Open Access

Helicity amplitude and branching fraction measurement of $χ_{c J} \to Λ \bar{Λ}$

M. Ablikim ¹, M. N. Achasov ^4,c, P. Adlarson ⁷⁷, X. C. Ai ⁸², R. Aliberti ³⁶, A. Amoroso ^76a,76c, Q. An^59,73,a, Y. Bai ⁵⁸, O. Bakina ³⁷ et al. (BESIII Collaboration)

O. Bakina ³⁷, Y. Ban ^47,h, H.-R. Bao ⁶⁵, V. Batozskaya ^1,45, K. Begzsuren³³, N. Berger ³⁶, M. Berlowski ⁴⁵, M. Bertani ^29a, D. Bettoni ^30a, F. Bianchi ^76a,76c, E. Bianco^76a,76c, A. Bortone ^76a,76c, I. Boyko ³⁷, R. A. Briere ⁵, A. Brueggemann ⁷⁰, H. Cai ⁷⁸, M. H. Cai ^39,k,l, X. Cai ^1,59, A. Calcaterra ^29a, G. F. Cao ^1,65, N. Cao ^1,65, S. A. Cetin ^63a, X. Y. Chai ^47,h, J. F. Chang ^1,59, G. R. Che ⁴⁴, Y. Z. Che ^1,59,65, C. H. Chen ⁹, Chao Chen ⁵⁶, G. Chen ¹, H. S. Chen ^1,65, H. Y. Chen ²¹, M. L. Chen ^1,59,65, S. J. Chen ⁴³, S. L. Chen ⁴⁶, S. M. Chen ⁶², T. Chen ^1,65, X. R. Chen ^32,65, X. T. Chen ^1,65, X. Y. Chen ^12,g, Y. B. Chen ^1,59, Y. Q. Chen ³⁵, Y. Q. Chen¹⁶, Z. Chen ²⁵, Z. J. Chen ^26,i, Z. K. Chen ⁶⁰, S. K. Choi ¹⁰, X. Chu ^12,g, G. Cibinetto ^30a, F. Cossio ^76c, J. Cottee-Meldrum ⁶⁴, J. J. Cui ⁵¹, H. L. Dai ^1,59, J. P. Dai ⁸⁰, A. Dbeyssi¹⁹, R. E. de Boer ³, D. Dedovich ³⁷, C. Q. Deng ⁷⁴, Z. Y. Deng ¹, A. Denig ³⁶, I. Denysenko ³⁷, M. Destefanis ^76a,76c, F. De Mori ^76a,76c, B. Ding ^1,68, X. X. Ding ^47,h, Y. Ding ⁴¹, Y. Ding ³⁵, Y. X. Ding ³¹, J. Dong ^1,59, L. Y. Dong ^1,65, M. Y. Dong ^1,59,65, X. Dong ⁷⁸, M. C. Du ¹, S. X. Du ⁸², S. X. Du ^12,g, Y. Y. Duan ⁵⁶, P. Egorov ^37,b, G. F. Fan ⁴³, J. J. Fan ²⁰, Y. H. Fan ⁴⁶, J. Fang ^1,59, J. Fang ⁶⁰, S. S. Fang ^1,65, W. X. Fang ¹, Y. Q. Fang^1,59, R. Farinelli ^30a, L. Fava ^76b,76c, F. Feldbauer ³, G. Felici ^29a, C. Q. Feng ^59,73, J. H. Feng ¹⁶, L. Feng ^39,k,l, Q. X. Feng ^39,k,l, Y. T. Feng ^59,73, M. Fritsch ³, C. D. Fu ¹, J. L. Fu ⁶⁵, Y. W. Fu ^1,65, H. Gao ⁶⁵, X. B. Gao ⁴², Y. Gao ^59,73, Y. N. Gao ^47,h, Y. N. Gao ²⁰, Y. Y. Gao ³¹, S. Garbolino ^76c, I. Garzia ^30a,30b, P. T. Ge ²⁰, Z. W. Ge ⁴³, C. Geng ⁶⁰, E. M. Gersabeck ⁶⁹, A. Gilman ⁷¹, K. Goetzen ¹³, J. D. Gong ³⁵, L. Gong ⁴¹, W. X. Gong ^1,59, W. Gradl ³⁶, S. Gramigna ^30a,30b, M. Greco ^76a,76c, M. H. Gu ^1,59, Y. T. Gu ¹⁵, C. Y. Guan ^1,65, A. Q. Guo ³², L. B. Guo ⁴², M. J. Guo ⁵¹, R. P. Guo ⁵⁰, Y. P. Guo ^12,g, A. Guskov ^37,b, J. Gutierrez ²⁸, K. L. Han ⁶⁵, T. T. Han ¹, F. Hanisch ³, K. D. Hao ^59,73, X. Q. Hao ²⁰, F. A. Harris ⁶⁷, K. K. He ⁵⁶, K. L. He ^1,65, F. H. Heinsius ³, C. H. Heinz ³⁶, Y. K. Heng ^1,59,65, C. Herold ⁶¹, P. C. Hong ³⁵, G. Y. Hou ^1,65, X. T. Hou ^1,65, Y. R. Hou ⁶⁵, Z. L. Hou ¹, H. M. Hu ^1,65, J. F. Hu ^57,j, Q. P. Hu ^59,73, S. L. Hu ^12,g, T. Hu ^1,59,65, Y. Hu ¹, Z. M. Hu ⁶⁰, G. S. Huang ^59,73, K. X. Huang ⁶⁰, L. Q. Huang ^32,65, P. Huang ⁴³, X. T. Huang ⁵¹, Y. P. Huang ¹, Y. S. Huang ⁶⁰, T. Hussain ⁷⁵, N. Hüsken ³⁶, N. in der Wiesche⁷⁰, J. Jackson ²⁸, Q. Ji ¹, Q. P. Ji ²⁰, W. Ji ^1,65, X. B. Ji ^1,65, X. L. Ji ^1,59, Y. Y. Ji ⁵¹, Z. K. Jia ^59,73, D. Jiang ^1,65, H. B. Jiang ⁷⁸, P. C. Jiang ^47,h, S. J. Jiang ⁹, T. J. Jiang ¹⁷, X. S. Jiang ^1,59,65, Y. Jiang ⁶⁵, J. B. Jiao ⁵¹, J. K. Jiao ³⁵, Z. Jiao ²⁴, S. Jin ⁴³, Y. Jin ⁶⁸, M. Q. Jing ^1,65, X. M. Jing ⁶⁵, T. Johansson ⁷⁷, S. Kabana ³⁴, N. Kalantar-Nayestanaki ⁶⁶, X. L. Kang ⁹, X. S. Kang ⁴¹, M. Kavatsyuk ⁶⁶, B. C. Ke ⁸², V. Khachatryan ²⁸, A. Khoukaz ⁷⁰, R. Kiuchi¹, O. B. Kolcu ^63a, B. Kopf ³, M. Kuessner ³, X. Kui ^1,65, N. Kumar ²⁷, A. Kupsc ^45,77, W. Kühn ³⁸, Q. Lan ⁷⁴, W. N. Lan ²⁰, T. T. Lei ^59,73, M. Lellmann ³⁶, T. Lenz ³⁶, C. Li ^59,73, C. Li ⁴⁸, C. Li ⁴⁴, C. H. Li ⁴⁰, C. K. Li ²¹, D. M. Li ⁸², F. Li ^1,59, G. Li ¹, H. B. Li ^1,65, H. J. Li ²⁰, H. N. Li ^57,j, Hui Li ⁴⁴, J. R. Li ⁶², J. S. Li ⁶⁰, K. Li ¹, K. L. Li ²⁰, K. L. Li^39,k,l, L. J. Li ^1,65, Lei Li ⁴⁹, M. H. Li ⁴⁴, M. R. Li ^1,65, P. L. Li ⁶⁵, P. R. Li ^39,k,l, Q. M. Li ^1,65, Q. X. Li ⁵¹, R. Li ^18,32, S. X. Li ¹², T. Li ⁵¹, T. Y. Li ⁴⁴, W. D. Li ^1,65, W. G. Li ^1,a, X. Li ^1,65, X. H. Li ^59,73, X. L. Li ⁵¹, X. Y. Li ^1,8, X. Z. Li ⁶⁰, Y. Li ²⁰, Y. G. Li ^47,h, Y. P. Li ³⁵, Z. J. Li ⁶⁰, Z. Y. Li ⁸⁰, H. Liang ^59,73, Y. F. Liang ⁵⁵, Y. T. Liang ^32,65, G. R. Liao ¹⁴, L. B. Liao ⁶⁰, M. H. Liao ⁶⁰, Y. P. Liao ^1,65, J. Libby ²⁷, A. Limphirat ⁶¹, C. C. Lin ⁵⁶, D. X. Lin ^32,65, L. Q. Lin ⁴⁰, T. Lin ¹, B. J. Liu ¹, B. X. Liu ⁷⁸, C. Liu ³⁵, C. X. Liu ¹, F. Liu ¹, F. H. Liu ⁵⁴, Feng Liu ⁶, G. M. Liu ^57,j, H. Liu ^39,k,l, H. B. Liu ¹⁵, H. H. Liu ¹, H. M. Liu ^1,65, Huihui Liu ²², J. B. Liu ^59,73, J. J. Liu ²¹, K. Liu ^39,k,l, K. Liu ⁷⁴, K. Y. Liu ⁴¹, Ke Liu ²³, L. C. Liu ⁴⁴, Lu Liu ⁴⁴, M. H. Liu ^12,g, P. L. Liu ¹, Q. Liu ⁶⁵, S. B. Liu ^59,73, T. Liu ^12,g, W. K. Liu ⁴⁴, W. M. Liu ^59,73, W. T. Liu ⁴⁰, X. Liu ^39,k,l, X. Liu ⁴⁰, X. K. Liu ^39,k,l, X. Y. Liu ⁷⁸, Y. Liu ^39,k,l, Y. Liu ⁸², Yuan Liu⁸², Y. B. Liu ⁴⁴, Z. A. Liu ^1,59,65, Z. D. Liu ⁹, Z. Q. Liu ⁵¹, X. C. Lou ^1,59,65, F. X. Lu ⁶⁰, H. J. Lu ²⁴, J. G. Lu ^1,59, X. L. Lu ¹⁶, Y. Lu ⁷, Y. H. Lu ^1,65, Y. P. Lu ^1,59, Z. H. Lu ^1,65, C. L. Luo ⁴², J. R. Luo ⁶⁰, J. S. Luo ^1,65, M. X. Luo⁸¹, T. Luo ^12,g, X. L. Luo ^1,59, Z. Y. Lv ²³, X. R. Lyu ^65,p, Y. F. Lyu ⁴⁴, Y. H. Lyu ⁸², F. C. Ma ⁴¹, H. L. Ma ¹, J. L. Ma ^1,65, L. L. Ma ⁵¹, L. R. Ma ⁶⁸, Q. M. Ma ¹, R. Q. Ma ^1,65, R. Y. Ma ²⁰, T. Ma ^59,73, X. T. Ma ^1,65, X. Y. Ma ^1,59, Y. M. Ma ³², F. E. Maas ¹⁹, I. MacKay ⁷¹, M. Maggiora ^76a,76c, S. Malde ⁷¹, Q. A. Malik ⁷⁵, H. X. Mao ^39,k,l, Y. J. Mao ^47,h, Z. P. Mao ¹, S. Marcello ^76a,76c, A. Marshall ⁶⁴, F. M. Melendi ^30a,30b, Y. H. Meng ⁶⁵, Z. X. Meng ⁶⁸, G. Mezzadri ^30a, H. Miao ^1,65, T. J. Min ⁴³, R. E. Mitchell ²⁸, X. H. Mo ^1,59,65, B. Moses ²⁸, N. Yu. Muchnoi ^4,c, J. Muskalla ³⁶, Y. Nefedov ³⁷, F. Nerling ^19,e, L. S. Nie ²¹, I. B. Nikolaev^4,c, Z. Ning ^1,59, S. Nisar^11,m, Q. L. Niu ^39,k,l, W. D. Niu ^12,g, C. Normand ⁶⁴, S. L. Olsen ^10,65, Q. Ouyang ^1,59,65, S. Pacetti ^29b,29c, X. Pan ⁵⁶, Y. Pan ⁵⁸, A. Pathak ¹⁰, Y. P. Pei ^59,73, M. Pelizaeus ³, H. P. Peng ^59,73, X. J. Peng ^39,k,l, Y. Y. Peng ^39,k,l, K. Peters ^13,e, K. Petridis ⁶⁴, J. L. Ping ⁴², R. G. Ping ^1,65, S. Plura ³⁶, V. Prasad ³⁵, F. Z. Qi ¹, H. R. Qi ⁶², M. Qi ⁴³, S. Qian ^1,59, W. B. Qian ⁶⁵, C. F. Qiao ⁶⁵, J. H. Qiao ²⁰, J. J. Qin ⁷⁴, J. L. Qin ⁵⁶, L. Q. Qin ¹⁴, L. Y. Qin ^59,73, P. B. Qin ⁷⁴, X. P. Qin ^12,g, X. S. Qin ⁵¹, Z. H. Qin ^1,59, J. F. Qiu ¹, Z. H. Qu ⁷⁴, J. Rademacker ⁶⁴, C. F. Redmer ³⁶, A. Rivetti ^76c, M. Rolo ^76c, G. Rong ^1,65, S. S. Rong ^1,65, F. Rosini ^29b,29c, Ch. Rosner ¹⁹, M. Q. Ruan ^1,59, N. Salone ⁴⁵, A. Sarantsev ^37,d, Y. Schelhaas ³⁶, K. Schoenning ⁷⁷, M. Scodeggio ^30a, K. Y. Shan ^12,g, W. Shan ²⁵, X. Y. Shan ^59,73, Z. J. Shang ^39,k,l, J. F. Shangguan ¹⁷, L. G. Shao ^1,65, M. Shao ^59,73, C. P. Shen ^12,g, H. F. Shen ^1,8, W. H. Shen ⁶⁵, X. Y. Shen ^1,65, B. A. Shi ⁶⁵, H. Shi ^59,73, J. L. Shi ^12,g, J. Y. Shi ¹, S. Y. Shi ⁷⁴, X. Shi ^1,59, H. L. Song ^59,73, J. J. Song ²⁰, T. Z. Song ⁶⁰, W. M. Song ³⁵, Y. J. Song ^12,g, Y. X. Song ^47,h,n, S. Sosio ^76a,76c, S. Spataro ^76a,76c, F. Stieler ³⁶, S. S Su ⁴¹, Y. J. Su ⁶⁵, G. B. Sun ⁷⁸, G. X. Sun ¹, H. Sun ⁶⁵, H. K. Sun ¹, J. F. Sun ²⁰, K. Sun ⁶², L. Sun ⁷⁸, S. S. Sun ^1,65, T. Sun ^52,f, Y. C. Sun ⁷⁸, Y. H. Sun ³¹, Y. J. Sun ^59,73, Y. Z. Sun ¹, Z. Q. Sun ^1,65, Z. T. Sun ⁵¹, C. J. Tang⁵⁵, G. Y. Tang ¹, J. Tang ⁶⁰, J. J. Tang ^59,73, L. F. Tang ⁴⁰, Y. A. Tang ⁷⁸, L. Y. Tao ⁷⁴, M. Tat ⁷¹, J. X. Teng ^59,73, J. Y. Tian ^59,73, W. H. Tian ⁶⁰, Y. Tian ³², Z. F. Tian ⁷⁸, I. Uman ^63b, B. Wang ¹, B. Wang ⁶⁰, Bo Wang ^59,73, C. Wang ^39,k,l, C. Wang ²⁰, Cong Wang ²³, D. Y. Wang ^47,h, H. J. Wang ^39,k,l, J. J. Wang ⁷⁸, K. Wang ^1,59, L. L. Wang ¹, L. W. Wang ³⁵, M. Wang ⁵¹, M. Wang ^59,73, N. Y. Wang ⁶⁵, S. Wang ^12,g, T. Wang ^12,g, T. J. Wang ⁴⁴, W. Wang ⁶⁰, Wei Wang⁷⁴, W. P. Wang ^36,59,73,o, X. Wang ^47,h, X. F. Wang ^39,k,l, X. J. Wang ⁴⁰, X. L. Wang ^12,g, X. N. Wang ¹, Y. Wang⁶², Y. D. Wang ⁴⁶, Y. F. Wang ^1,8,65, Y. H. Wang ^39,k,l, Y. J. Wang ^59,73, Y. L. Wang ²⁰, Y. N. Wang ⁷⁸, Y. Q. Wang ¹, Yaqian Wang ¹⁸, Yi Wang ⁶², Yuan Wang ^18,32, Z. Wang ^1,59, Z. L. Wang ⁷⁴, Z. L. Wang², Z. Q. Wang ^12,g, Z. Y. Wang ^1,65, D. H. Wei ¹⁴, H. R. Wei ⁴⁴, F. Weidner ⁷⁰, S. P. Wen ¹, Y. R. Wen ⁴⁰, U. Wiedner ³, G. Wilkinson ⁷¹, M. Wolke⁷⁷, C. Wu ⁴⁰, J. F. Wu ^1,8, L. H. Wu ¹, L. J. Wu ^1,65, L. J. Wu²⁰, Lianjie Wu ²⁰, S. G. Wu ^1,65, S. M. Wu ⁶⁵, X. Wu ^12,g, X. H. Wu ³⁵, Y. J. Wu ³², Z. Wu ^1,59, L. Xia ^59,73, X. M. Xian ⁴⁰, B. H. Xiang ^1,65, D. Xiao ^39,k,l, G. Y. Xiao ⁴³, H. Xiao ⁷⁴, Y. L. Xiao ^12,g, Z. J. Xiao ⁴², C. Xie ⁴³, K. J. Xie ^1,65, X. H. Xie ^47,h, Y. Xie ⁵¹, Y. G. Xie ^1,59, Y. H. Xie ⁶, Z. P. Xie ^59,73, T. Y. Xing ^1,65, C. F. Xu^1,65, C. J. Xu ⁶⁰, G. F. Xu ¹, H. Y. Xu ^2,68, H. Y. Xu², M. Xu ^59,73, Q. J. Xu ¹⁷, Q. N. Xu ³¹, T. D. Xu ⁷⁴, W. Xu ¹, W. L. Xu ⁶⁸, X. P. Xu ⁵⁶, Y. Xu ⁴¹, Y. Xu^12,g, Y. C. Xu ⁷⁹, Z. S. Xu ⁶⁵, F. Yan ^12,g, H. Y. Yan ⁴⁰, L. Yan ^12,g, W. B. Yan ^59,73, W. C. Yan ⁸², W. H. Yan ⁶, W. P. Yan ²⁰, X. Q. Yan ^1,65, H. J. Yang ^52,f, H. L. Yang ³⁵, H. X. Yang ¹, J. H. Yang ⁴³, R. J. Yang ²⁰, T. Yang ¹, Y. Yang ^12,g, Y. F. Yang ⁴⁴, Y. H. Yang ⁴³, Y. Q. Yang ⁹, Y. X. Yang ^1,65, Y. Z. Yang ²⁰, M. Ye ^1,59, M. H. Ye^8,a, Z. J. Ye ^57,j, Junhao Yin ⁴⁴, Z. Y. You ⁶⁰, B. X. Yu ^1,59,65, C. X. Yu ⁴⁴, G. Yu ¹³, J. S. Yu ^26,i, L. Q. Yu ^12,g, M. C. Yu ⁴¹, T. Yu ⁷⁴, X. D. Yu ^47,h, Y. C. Yu ⁸², C. Z. Yuan ^1,65, H. Yuan ^1,65, J. Yuan ³⁵, J. Yuan ⁴⁶, L. Yuan ², S. C. Yuan ^1,65, X. Q. Yuan ¹, Y. Yuan ^1,65, Z. Y. Yuan ⁶⁰, C. X. Yue ⁴⁰, Ying Yue ²⁰, A. A. Zafar ⁷⁵, S. H. Zeng ⁶⁴, X. Zeng ^12,g, Y. Zeng^26,i, Yujie Zeng⁶⁰, Y. J. Zeng ^1,65, X. Y. Zhai ³⁵, Y. H. Zhan ⁶⁰, A. Q. Zhang ^1,65, B. L. Zhang ^1,65, B. X. Zhang ¹, D. H. Zhang ⁴⁴, G. Y. Zhang ²⁰, G. Y. Zhang ^1,65, H. Zhang ^59,73, H. Zhang ⁸², H. C. Zhang ^1,59,65, H. H. Zhang ⁶⁰, H. Q. Zhang ^1,59,65, H. R. Zhang ^59,73, H. Y. Zhang ^1,59, Jin Zhang⁸², J. Zhang ⁶⁰, J. J. Zhang ⁵³, J. L. Zhang ²¹, J. Q. Zhang ⁴², J. S. Zhang ^12,g, J. W. Zhang ^1,59,65, J. X. Zhang ^39,k,l, J. Y. Zhang ¹, J. Z. Zhang ^1,65, Jianyu Zhang ⁶⁵, L. M. Zhang ⁶², Lei Zhang ⁴³, N. Zhang ⁸², P. Zhang ^1,8, Q. Zhang ²⁰, Q. Y. Zhang ³⁵, R. Y. Zhang ^39,k,l, S. H. Zhang ^1,65, Shulei Zhang ^26,i, X. M. Zhang ¹, X. Y Zhang ⁴¹, X. Y. Zhang⁵¹, Y. Zhang ¹, Y. Zhang ⁷⁴, Y. T. Zhang ⁸², Y. H. Zhang ^1,59, Y. M. Zhang ⁴⁰, Y. P. Zhang ^59,73, Z. D. Zhang ¹, Z. H. Zhang ¹, Z. L. Zhang ³⁵, Z. L. Zhang ⁵⁶, Z. X. Zhang ²⁰, Z. Y. Zhang ⁷⁸, Z. Y. Zhang ⁴⁴, Z. Z. Zhang ⁴⁶, Zh. Zh. Zhang ²⁰, G. Zhao ¹, J. Y. Zhao ^1,65, J. Z. Zhao ^1,59, L. Zhao ¹, L. Zhao ^59,73, M. G. Zhao ⁴⁴, N. Zhao ⁸⁰, R. P. Zhao ⁶⁵, S. J. Zhao ⁸², Y. B. Zhao ^1,59, Y. L. Zhao ⁵⁶, Y. X. Zhao ^32,65, Z. G. Zhao ^59,73, A. Zhemchugov ^37,b, B. Zheng ⁷⁴, B. M. Zheng ³⁵, J. P. Zheng ^1,59, W. J. Zheng ^1,65, X. R. Zheng ²⁰, Y. H. Zheng ^65,p, B. Zhong ⁴², C. Zhong ²⁰, H. Zhou ^36,51,o, J. Q. Zhou ³⁵, J. Y. Zhou ³⁵, S. Zhou ⁶, X. Zhou ⁷⁸, X. K. Zhou ⁶, X. R. Zhou ^59,73, X. Y. Zhou ⁴⁰, Y. X. Zhou ⁷⁹, Y. Z. Zhou ^12,g, A. N. Zhu ⁶⁵, J. Zhu ⁴⁴, K. Zhu ¹, K. J. Zhu ^1,59,65, K. S. Zhu ^12,g, L. Zhu ³⁵, L. X. Zhu ⁶⁵, S. H. Zhu ⁷², T. J. Zhu ^12,g, W. D. Zhu ⁴², W. D. Zhu^12,g, W. J. Zhu ¹, W. Z. Zhu ²⁰, Y. C. Zhu ^59,73, Z. A. Zhu ^1,65, X. Y. Zhuang ⁴⁴, J. H. Zou ¹, and J. Zu ^59,73 (BESIII Collaboration)

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

^*Full author list given at the end of the article.
^aDeceased.
^bAlso at the Moscow Institute of Physics and Technology, Moscow 141700, Russia.
^cAlso at the Novosibirsk State University, Novosibirsk, 630090, Russia.
^dAlso at the NRC “Kurchatov Institute,” PNPI, 188300, Gatchina, Russia.
^eAlso at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany.
^fAlso at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China.
^gAlso at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, People’s Republic of China.
^hAlso at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’s Republic of China.
ⁱAlso at School of Physics and Electronics, Hunan University, Changsha 410082, China.
^jAlso at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China.
^kAlso at MOE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, People’s Republic of China.
^lAlso at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, People’s Republic of China.
^mAlso at the Department of Mathematical Sciences, IBA, Karachi 75270, Pakistan.
ⁿAlso at Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
^oAlso at Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany.
^pAlso at Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, China.

PDF

Phys. Rev. D 113, 012004 – Published 12 January, 2026

DOI: https://doi.org/10.1103/64lr-8c9k

Abstract

Utilizing $2712.4 \pm 14.3 million$ $ψ (3686)$ events accumulated by the BESIII experiment, we perform a partial wave analysis of $ψ (3686) \to γ χ_{c J} \to γ Λ \bar{Λ}$ decay ( $J = 0$ , 1, 2). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for $χ_{c 2} \to Λ \bar{Λ}$ decay is determined for the first time to be $R_{χ_{c 2}} = 0.575 \pm 0.048 \pm 0.018$ , with a relative phase angle $Δ Φ_{χ_{c 2}} = 0.37 \pm 0.15 \pm 0.05 rad$ . The parameters of the angular distribution of $χ_{c 2}$ are determined to be $α_{χ_{c 2}} = - 0.211 \pm 0.100 \pm 0.050$ and $β_{χ_{c 2}} = - 0.039 \pm 0.089 \pm 0.033$ , based on the distribution $d N / d \cos θ = 1 + α_{χ_{c 2}} \cos^{2} θ + β_{χ_{c 2}} \cos^{4} θ$ . The width of $χ_{c 0}$ is determined to be $12.31 \pm 0.26 \pm 0.12 MeV$ . Additionally, the branching fractions for $χ_{c J} \to Λ \bar{Λ}$ are measured to be $(3.662 \pm 0.048 \pm 0.111) \times 10^{- 4}$ , $(1.182 \pm 0.026 \pm 0.042) \times 10^{- 4}$ , and $(1.704 \pm 0.035 \pm 0.057) \times 10^{- 4}$ for $χ_{c 0}$ , $χ_{c 1}$ and $χ_{c 2}$ , respectively, where the first uncertainty is statistical and the second systematic.

Physics Subject Headings (PhySH)

Article Text

References (45)

M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 87, 032007 (2013); 87, 059901(E) (2013).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 97, 052011 (2018).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 101, 092002 (2020).
Y. F. Wang and M. Ablikim (BESIII Collaboration), Phys. Rev. D 83, 112009 (2011).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 107, 092004 (2023).
S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24, 2848 (1981).
R. L. Workman et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
M. Anselmino, M. Genovese, and E. Predazzi, Phys. Rev. D 44, 1597 (1991).
S. M. H. Wong, Eur. Phys. J. C 14, 643 (2000).
M. Anselmino, R. Cancelliere, and F. Murgia, Phys. Rev. D 46, 5049 (1992).
R. G. Ping, B. S. Zou, and H. C. Chiang, Eur. Phys. J. A 23, 129 (2004).
M. Anselmino, F. Caruso, and S. Forte, Phys. Rev. D 44, 1438 (1991).
X.-H. Liu and Q. Zhao, J. Phys. G 38, 035007 (2011).
B. Lan, X.-P. Fan, and R.-M. Wang, Phys. Rev. D 110, 056007 (2024).
M. Ablikim et al. (BESIII Collaboration), Chin. Phys. C 48, 093001 (2024).
M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 614, 345 (2010).
C. Yu et al., in Proceedings of the 7th International Particle Accelerator Conference (JACoW Publishing, Geneva, Switzerland, 2016), p. TUYA01.
M. Ablikim et al. (BESIII Collaboration), Chin. Phys. C 44, 040001 (2020).
J. Lu et al., Radiat. Detect. Technol. Methods 4, 337 (2020).
J.-W. Zhang et al., Radiat. Detect. Technol. Methods 6, 289 (2022).
X. Li et al., Radiat. Detect. Technol. Methods 1, 1 (2017).
Y.-X. Guo et al., Radiat. Detect. Technol. Methods 1, 15 (2017).
P. Cao et al., Nucl. Instrum. Methods Phys. Res., Sect. A 953, 163053 (2020).
S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 506, 250 (2003).
S. Jadach, B. F. L. Ward, and Z. Was, Phys. Rev. D 63, 113009 (2001).
D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A 462, 152 (2001).
J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang, and Y. S. Zhu, Phys. Rev. D 62, 034003 (2000).
E. Richter-Was, Phys. Lett. B 303, 163 (1993).
A. Fotopoulos, and M. Tsulaia, Int. J. Mod. Phys. A 24, S1 (2009).
M. Ablikim et al. (BESIII Collaboration), J. High Energy Phys. 11 (2023) 137.
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
M. Xu et al., Chin. Phys. C 33, 428 (2009).
S. U. Chung, CERN Yellow Reports: Monographs, (1971), 10.5170/CERN-1971-008.
J. D. Richman, An experimenter’s guide to the helicity formalism, Technical Report No. CALT-68-1148, Caltech, 1984.
H. Chen and R.-G. Ping, Phys. Rev. D 102, 016021 (2020).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 129, 131801 (2022).
M. Ablikim et al. (BESIII Collaboration), J. High Energy Phys. 12 (2022) 033.
Y. Jiang, Nuovo Cimento Soc. Ital. Fis. 47, 203 (2024).
M. Abadi et al., arXiv:1603.04467.
F. Von Hippel and C. Quigg, Phys. Rev. D 5, 624 (1972).
B. S. Zou and D. V. Bugg, Eur. Phys. J. A 16, 537 (2003).
H.-J. Jing, D. Ben, S.-M. Wu, J.-J. Wu, and B.-S. Zou, J. High Energy Phys. 06 (2023) 039.
V. M. Malyshev, Int. J. Mod. Phys. Conf. Ser. 02, 188 (2011).
M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 87, 012002 (2013).
https://cstr.cn/31109.02.BEPC.

Phys. Rev. D 113, 012004– Published 12 January, 2026

Vol. 113, Iss. 1 — 1 January 2026

Received 2 September 2025
Accepted 12 December 2025

DOI: https://doi.org/10.1103/64lr-8c9k

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

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Helicity amplitude and branching fraction measurement of $χ_{c J} \to Λ \bar{Λ}$

Abstract

Physics Subject Headings (PhySH)

Article Text

References (45)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Helicity amplitude and branching fraction measurement of χcJ→ΛΛ¯

Abstract

Physics Subject Headings (PhySH)

Article Text

References (45)

Helicity amplitude and branching fraction measurement of $χ_{c J} \to Λ \bar{Λ}$