horizontal band for theprocess D + s → φπ + and a vertical band for the process D + s → K + K ∗ (892) are clearly visible. To improve the sig-nal significance in Fig. 1(b), only the D + s candidates whichsatisfy M ( K + K − ) < .
05 GeV /c (region A) or . 930 GeV /c (region B) are retained. Thecorresponding M ( K − K + π + ) distributions for events in re-gion A+B and A are plotted in Figs. 1(c) and (d), respectively,showing improved signal significance. The final D + s candi-dates must have a reconstructed mass M ( K − K + π + ) in theregion (1 . , . /c .In this analysis, the resolution of the recoiling mass is im-proved by using the variables RQ ( K − D + s ) ≡ RM ( K − D + s )+ M ( D + s ) − m ( D + s ) and RQ ( D + s ) ≡ RM ( D + s ) + M ( D + s ) − m ( D + s ) . Here, RM ( D + s ) and RM ( K − D + s ) are the recon-structed recoiling masses against the D + s and K − D + s system,respectively, and m ( D + s ) is the nominal D + s mass taken fromthe world average [5]. e + e − → D + s D ( ∗ )0 K − To reject the backgrounds from Λ + c decays in the measure-ment of the cross section of e + e − → D + s D ( ∗ )0 K − , we fur-ther demand that RQ ( D + s ) < . 59 GeV /c . Figure 2 presentsevident peaks in the distribution of RQ ( K − D + s ) around thesignal positions of D ∗ and D , which correspond to the pro-cesses e + e − → D + s D ∗ K − and D + s D K − , respectively.To determine the signal yields of the processes e + e − → D + s D ( ∗ )0 K − at 4.600 GeV, an unbinned maximum likelihoodfit is performed to the RQ ( K − D + s ) spectrum as shown inFig. 2. The signal peaks are described by the MC-determinedsignal shapes and the background shapes are taken as AR-GUS functions [50]. In the fit to data, the endpoint of the background shape is fixed at the value obtained from a fitof an ARGUS function to the RQ ( K − D + s ) spectrum in thebackground MC sample. The Born cross section is calculatedas σ B = N obs L (1 + δ ) | − Π | B ǫ , (1)where N obs is the number of the observed signal candidates, L is the integrated luminosity, ǫ is the detection efficiency de-termined from MC simulations, (1+ δ ) is the radiative correc-tion factor [47], | − Π | is the vacuum polarization factor [48],and B is branching fraction of D + s → K + K − π + . The de-tection efficiencies are estimated based on MC simulations,assuming the two body final states of D + s D s (2536) − and D + s D ∗ s (2573) − dominate the decays to D + s D ( ∗ )0 K − accord-ing to the studies in Secs. and . The numerical resultsare given in Table 1. D s (2536) − For the candidates surviving the basic event selections, wefurther select the signal candidates for e + e − → D + s D ∗ K − by requiring . < RQ ( K − D + s ) < . 024 GeV /c , asshown in Fig. 3(a). The RQ ( D + s ) distribution of the remain-ing events is displayed in Fig. 4(a), where a clear D s (2536) − signal peak near the nominal D s (2536) − mass is visible. Anunbinned maximum likelihood fit is performed to the dis-tribution, where the signal shape is taken as a sum of theefficiency-weighted D -wave and S -wave Breit-Wigner func-tion convolved with the detector resolution function, [ E · ( f · BW S +(1 − f ) · BW D )] ⊗ R . Here, the resolution function R (plotted in Fig. 4(c)) and the efficiency E (plotted in Fig. 4(b)) are determined from MC simulations, and f is the fraction ofthe S -wave Breit-Wigner function. The S -wave and D -waveBreit-Wigner functions are BW S = RQ − m ) + m Γ · p · q , and BW D = RQ − m ) + m Γ · p · q , respectively, where m and Γ are the mass and width of the D s (2536) − to be determinedand p ( q ) is the momentum of K − ( D + s ) in the rest frame of K − D ∗ ( e + e − ) system. The backgrounds are described witha first-order polynomial function. The parameter f is fixed to0.72 [46], while the other parameters are determined in the fit.In this fit, the number of signal candidates is estimated tobe . ± . . The mass and width of the D s (2536) − are measured to be (2537 . ± . ± . / c ,and (1 . ± . ± . , respectively. Thebranching fraction weighted Born cross section is determinedto be σ B ( e + e − → D + s D s (2536) − + c.c. ) · B ( D s (2536) − → D ∗ K − ) = (7 . ± . ± . 7) pb . The relevant systematicuncertainties are discussed later and summarized in Table 3. D ∗ s (2573) − To study the D ∗ s (2573) − properties, we select thesignal candidates of the process e + e − → D + s D K − by requiring RQ ( K − D + s ) in the D signal region of (1 . , . /c , as shown in Fig. 3(b). To reject back- ) ) (GeV/c + π - M(K ) ) ( G e V / c - K + M ( K AB (a) ) GeV/c + π + K - M(K ) E v en t s / ( M e V / c ) GeV/c + π + K - M(K ) E v en t s / ( M e V / c (b) ) GeV/c + π + K - M(K ) E v en t s / ( M e V / c ) GeV/c + π + K - M(K ) E v en t s / ( M e V / c (c) regions A+B ) GeV/c + π + K - M(K ) E v en t s / ( M e V / c ) GeV/c + π + K - M(K ) E v en t s / ( M e V / c (d) region A Figure 1. Scatter plot of M ( K + K − ) versus M ( K − π + ) for the D + s → K + K − π + candidates (a) and the corresponding invari-ant mass M ( K + K − π + ) distribution (b) for data at √ s = 4 . 600 GeV . The M ( K + K − π + ) distributions of the subsamples fromthe regions A+B and from the region A are shown in plot (c) and (d), respectively. In plots (b), (c) and (d), fits with the sum of aGaussian function and a polynomial function are implemented to determine the signal regions for the D + s candidates. The signalwindows are shown with arrows. ) ) (GeV/c +s D - RQ(K1.8 1.9 2 2.1 ) E v en t s / ( M e V / c ) (GeV/c +s D - RQ(K1.8 1.9 2 2.1 ) E v en t s / ( M e V / c Figure 2. Distributions of RQ ( K − D + s ) for the D + s signal candidates in regions A + B in Fig. 1(c), for data taken at √ s = 4 . 600 GeV . The solid line shows the total fit to the data points and the dashed lines represent the D and D ∗ signals.010201-6hinese Physics C Vol. **, No. * (20**) ****** ) ) (GeV/c +s D - RQ(K1.95 2 2.05 ) E v en t s / ( M e V / c ) (GeV/c +s D - RQ(K1.95 2 2.05 ) E v en t s / ( M e V / c (a) ) ) (GeV/c +s D - RQ(K1.85 1.9 ) E v en t s / ( M e V / c ) (GeV/c +s D - RQ(K1.85 1.9 ) E v en t s / ( M e V / c (b) Figure 3. At 4.600 GeV, (a) the RQ ( K − D + s ) distribution for the D + s candidates from signal regions A and B in Fig. 1(c); (b)the RQ ( K − D + s ) distribution for the D + s candidates from signal regions A in Fig. 1(d). Fits with the sum of a Gaussian functionand a polynomial function are implemented to determine the signal regions for the D ( ∗ )0 candidates, which are indicated witharrows. ) )(GeV/c +s RQ(D ) E v en t s / ( M e V / c ) )(GeV/c +s RQ(D ) E v en t s / ( M e V / c E ff i c i en cy ) ))(GeV/c +s (RQ(D δ -0.01 0 0.01 ) ))(GeV/c +s (RQ(D δ -0.01 0 0.01 (c)(b)(a) ) )(GeV/c +s RQ(D ) E v en t s / ( M e V / c ) )(GeV/c +s RQ(D ) E v en t s / ( M e V / c E ff i c i en cy ) ))(GeV/c +s (RQ(D δ -0.01 0 0.01 ) ))(GeV/c +s (RQ(D δ -0.01 0 0.01 (d)(e)(f) Figure 4. At 4.600 GeV, the RQ ( D + s ) spectra in the samples of e + e − → D + s D ∗ K − (left) and e + e − → D + s D K − (right).Plots (a) and (d) show the result of the unbinned maximum likelihood fits. Data are denoted by the dots with error bars. Thedash-dotted and dotted lines are the background and signal contributions, respectively. Plots (b) and (e) show the efficiencyfunctions. Plots (c) and (f) show the RQ ( D + s ) resolution functions determined from MC simulations.010201-7hinese Physics C Vol. **, No. * (20**) ****** grounds from e + e − → Λ + c Λ − c , only the D + s candidates in re-gion A of Fig. 1 are used. For the selected events, the corre-sponding RQ ( D + s ) distribution is plotted in Fig. 4(d), wherea clear D ∗ s (2573) − signal peak near the known D ∗ s (2573) − mass is observed.An unbinned maximum likelihood fit is performed tothe RQ ( D + s ) spectrum in Fig. 4(d). The spin-parity of the D ∗ s (2573) − meson is fixed to be + , following the studies inSec. , and the D ∗ s (2573) − meson is assumed to decay to D K − predominantly via D -wave [2]. Hence, we take the D -wave Breit-Wigner function BW = RQ − m ) + m Γ · p · q convolved with the resolution function (shown in Fig. 4(f)), BW ⊗ R , to describe the signal, and a flat line to representbackgrounds. Here, p ( q ) is the momentum of K − ( D + s ) in therest frame of the K − D ( e + e − ) system. Figure 4 (e) shows theefficiency distribution with the assignment J P = 2 + , which isconsistent with a flat line. All parameters are left free in thefit. The fit yields . ± . signal events. The massand width of the D ∗ s (2573) − are measured to be (2570 . ± . ± . / c , and (17 . ± . ± . , respectively, where the systematic uncer-tainties are summarized in Table 2. The branching frac-tion weighted Born cross section is given to be σ B ( e + e − → D + s D ∗ s (2573) − + c.c. ) ·B ( D ∗ s (2573) − → D K − ) = (19 . ± . ± . 0) pb . The relevant systematic uncertainties are dis-cussed later and summarized in Table 3. D ∗ s (2573) − At √ s = 4 . 600 GeV , the exclusive process e + e − → D + s D ∗ s (2573) − → D + s D K − is observed just above the pro-duction threshold. For the D ∗ s (2573) − meson, the J P as-signments with high spins would be strongly suppressed inthis process. Hence, we assume that the D ∗ s (2573) − mesoncan only have two possible J P assignments, − or + . Underthese two hypotheses, the differential decay rates as a func-tion of the helicity angle θ ′ of the K − in the rest frame ofthe D ∗ s (2573) − , dN / d cos θ ′ , follow two very distinctive for-mulae of (1 − cos θ ′ ) for − and cos θ ′ (1 − cos θ ′ ) for + .We can determine the true spin-parity from tests of the twohypotheses based on data.In each | cos θ ′ | interval of width 0.2, the number of back-ground events is estimated from the RQ ( D + s ) sideband re-gion (2.44, 2.50) GeV /c according to the global fit shownin Fig. 4 (d) and subtracted from the signal candidates inthe signal region, (2.54, 2.60) GeV /c . Then we obtain theefficiency-corrected angular distribution of d σ/ d | cos θ ′ | , asdepicted in Fig. 5 for the D ∗ s (2573) − signals. The efficiencydistributions in Figs. 5 (a) and (c) are obtained from the signalMC simulation samples, which assume the spin-parity of the D ∗ s (2573) − as − and + , respectively.The shapes of the two spin-parity hypotheses are con-structed as a (1 − cos θ ′ ) and a cos θ ′ (1 − cos θ ′ ) for − and + , respectively. Here, a and a normalize the shapes to the area of the efficiency corrected angular distributions. To testthe two different assumptions, we calculate χ = Σ( y i − µ i σ i ) ,where i is the index of the interval in the angular distributions, y i is the estimated signal yield in interval i , σ i is the corre-sponding statistical uncertainty, and µ i is the expected num-ber of signal events. The values of χ for the J P = 1 − and + assumptions are evaluated as . and . , respectively.Hence, our results strongly favor the J P = 2 + assignmentand disfavor the J P = 1 − assignment for the D ∗ s (2573) − . The process e + e − → D + s D ( ∗ )0 K − is also searched for atfour (two) other energy points. The corresponding integratedluminosities [33] and center-of-mass energies [34] are shownin Table 1. The analysis strategy and event selection are thesame as those explained in Sec. . The resultant RQ ( K − D + s ) distributions are shown in Fig. 6, together with the results ofunbinned maximum likelihood fits as described in Sec. .The fit results are given in Table 1.As has been studied with the largest statistics dataat √ s = 4 . 600 GeV , the processes D + s D s (2536) − and D + s D ∗ s (2573) − dominate the processes e + e − → D + s D ∗ K − and e + e − → D + s D K − , respectively. We assume thatthis conclusion still holds for the MC simulations of the fi-nal states of D + s D ( ∗ )0 K − for the energy points above the D + s D s (2536) − or D + s D ∗ s (2573) − mass thresholds. For theenergy points below the mass thresholds, the signal MC simu-lation samples of the three-body processes are generated withaverage momentum distributions in the phase space.Since the four data samples taken at lower energies suf-fer from low statistics, we also present upper limits at the confidence level on the cross sections. The upper lim-its are determined using a Bayesian approach with a flat prior.The systematic uncertainties are considered by convolving thelikelihood distribution with a Gaussian function representingthe systematic uncertainties. The numerical results are sum-marized in Table 1. The systematic uncertainties on the resonance parametersand cross section measurements are summarized in Tables 2and 3, respectively, where the total systematic uncertaintiesare obtained by adding all items in quadrature. For each item,details are elaborated as follows.1. Tracking efficiency. The difference in tracking effi-ciency for the kaon and pion reconstruction betweenthe MC simulation and the real data is estimated to be . per track [49]. Hence, . is taken as the sys-tematic uncertainty for four charged tracks.2. PID efficiency. The uncertainty of identifying the par-ticle types of kaon and pion is estimated to be per E ff i c i en cy ’| θ |cos ’ θ d N / d c o s (a) J P = 1 − (b) E ff i c i en cy ’| θ |cos ’ θ d N / d c o s (c) J P = 2 + (d) Figure 5. At 4.600 GeV, the efficiency-corrected | cos θ ′ | distribution for the background-subtracted D ∗ s (2573) − signals areshown in plots (b) and (d). Plots (a) and (c) are the corresponding efficiency distributions under the J P assumptions of − and + , respectively. The shapes to be tested are shown in (b) and (d) for the two hypotheses, normalized to the area of datadistribution.Table 1. Cross section measurements at different energy points. For the cross sections, the first set of uncertainties are statisticaland the second are systematic. The uncertainties of the number of observed signals are statistical only. The four samples withlower center-of-mass energies suffer from low statistics, we therefore set the lower and upper boundary of the uncertainties of N obs as 0 and the upper limits at the 68.3% confidence level, respectively. √ s ( GeV) L ( pb − ) 567 48 110 110 1029 | − Π | δ ǫ (%) 16.1 14.3 13.2 D + s D ∗ K − N obs . ± . . +2 . − . . +3 . − . σ B ( pb ) . ± . ± . . +7 . . − . − . . +6 . − . ± . N up σ BU.L. ( pb ) δ ǫ (%) 22.3 23.9 20.3 18.2 14.6 D + s D K − N obs . ± . . +3 . − . . +4 . − . . +7 . − . . +8 . − . σ B ( pb ) . ± . ± . . +6 . . − . − . . +5 . − . ± . . +8 . − . ± . . +1 . − . ± . N up σ BU.L. ( pb ) D s (2536) − and D ∗ s (2573) − resonance parameters measured at √ s =4 . 600 GeV . “ · · · ” means the uncertainty is negligible. Mass ( MeV / c ) Width ( MeV)Source D s (2536) − D ∗ s (2573) − D s (2536) − D ∗ s (2573) − Mass shift 3.0 1.3 · · · · · · Detector resolution · · · · · · · · · · · · Background shape 0.2 0.4 0.2 0.3Fit range · · · · · · Table 3. Relative systematic uncertainties (in %) on the cross section measurement. The first value in brackets is for D + s D K − ,and the second for D + s D ∗ K − . “ · · · ” means the uncertainty is negligible. “-” means unavailable due to √ s being below theproduction threshold. σ B ( e + e − → D + s D ( ∗ )0 K − ) at different √ s ( GeV) e + e − → D + s D − sJ at 4.600 GeVSource 4.600 4.575 4.527 4.467 4.416 D s (2536) − D ∗ s (2573) − Tracking 4 4 4 4 4 4 4Particle ID 4 4 4 4 4 4 4Luminosity 1 1 1 1 1 1 1Branching faction 3 3 3 3 3 3 3center-of-mass energy · · · · · · · · · · · · · · · · · · · · · Fit range ( · · · , 2) (2, · · · ) (4, 3) ( · · · ,-) ( · · · ,-) 3 4Background shape (3, 1) (1, 4) (4, 5) (5,-) (6,-) 4 5Line shape (3, 4) (2, 3) (1, 1) (1,-) ( · · · ,-) 4 3Total: (8, 8) (7, 8) (9, 9) (8,-) (9,-) 9 10 ) ) (GeV/c +s D - RQ(K1.8 1.9 2 2.1 ) E v en t s / ( M e V / c ) (GeV/c +s D - RQ(K1.8 1.9 2 2.1 ) E v en t s / ( M e V / c (a) ) ) (GeV/c +s D - RQ(K1.8 1.9 2 2.1 ) E v en t s / ( M e V / c ) (GeV/c +s D - RQ(K1.8 1.9 2 2.1 ) E v en t s / ( M e V / c (b) ) ) (GeV/c +s D - RQ(K1.8 1.9 2 ) E v en t s / ( M e V / c ) (GeV/c +s D - RQ(K1.8 1.9 2 ) E v en t s / ( M e V / c (c) ) ) (GeV/c +s D - RQ(K1.8 1.9 2 ) E v en t s / ( M e V / c ) (GeV/c +s D - RQ(K1.8 1.9 2 ) E v en t s / ( M e V / c (d) Figure 6. RQ ( K − D + s ) distributions and the fit results at each energy point. Points with error bars are data, the dotted linespeaking at the nominal mass of the D ( D ∗ ) are the signal shapes for e + e − → D + s D K − ( D + s D ∗ K − ) process.010201-10hinese Physics C Vol. **, No. * (20**) ****** charged track [49]. Therefore, . is taken as the sys-tematic uncertainty for the PID efficiency of the fourdetected charged tracks.3. Signal Model. In the fits of the D s (2536) − , the frac-tion of the D -wave and S -wave components is variedaccording to the Belle measurement [46], and the max-imum changes on the fit results are taken as systematicuncertainties. In the measurement of the D ∗ s (2573) − resonance parameters, the uncertainty stemming fromthe signal model is negligible as the D -wave amplitudedominates in the heavy quark limit.4. Background Shape. In the measurements of the D s (2536) − and D ∗ s (2573) − resonance parameters,linear background functions are used in the nominalfits. To estimate the uncertainties due to the backgroundparametrization, higher order polynomial functions arestudied, and the largest changes on the final results aretaken as the systematic uncertainty. In the measurementof σ B ( e + e − → D + s D ( ∗ )0 K − ), we replace the ARGUSbackground shape in the nominal fit with a second-order polynomial function a ( m − m ) + b , where m isthe threshold value and is the same as that in the nom-inal fit, while a and b are free parameters. We take thedifference on the final results as the systematic uncer-tainty.5. Fit Range. We vary the boundaries of the fit rangesto estimate the relevant systematic uncertainty, whichare taken as the maximum changes on the numericalresults.6. Mass Shift and Detector Resolution. In the nominalfits to measure the D s (2536) − and D ∗ s (2573) − res-onance parameters, the effects of a mass shift and thedetector resolution are included in the MC determineddetector resolution shape. The potential bias from theMC simulations are studied using the control sample of e + e − → D + s D ∗− s . We select the D + s candidates follow-ing the aforementioned selection criteria and plot the RQ ( D + s ) distribution to be fitted to the D ∗− s peak. Thesignal function is composed of a Breit-Wigner shapeconvolved with a Gaussian function. We extract thedetector resolution parameters from a series of fits atdifferent momentum intervals of the D + s candidates.Hence, the absolute resolution parameters for the fitsto the D s (2536) − or D ∗ s (2573) − are extrapolated ac-cording to the detected D + s momentum. In an alter-native fit, we fix the resolution parameters accordingto this study, instead of to the MC-determined resolu-tion shape. The resultant change in the new fit from theoriginal fit is considered as the systematic uncertainty.7. Branching Fraction. The systematic uncertainty in thebranching fraction for the process D + s → K + K − π + istaken from PDG [5]. 8. Luminosity. The integrated luminosity of each sampleis measured with a precision of with Bhabha scat-tering events [33].9. Center-of-mass energy. We change the values of center-of-mass energy of each sample according to the uncer-tainties in Ref. [34] to estimate the systematic uncer-tainties due to the center-of-mass energy.10. Line Shape of Cross Section. The line shape of the e + e − → D + s D ( ∗ )0 K − cross section (including theintermediate D s (2536) − and D ∗ s (2573) − states) af-fects the radiative correction factor and the detectionefficiency. This uncertainty is estimated by changingthe input of the observed line shape to the simula-tion. In the nominal measurement, a power functionof c · ( √ s − E ) d is taken as the input of the observedline shape. Here, E is the production threshold en-ergy for the process e + e − → D + s D ( ∗ )0 K − , and c and d are parameters determined from fits to the observedline shape. To estimate the uncertainty, we change theexponent of the nominal input power function to d ± and compare the results with the nominal measurement.The largest difference is taken as the systematic uncer-tainty. We study the process e + e − → D + s D ( ∗ )0 K − at 4.600GeV and observe the two P -wave charmed-strange mesons, D s (2536) − and D ∗ s (2573) − . The D s (2536) − mass is mea-sured to be (2537 . ± . ± . 1) MeV / c and its width is (1 . ± . ± . 6) MeV , both consistent with the currentworld-average values in PDG [5]. The mass and width ofthe D ∗ s (2573) − meson are measured to be (2570 . ± . ± . 7) MeV / c and (17 . ± . ± . 1) MeV , respectively,which are compatible with the LHCb [6, 7] and PDG [5]values. The spin-parity of the D ∗ s (2573) − meson is de-termined to be J P = 2 + , which confirms the LHCb re-sult [11]. The Born cross sections are measured to be σ B ( e + e − → D + s D ∗ K − ) = (10 . ± . ± . 8) pb and σ B ( e + e − → D + s D K − ) = (19 . ± . ± . 6) pb . Theproducts of the Born cross section and the decay branchingfraction are measured to be σ B ( e + e − → D + s D s (2536) − + c.c. ) · B ( D s (2536) − → D ∗ K − ) = (7 . ± . ± . 7) pb and σ B ( e + e − → D + s D ∗ s (2573) − + c.c. ) · B ( D ∗ s (2573) − → D K − ) = (19 . ± . ± . 0) pb . In addition, the pro-cesses e + e − → D + s D ( ∗ )0 K − are searched for using smalldata samples taken at four (two) center-of-mass energies be-tween 4.416 (4.527) and 4.575 GeV, and upper limits at the confidence level on the cross sections are determined. The BESIII collaboration thanks the staff of BEPCII andthe IHEP computing center for their strong support. This work is supported in part by National Key Basic ResearchProgram of China under Contract No. 2015CB856700; Na-tional Natural Science Foundation of China (NSFC) underContracts Nos. 11335008, 11425524, 11625523, 11635010,11735014; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Ex-cellence in Particle Physics (CCEPP); Joint Large-Scale Sci-entific Facility Funds of the NSFC and CAS under Con-tracts Nos. 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