# Measurement of the absolute branching fraction of the inclusive decay
$\bar{\Lambda}_{c}^{-}\to\bar{n}+X$

M. Ablikim1, M. N. Achasov11,b, P. Adlarson70, M. Albrecht4, R. Aliberti31, A.
Amoroso69A,69C, M. R. An35, Q. An66,53, X. H. Bai61, Y. Bai52, O. Bakina32, R.
Baldini Ferroli26A, I. Balossino27A, Y. Ban42,g, V. Batozskaya1,40, D.
Becker31, K. Begzsuren29, N. Berger31, M. Bertani26A, D. Bettoni27A, F.
Bianchi69A,69C, J. Bloms63, A. Bortone69A,69C, I. Boyko32, R. A. Briere5, A.
Brueggemann63, H. Cai71, X. Cai1,53, A. Calcaterra26A, G. F. Cao1,58, N.
Cao1,58, S. A. Cetin57A, J. F. Chang1,53, W. L. Chang1,58, G. Chelkov32,a, C.
Chen39, Chao Chen50, G. Chen1, H. S. Chen1,58, M. L. Chen1,53, S. J. Chen38,
S. M. Chen56, T. Chen1, X. R. Chen28,58, X. T. Chen1, Y. B. Chen1,53, Z. J.
Chen23,h, W. S. Cheng69C, S. K. Choi 50, X. Chu39, G. Cibinetto27A, F.
Cossio69C, J. J. Cui45, H. L. Dai1,53, J. P. Dai73, A. Dbeyssi17, R. E. de
Boer4, D. Dedovich32, Z. Y. Deng1, A. Denig31, I. Denysenko32, M.
Destefanis69A,69C, F. De Mori69A,69C, Y. Ding36, J. Dong1,53, L. Y. Dong1,58,
M. Y. Dong1,53,58, X. Dong71, S. X. Du75, P. Egorov32,a, Y. L. Fan71, J.
Fang1,53, S. S. Fang1,58, W. X. Fang1, Y. Fang1, R. Farinelli27A, L.
Fava69B,69C, F. Feldbauer4, G. Felici26A, C. Q. Feng66,53, J. H. Feng54, K
Fischer64, M. Fritsch4, C. Fritzsch63, C. D. Fu1, H. Gao58, Y. N. Gao42,g,
Yang Gao66,53, S. Garbolino69C, I. Garzia27A,27B, P. T. Ge71, Z. W. Ge38, C.
Geng54, E. M. Gersabeck62, A Gilman64, K. Goetzen12, L. Gong36, W. X.
Gong1,53, W. Gradl31, M. Greco69A,69C, L. M. Gu38, M. H. Gu1,53, Y. T. Gu14,
C. Y Guan1,58, A. Q. Guo28,58, L. B. Guo37, R. P. Guo44, Y. P. Guo10,f, A.
Guskov32,a, T. T. Han45, W. Y. Han35, X. Q. Hao18, F. A. Harris60, K. K. He50,
K. L. He1,58, F. H. Heinsius4, C. H. Heinz31, Y. K. Heng1,53,58, C. Herold55,
G. Y. Hou1,58, Y. R. Hou58, Z. L. Hou1, H. M. Hu1,58, J. F. Hu51,i, T.
Hu1,53,58, Y. Hu1, G. S. Huang66,53, K. X. Huang54, L. Q. Huang28,58, X. T.
Huang45, Y. P. Huang1, Z. Huang42,g, T. Hussain68, N Hüsken25,31, W. Imoehl25,
M. Irshad66,53, J. Jackson25, S. Jaeger4, S. Janchiv29, E. Jang50, J. H.
Jeong50, Q. Ji1, Q. P. Ji18, X. B. Ji1,58, X. L. Ji1,53, Y. Y. Ji45, Z. K.
Jia66,53, H. B. Jiang45, S. S. Jiang35, X. S. Jiang1,53,58, Y. Jiang58, J. B.
Jiao45, Z. Jiao21, S. Jin38, Y. Jin61, M. Q. Jing1,58, T. Johansson70, N.
Kalantar-Nayestanaki59, X. S. Kang36, R. Kappert59, M. Kavatsyuk59, B. C.
Ke75, I. K. Keshk4, A. Khoukaz63, R. Kiuchi1, R. Kliemt12, L. Koch33, O. B.
Kolcu57A, B. Kopf4, M. Kuemmel4, M. Kuessner4, A. Kupsc40,70, W. Kühn33, J. J.
Lane62, J. S. Lange33, P. Larin17, A. Lavania24, L. Lavezzi69A,69C, Z. H.
Lei66,53, H. Leithoff31, M. Lellmann31, T. Lenz31, C. Li39, C. Li43, C. H.
Li35, Cheng Li66,53, D. M. Li75, F. Li1,53, G. Li1, H. Li47, H. Li66,53, H. B.
Li1,58, H. J. Li18, H. N. Li51,i, J. Q. Li4, J. S. Li54, J. W. Li45, Ke Li1,
L. J Li1, L. K. Li1, Lei Li3, M. H. Li39, P. R. Li34,j,k, S. X. Li10, S. Y.
Li56, T. Li45, W. D. Li1,58, W. G. Li1, X. H. Li66,53, X. L. Li45, Xiaoyu
Li1,58, Y. G. Li42,g, Z. X. Li14, H. Liang66,53, H. Liang30, H. Liang1,58, Y.
F. Liang49, Y. T. Liang28,58, G. R. Liao13, L. Z. Liao45, J. Libby24, A.
Limphirat55, C. X. Lin54, D. X. Lin28,58, T. Lin1, B. J. Liu1, C. X. Liu1, D.
Liu17,66, F. H. Liu48, Fang Liu1, Feng Liu6, G. M. Liu51,i, H. Liu34,j,k, H.
B. Liu14, H. M. Liu1,58, Huanhuan Liu1, Huihui Liu19, J. B. Liu66,53, J. L.
Liu67, J. Y. Liu1,58, K. Liu1, K. Y. Liu36, Ke Liu20, L. Liu66,53, Lu Liu39,
M. H. Liu10,f, P. L. Liu1, Q. Liu58, S. B. Liu66,53, T. Liu10,f, W. K. Liu39,
W. M. Liu66,53, X. Liu34,j,k, Y. Liu34,j,k, Y. B. Liu39, Z. A. Liu1,53,58, Z.
Q. Liu45, X. C. Lou1,53,58, F. X. Lu54, H. J. Lu21, J. G. Lu1,53, X. L. Lu1,
Y. Lu7, Y. P. Lu1,53, Z. H. Lu1, C. L. Luo37, M. X. Luo74, T. Luo10,f, X. L.
Luo1,53, X. R. Lyu58, Y. F. Lyu39, F. C. Ma36, H. L. Ma1, L. L. Ma45, M. M.
Ma1,58, Q. M. Ma1, R. Q. Ma1,58, R. T. Ma58, X. Y. Ma1,53, Y. Ma42,g, F. E.
Maas17, M. Maggiora69A,69C, S. Maldaner4, S. Malde64, Q. A. Malik68, A.
Mangoni26B, Y. J. Mao42,g, Z. P. Mao1, S. Marcello69A,69C, Z. X. Meng61, J.
Messchendorp12,59, G. Mezzadri27A, H. Miao1, T. J. Min38, R. E. Mitchell25, X.
H. Mo1,53,58, N. Yu. Muchnoi11,b, Y. Nefedov32, F. Nerling17,d, I. B.
Nikolaev11,b, Z. Ning1,53, S. Nisar9,l, Y. Niu 45, S. L. Olsen58, Q.
Ouyang1,53,58, S. Pacetti26B,26C, X. Pan10,f, Y. Pan52, A. Pathak30, M.
Pelizaeus4, H. P. Peng66,53, K. Peters12,d, J. L. Ping37, R. G. Ping1,58, S.
Plura31, S. Pogodin32, V. Prasad66,53, F. Z. Qi1, H. Qi66,53, H. R. Qi56, M.
Qi38, T. Y. Qi10,f, S. Qian1,53, W. B. Qian58, Z. Qian54, C. F. Qiao58, J. J.
Qin67, L. Q. Qin13, X. P. Qin10,f, X. S. Qin45, Z. H. Qin1,53, J. F. Qiu1, S.
Q. Qu56, K. H. Rashid68, C. F. Redmer31, K. J. Ren35, A. Rivetti69C, V.
Rodin59, M. Rolo69C, G. Rong1,58, Ch. Rosner17, S. N. Ruan39, H. S. Sang66, A.
Sarantsev32,c, Y. Schelhaas31, C. Schnier4, K. Schoenning70, M.
Scodeggio27A,27B, K. Y. Shan10,f, W. Shan22, X. Y. Shan66,53, J. F.
Shangguan50, L. G. Shao1,58, M. Shao66,53, C. P. Shen10,f, H. F. Shen1,58, X.
Y. Shen1,58, B. A. Shi58, H. C. Shi66,53, J. Y. Shi1, Q. Q. Shi50, R. S.
Shi1,58, X. Shi1,53, X. D Shi66,53, J. J. Song18, W. M. Song30,1, Y. X.
Song42,g, S. Sosio69A,69C, S. Spataro69A,69C, F. Stieler31, K. X. Su71, P. P.
Su50, Y. J. Su58, G. X. Sun1, H. Sun58, H. K. Sun1, J. F. Sun18, L. Sun71, S.
S. Sun1,58, T. Sun1,58, W. Y. Sun30, X Sun23,h, Y. J. Sun66,53, Y. Z. Sun1, Z.
T. Sun45, Y. H. Tan71, Y. X. Tan66,53, C. J. Tang49, G. Y. Tang1, J. Tang54,
L. Y Tao67, Q. T. Tao23,h, M. Tat64, J. X. Teng66,53, V. Thoren70, W. H.
Tian47, Y. Tian28,58, I. Uman57B, B. Wang1, B. L. Wang58, C. W. Wang38, D. Y.
Wang42,g, F. Wang67, H. J. Wang34,j,k, H. P. Wang1,58, K. Wang1,53, L. L.
Wang1, M. Wang45, M. Z. Wang42,g, Meng Wang1,58, S. Wang13, S. Wang10,f, T.
Wang10,f, T. J. Wang39, W. Wang54, W. H. Wang71, W. P. Wang66,53, X. Wang42,g,
X. F. Wang34,j,k, X. L. Wang10,f, Y. Wang56, Y. D. Wang41, Y. F. Wang1,53,58,
Y. H. Wang43, Y. Q. Wang1, Yaqian Wang16,1, Z. Wang1,53, Z. Y. Wang1,58, Ziyi
Wang58, D. H. Wei13, F. Weidner63, S. P. Wen1, D. J. White62, U. Wiedner4, G.
Wilkinson64, M. Wolke70, L. Wollenberg4, J. F. Wu1,58, L. H. Wu1, L. J.
Wu1,58, X. Wu10,f, X. H. Wu30, Y. Wu66, Y. J Wu28, Z. Wu1,53, L. Xia66,53, T.
Xiang42,g, D. Xiao34,j,k, G. Y. Xiao38, H. Xiao10,f, S. Y. Xiao1, Y. L.
Xiao10,f, Z. J. Xiao37, C. Xie38, X. H. Xie42,g, Y. Xie45, Y. G. Xie1,53, Y.
H. Xie6, Z. P. Xie66,53, T. Y. Xing1,58, C. F. Xu1, C. J. Xu54, G. F. Xu1, H.
Y. Xu61, Q. J. Xu15, X. P. Xu50, Y. C. Xu58, Z. P. Xu38, F. Yan10,f, L.
Yan10,f, W. B. Yan66,53, W. C. Yan75, H. J. Yang46,e, H. L. Yang30, H. X.
Yang1, L. Yang47, S. L. Yang58, Tao Yang1, Y. F. Yang39, Y. X. Yang1,58, Yifan
Yang1,58, M. Ye1,53, M. H. Ye8, J. H. Yin1, Z. Y. You54, B. X. Yu1,53,58, C.
X. Yu39, G. Yu1,58, T. Yu67, X. D. Yu42,g, C. Z. Yuan1,58, L. Yuan2, S. C.
Yuan1, X. Q. Yuan1, Y. Yuan1,58, Z. Y. Yuan54, C. X. Yue35, A. A. Zafar68, F.
R. Zeng45, X. Zeng6, Y. Zeng23,h, Y. H. Zhan54, A. Q. Zhang1, B. L. Zhang1, B.
X. Zhang1, D. H. Zhang39, G. Y. Zhang18, H. Zhang66, H. H. Zhang30, H. H.
Zhang54, H. Y. Zhang1,53, J. L. Zhang72, J. Q. Zhang37, J. W. Zhang1,53,58, J.
X. Zhang34,j,k, J. Y. Zhang1, J. Z. Zhang1,58, Jianyu Zhang1,58, Jiawei
Zhang1,58, L. M. Zhang56, L. Q. Zhang54, Lei Zhang38, P. Zhang1, Q. Y.
Zhang35,75, Shuihan Zhang1,58, Shulei Zhang23,h, X. D. Zhang41, X. M. Zhang1,
X. Y. Zhang45, X. Y. Zhang50, Y. Zhang64, Y. T. Zhang75, Y. H. Zhang1,53, Yan
Zhang66,53, Yao Zhang1, Z. H. Zhang1, Z. Y. Zhang39, Z. Y. Zhang71, G. Zhao1,
J. Zhao35, J. Y. Zhao1,58, J. Z. Zhao1,53, Lei Zhao66,53, Ling Zhao1, M. G.
Zhao39, S. J. Zhao75, Y. B. Zhao1,53, Y. X. Zhao28,58, Z. G. Zhao66,53, A.
Zhemchugov32,a, B. Zheng67, J. P. Zheng1,53, Y. H. Zheng58, B. Zhong37, C.
Zhong67, X. Zhong54, H. Zhou45, L. P. Zhou1,58, X. Zhou71, X. K. Zhou58, X. R.
Zhou66,53, X. Y. Zhou35, Y. Z. Zhou10,f, J. Zhu39, K. Zhu1, K. J. Zhu1,53,58,
L. X. Zhu58, S. H. Zhu65, S. Q. Zhu38, T. J. Zhu72, W. J. Zhu10,f, Y. C.
Zhu66,53, Z. A. Zhu1,58, J. H. Zou1 (BESIII Collaboration) 1 Institute of High
Energy Physics, Beijing 100049, People’s Republic of China
2 Beihang University, Beijing 100191, People’s Republic of China
3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s
Republic of China
4 Bochum Ruhr-University, D-44780 Bochum, Germany
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6 Central China Normal University, Wuhan 430079, People’s Republic of China
7 Central South University, Changsha 410083, People’s Republic of China
8 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
9 COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road,
54000 Lahore, Pakistan
10 Fudan University, Shanghai 200433, People’s Republic of China
11 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
12 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
13 Guangxi Normal University, Guilin 541004, People’s Republic of China
14 Guangxi University, Nanning 530004, People’s Republic of China
15 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
16 Hebei University, Baoding 071002, People’s Republic of China
17 Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
18 Henan Normal University, Xinxiang 453007, People’s Republic of China
19 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
20 Henan University of Technology, Zhengzhou 450001, People’s Republic of
China
21 Huangshan College, Huangshan 245000, People’s Republic of China
22 Hunan Normal University, Changsha 410081, People’s Republic of China
23 Hunan University, Changsha 410082, People’s Republic of China
24 Indian Institute of Technology Madras, Chennai 600036, India
25 Indiana University, Bloomington, Indiana 47405, USA
26 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
27 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara,
Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
28 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
29 Institute of Physics and Technology, Peace Avenue 54B, Ulaanbaatar 13330,
Mongolia
30 Jilin University, Changchun 130012, People’s Republic of China
31 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
32 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
33 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
34 Lanzhou University, Lanzhou 730000, People’s Republic of China
35 Liaoning Normal University, Dalian 116029, People’s Republic of China
36 Liaoning University, Shenyang 110036, People’s Republic of China
37 Nanjing Normal University, Nanjing 210023, People’s Republic of China
38 Nanjing University, Nanjing 210093, People’s Republic of China
39 Nankai University, Tianjin 300071, People’s Republic of China
40 National Centre for Nuclear Research, Warsaw 02-093, Poland
41 North China Electric Power University, Beijing 102206, People’s Republic of
China
42 Peking University, Beijing 100871, People’s Republic of China
43 Qufu Normal University, Qufu 273165, People’s Republic of China
44 Shandong Normal University, Jinan 250014, People’s Republic of China
45 Shandong University, Jinan 250100, People’s Republic of China
46 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
47 Shanxi Normal University, Linfen 041004, People’s Republic of China
48 Shanxi University, Taiyuan 030006, People’s Republic of China
49 Sichuan University, Chengdu 610064, People’s Republic of China
50 Soochow University, Suzhou 215006, People’s Republic of China
51 South China Normal University, Guangzhou 510006, People’s Republic of China
52 Southeast University, Nanjing 211100, People’s Republic of China
53 State Key Laboratory of Particle Detection and Electronics, Beijing 100049,
Hefei 230026, People’s Republic of China
54 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
55 Suranaree University of Technology, University Avenue 111, Nakhon
Ratchasima 30000, Thailand
56 Tsinghua University, Beijing 100084, People’s Republic of China
57 Turkish Accelerator Center Particle Factory Group, (A)Istinye University,
34010, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus,
Mersin 10, Turkey
58 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
59 University of Groningen, NL-9747 AA Groningen, The Netherlands
60 University of Hawaii, Honolulu, Hawaii 96822, USA
61 University of Jinan, Jinan 250022, People’s Republic of China
62 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
63 University of Muenster, Wilhelm-Klemm-Strasse 9, 48149 Muenster, Germany
64 University of Oxford, Keble Road, Oxford OX13RH, United Kingdom
65 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
66 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
67 University of South China, Hengyang 421001, People’s Republic of China
68 University of the Punjab, Lahore-54590, Pakistan
69 University of Turin and INFN, (A)University of Turin, I-10125, Turin,
Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy;
(C)INFN, I-10125, Turin, Italy
70 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
71 Wuhan University, Wuhan 430072, People’s Republic of China
72 Xinyang Normal University, Xinyang 464000, People’s Republic of China
73 Yunnan University, Kunming 650500, People’s Republic of China
74 Zhejiang University, Hangzhou 310027, People’s Republic of China
75 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at the Moscow Institute of Physics and Technology, Moscow 141700,
Russia
b Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
c Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
d Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany
e Also 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
f Also 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
g Also at State Key Laboratory of Nuclear Physics and Technology, Peking
University, Beijing 100871, People’s Republic of China
h Also at School of Physics and Electronics, Hunan University, Changsha
410082, China
i Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of
Quantum Matter, South China Normal University, Guangzhou 510006, China
j Also at Frontiers Science Center for Rare Isotopes, Lanzhou University,
Lanzhou 730000, People’s Republic of China
k Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou
730000, People’s Republic of China
l Also at the Department of Mathematical Sciences, IBA, Karachi , Pakistan

###### Abstract

Based on $e^{+}e^{-}$ collision data corresponding to an integrated luminosity
of 4.5 $\mathrm{fb}^{-1}$ collected at the center-of-mass energies between
4.600 and 4.699 $\ \mathrm{GeV}$ with the BESIII detector at BEPCII, the
absolute branching fraction of the inclusive decay
$\bar{\Lambda}_{c}^{-}\to\bar{n}+X$, where $X$ refers to any possible final
state particles, is measured. The absolute branching fraction is determined to
be $\mathcal{B}(\bar{\Lambda}_{c}^{-}\to\bar{n}+X)=(33.5\pm 0.7\pm 1.2)\%$,
where the first uncertainty is statistical and the second systematic.
Neglecting the effect of $C\\!P$ violation, the measurement indicates that
about one-fourth of $\Lambda^{+}_{c}$ decay modes with a neutron in the final
state have not been observed.

The $\Lambda^{+}_{c}$ is the lightest charmed baryon, and the measurement of
the properties of $\Lambda^{+}_{c}$ provides key input for studying heavier
charmed baryons Sheng:2018dc  and bottom baryons Rupak:2016bb ; Detmold:2015bb
, as well as understanding the dynamics of light quarks in the environment
with a heavy quark Cheng:2021qpd . However, there is no reliable
phenomenological model calculation describing the complicated physics in
charmed baryon decays, which strongly rely on experimental results. Therefore,
the comprehensive and precise experimental studies of the $\Lambda^{+}_{c}$
decays are highly desirable.

Experimentally, since the discovery of the $\Lambda^{+}_{c}$ baryon in 1979
Abrams:1980Lc , which eventually decays to a proton or a neutron, its decays
with a proton in the final state have been studied extensively. However,
information about decays with a neutron in the final state is sparse.
Recently, the BESIII collaboration measured the absolute branching fraction of
decay $\Lambda^{+}_{c}\to n\pi^{+}$ to be $(6.6\pm 1.2\pm 0.4)\times 10^{-4}$
Ablikim:2022SCS , where the double-tag (DT) approach MarkIII:DT  is used, and
the neutrons are treated as missing particles and inferred under the laws of
conservation of energy and momentum. This is the first-time measurement of
singly Cabibbo suppressed mode involving a neutron directly in the final state
in the $\Lambda^{+}_{c}$ decays. Up to now, there are still very few
measurements that directly observed neutron signals in the $\Lambda^{+}_{c}$
decays Ablikim:2022SCS ; Ablikim:2016mcr ; Ablikim:2022nXpi , including the
decays $\Lambda^{+}_{c}\to\Sigma^{-}2\pi^{+}$ and $\Sigma^{-}\pi^{0}2\pi^{+}$
Ablikim:sigmaXpi  where the $\Sigma^{-}$ is reconstructed with its dominant
decay mode $\Sigma^{-}\to n\pi^{-}$. Combing all the known exclusive decays of
$\Lambda^{+}_{c}$ summarized by the Particle Data Group (PDG) PDG:2020 , the
total branching fraction of the decays with a proton or a neutron in the final
state is about 44% or 25%, respectively, which include both the direct decay
channels of $\Lambda^{+}_{c}$ and the decays from intermediate particles,
$i.e.$ $\Lambda$, $\Sigma$ and $\Xi$. There are still lots of unknown decay
channels of $\Lambda^{+}_{c}$ baryon to be explored experimentally.

The inclusive decay $\Lambda^{+}_{c}\to n+X$, where $X$ refers to any possible
particle system, has not yet been studied experimentally, due to the
difficulty in discriminating neutron signals from neutral noises. In 1992,
Ref. Crawford:1992  estimated the inclusive branching fractions of both
$\Lambda^{+}_{c}\to p+X$ and $\Lambda^{+}_{c}\to n+X$ to be 50% with a large
uncertainty of 32%, inferred from the known exclusive $B$-meson decays and the
fact that all $\Lambda^{+}_{c}$ must decay to either proton or neutron. High
precision measurements on the inclusive decays of $\Lambda^{+}_{c}$ are
crucial to point out the direction of searches for unknown channels.
Furthermore, the results of inclusive decays will provide direct information
whether there exists an asymmetry between the decays of $\Lambda^{+}_{c}$ with
a proton and a neutron in the final state.

Comparing to the neutron, an anti-neutron has larger energy deposition in an
electromagnetic calorimeter (EMC) due to its annihilation reaction with
materials, which allows for good discrimination against the contamination from
the electromagnetic showers of photon. Hence, our measurement is conducted
with the anti-particle decay $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$, which is
supposed to yield the same result as the $\Lambda^{+}_{c}\to n+X$ if the
$C\\!P$ violation effect is ignored.

In this Letter, taking advantage of the excellent BESIII detector performance
and of the $\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ production just above the
mass threshold, the first measurement of absolute branching fraction of the
$\bar{\Lambda}_{c}^{-}\to\bar{n}+X$ decay is reported using $e^{+}e^{-}$
collision data collected with the BESIII detector at seven center-of-mass
(c.m.) energies between 4.600 and 4.699 $\ \mathrm{GeV}$, corresponding to an
integrated luminosity of 4.5 $\mathrm{fb}^{-1}$. The details of integrated
luminosities of each c.m. energy BESIII:Lumi1 ; BESIII:Lumi2  are summarized
in Table 1.

A detailed description of the design and performance of the BESIII detector
can be found in Ref. Ablikim:2009aa . Simulated samples are produced with a
geant4-based Agostinelli:2002hh  Monte Carlo (MC) toolkit, which includes the
geometric description of the BESIII detector. The signal MC samples of
$e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$, with $\Lambda^{+}_{c}$
decaying into the specific tag mode $\Lambda^{+}_{c}\to pK^{-}\pi^{+}$ and
$\bar{\Lambda}_{c}^{-}$ going to any possible processes containing an
$\bar{n}$ in the final state, are used to determine the detection efficiencies
and generated for each individual c.m. energy with the generator kkmc
Jadach:2000ir  by incorporating initial-state radiation (ISR) effects and the
beam energy spread. The $\bar{n}$ candidates include the ones both from the
interaction point (IP) and from intermediate particles, $i.e.$ $\Lambda$,
$\Sigma$ and $\Xi$. The inclusive MC samples, which consist of
$\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$, charmed meson $D_{(s)}^{(\ast)}$ pair
production, ISR return to the charmonium(-like) $\psi$ states at lower masses,
and continuum processes $e^{+}e^{-}\rightarrow q\bar{q}$ ($q=u,d,s$), are
generated to survey potential backgrounds. Particle decays are modeled with
evtgen Lange:2001uf ; Ping:2008zz  using branching fractions taken from the
PDG PDG:2020 , when available, or otherwise estimated with lundcharm
Chen:2000tv ; YANG:2014 . Final state radiation from charged final state
particles is incorporated using photos Richter-Was:1992hxq .

The DT approach MarkIII:DT  is implemented to measure the absolute branching
fraction of $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$. Taking advantage of a large
branching fraction and a high signal-to-background ratio, $\Lambda^{+}_{c}$
baryons are reconstructed in the $\Lambda^{+}_{c}\to pK^{-}\pi^{+}$ decay
mode, and are referred to as the single-tag (ST) candidates. Events in which
the signal decay $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$ is reconstructed in the
system recoiling against the $\Lambda^{+}_{c}$ candidates of the ST sample,
denoted as the DT candidates.

Charged tracks detected in the helium-based multilayer drift chamber (MDC) are
required to be within a polar angle ($\theta$) range of
$|\\!\cos\theta|<0.93$, where $\theta$ is defined with respect to the $z$
axis, which is the symmetry axis of the MDC. Their distances of the closest
approach to the IP must be less than 10 cm along the $z$ axis, and less than 1
cm in the transverse plane. The particle identification (PID) is implemented
by combining measurements of the ionization energy loss
($\mathrm{d}E/\mathrm{d}x$) in the MDC and the flight time in the time-of-
flight system, and each charged track is assigned a particle type of pion,
kaon or proton, according to which assignment has the highest probability.

The ST $\Lambda^{+}_{c}$ candidates are identified using the beam constrained
mass
$M_{\mathrm{BC}}=\sqrt{E_{\mathrm{beam}}^{2}/c^{4}-|\vec{p}_{\Lambda^{+}_{c}}|^{2}/c^{2}}$
and energy difference $\Delta E=E_{\Lambda^{+}_{c}}-E_{\mathrm{beam}}$, where
$E_{\mathrm{beam}}$ is the beam energy, and $E_{\Lambda^{+}_{c}}$
($\vec{p}_{\Lambda^{+}_{c}}$) is the energy (momentum) of the
$\Lambda^{+}_{c}$ candidates in the c.m. frame. The $\Lambda^{+}_{c}$
candidates are required to satisfy the requirement $\Delta E\in(-34,~{}20)$
MeV. The asymmetric interval takes into account the effects of ISR and
corresponds to three times the resolution around the peak. If there is more
than one $pK^{-}\pi^{+}$ combination satisfying the above requirements, the
one with the minimum $|\Delta E|$ is kept.

The $M_{\mathrm{BC}}$ distributions of candidate events for the ST mode with
data samples at different c.m. energies are illustrated in Figure 1, where
clear $\Lambda^{+}_{c}$ signals are observed. No peaking backgrounds are found
with the investigation of the inclusive MC samples. To obtain the ST yields,
unbinned maximum likelihood fits on these $M_{\mathrm{BC}}$ distributions are
performed, where the signal is modeled with the MC-simulated distribution
convolved with a Gaussian function taking into account the resolution
difference between data and MC simulation, and the background distribution is
described by an ARGUS function ARGUS:1990hfq  with the truncation parameter
fixed to the corresponding $E_{\mathrm{beam}}$. The candidates within
$M_{\mathrm{BC}}\in(2.275,2.31)$ GeV/$c^{2}$ are retained for further
analysis, and the signal yields for the data samples at different c.m.
energies are summarized in Table 1. The sum of ST yields for all data samples
is $24,577\pm 179$, where the uncertainty is statistical.

Figure 1:  The $M_{\mathrm{BC}}$ distributions of $\Lambda^{+}_{c}$ at seven
c.m. energies, and the data distributions are described by points (left
column) or triangles (right column) with error bars. The seven figures on the
left column represent the results after the ST selections, and those on the
right are obtained with both ST and $\bar{n}$ selections. The (red) solid
curves indicate the fit results and the (green) dashed curves describe the
background shapes after the ST selections. The (blue) solid curves indicate
the fit results and the (pink) dashed curves describe the background shapes
after applying the $\bar{n}$ selections.  Table 1: The integrated luminosity
($\mathcal{L}_{\rm int}$), ST yields, and the detection efficiencies of the ST
and DT selections for the data samples at seven c.m. energies. The
uncertainties are statistical only.

$\sqrt{s}$ (GeV) |  $\mathcal{L}_{\rm int}$ (pb-1) | $N_{i}^{\mathrm{ST}}$ | $\epsilon_{i}^{\mathrm{ST}}$(%) | $\epsilon_{i}^{\mathrm{DT}}$ (%)
---|---|---|---|---
4.600 |  586.90 $\pm$ |  0.10 |  3266 $\pm$ |  62 | 51.0 $\pm$ 0.2 | 20.5 $\pm$ 0.1
4.612 |  103.83 $\pm$ |  0.05 |  587 $\pm$ |  28 | 50.6 $\pm$ 0.2 | 20.3 $\pm$ 0.1
4.628 |  521.52 $\pm$ |  0.11 |  2967 $\pm$ |  64 | 50.5 $\pm$ 0.2 | 20.1 $\pm$ 0.1
4.641 |  552.41 $\pm$ |  0.12 |  3201 $\pm$ |  66 | 50.6 $\pm$ 0.2 | 19.8 $\pm$ 0.1
4.661 |  529.63 $\pm$ |  0.12 |  3080 $\pm$ |  63 | 50.6 $\pm$ 0.2 | 19.5 $\pm$ 0.1
4.682 |  1669.31 $\pm$ |  0.21 |  8863 $\pm$ |  107 | 48.8 $\pm$ 0.2 | 19.1 $\pm$ 0.1
4.699 |  536.45 $\pm$ |  0.12 |  2613 $\pm$ |  59 | 48.8 $\pm$ 0.2 | 18.8 $\pm$ 0.1

The decay $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$ is searched for among the
remaining tracks and showers recoiling against the ST $\Lambda^{+}_{c}$
candidates. Neutral showers are identified in the EMC. The deposited energy of
each shower must be more than 25 MeV in the barrel region
($|\\!\cos\theta|<0.8$) and more than 50 MeV in the end cap region
($0.86<|\\!\cos\theta|<0.92$). To suppress electronic noise and showers
unrelated to the event, the difference between the EMC time and the event
start time is required to be within [0, 700] ns. The most energetic shower is
taken as the $\bar{n}$ candidate. To discriminate the $\bar{n}$ shower from
showers caused by photons and neutrons, three variables are used for further
selection: the deposited energy ($E_{\bar{n}}$) in the EMC, the second moment
of shower shape ($S_{\bar{n}}=\Sigma_{i}E_{i}r_{i}^{2}/\Sigma_{i}E_{i}$, where
$E_{i}$ is the energy deposited in the $i^{\rm th}$ crystal of the shower and
$r_{i}$ is the distance from the center of that crystals to the center of the
shower), and the number of hit crystals ($H_{\bar{n}}$) for the primary
shower. The most energetic shower is required to have $E_{\bar{n}}>0.48$ GeV,
$H_{\bar{n}}>20$, and $S_{\bar{n}}>18$ cm2. To suppress contamination from the
decays with a $\bar{p}$ particle in the final state, the candidate events are
further required to be without any tracks identified as $\bar{p}$ and having a
distance of closest approach to the IP within 20 cm along the $z$ axis.

In contrast to photons and electrons, the interaction of $\bar{n}$ with
materials is very difficult to model, and there exists more than 10% deviation
between data and MC simulation for the $\bar{n}$ induced clusters in the EMC.
To solve this issue, a model-independent data-driven method Liang:2021nC  has
been developed to simulate the detector response of the $\bar{n}$ at BESIII.
After imposing all the selections mentioned above, the distribution of
$E_{\bar{n}}$ for the accepted DT candidates from the combined data samples at
seven c.m. energies is shown in Figure 2, where the data-driven method has
been applied in the prediction of signal process
$\bar{\Lambda}_{c}^{-}\to\bar{n}+X$ and the simulated shape describes the data
well.

Figure 2:  The stacked distribution of $E_{\bar{n}}$ for the accepted DT
candidates in the region $M_{\mathrm{BC}}\in(2.275,2.31)$ GeV/$c^{2}$ from the
combined seven data samples. The black points with error bars are data. The
red shaded histogram is the signal that is obtained with the data-driven
method. The blue and brown shaded histograms are the two background
components, where the $\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ is modeled with
the inclusive MC sample of $\Lambda^{+}_{c}\to p+X$ and the $q\bar{q}$ is
estimated with events in the sideband region of
$M_{\mathrm{BC}}\in(2.20,2.26)$ GeV/$c^{2}$ and normalized to the region
$M_{\mathrm{BC}}\in(2.275,2.31)$ GeV/$c^{2}$.

The potential backgrounds can be classified into two categories: those
directly originated from continuum hadron production in the $e^{+}e^{-}$
annihilation (denoted as $q\bar{q}$ background hereafter) and those from the
$e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ events (denoted as
$\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ background hereafter) except for the
signal of $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$. The resultant $E_{\bar{n}}$
distribution is depicted in Figure 2, where the events are selected in the
region $M_{\mathrm{BC}}\in(2.275,2.31)$ GeV/$c^{2}$. In Figure 2, the
$q\bar{q}$ contamination, which is the major background component, is
estimated with events in the sideband region $M_{\mathrm{BC}}\in(2.20,2.26)$
GeV/$c^{2}$ and normalized to the region $M_{\mathrm{BC}}\in(2.275,2.31)$
GeV/$c^{2}$. The $\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ background is modeled
with the inclusive MC sample of $\Lambda^{+}_{c}\to p+X$.

The yield of signal $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$ is obtained by
performing unbinned maximum-likelihood fits on the $M_{\mathrm{BC}}$
distributions of ST $\Lambda^{+}_{c}$ after applying the $\bar{n}$ selections.
The procedure is similar to the one used to obtain the ST yields. The fitting
curves for data samples at different c.m. energies are illustrated in Figure
1, and the signal yields are obtained within $M_{\mathrm{BC}}\in(2.275,2.31)$
GeV/$c^{2}$. The $\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ contamination has the
same shape as the signal process due to the undetected $\bar{p}$ tracks and
mis-identified $\bar{n}$ showers, and it is estimated with the inclusive MC
samples and subtracted from observed signal yields. The fitting results and
$\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ background are summarized in Table 2.

Table 2: Yields of the fitting results and the corresponding background estimation for the data samples at different c.m. energies. The uncertainty is statistical only.  $\sqrt{s}$ (GeV) | $N_{\mathrm{sig}}^{\mathrm{fit}}$ | $N_{\mathrm{bkg}}^{\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}}$
---|---|---
4.600 |  441 $\pm$ |  23 |  5.7 $\pm$ |  0.4
4.612 |  70 $\pm$ |  9 |  1.5 $\pm$ |  0.2
4.628 |  429 $\pm$ |  23 |  8.4 $\pm$ |  0.5
4.641 |  433 $\pm$ |  24 |  8.6 $\pm$ |  0.5
4.661 |  429 $\pm$ |  23 |  8.4 $\pm$ |  0.5
4.682 |  1162 $\pm$ |  37 |  26.4 $\pm$ |  0.8
4.699 |  326 $\pm$ |  20 |  8.0 $\pm$ |  0.4
sum |  3290 $\pm$ |  62 |  67.0 $\pm$ |  1.3

The branching fraction ($\mathcal{B}$) of decay
$\bar{\Lambda}_{c}^{-}\to\bar{n}+X$ is determined as

$\mathcal{B}=\frac{N_{\mathrm{sig}}^{\mathrm{DT}}-N_{\mathrm{bkg}}^{\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}}}{\sum_{i}N_{i}^{\mathrm{ST}}\cdot(\epsilon_{i}^{\mathrm{DT}}/\epsilon_{i}^{\mathrm{ST}})}$

where $N_{\mathrm{sig}}^{\mathrm{DT}}$ is the signal yield from the unbinned
maximum-likelihood fit, and
$N_{\mathrm{bkg}}^{\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}}$ is the estimated
$\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ background from the inclusive MC
samples. The subscripts $i$ represents the data samples at different c.m.
energies. The parameters $N_{i}^{\mathrm{ST}}$, $\epsilon_{i}^{\mathrm{ST}}$
and $\epsilon_{i}^{\mathrm{DT}}$ are the ST yields, ST and DT efficiencies,
respectively. The ST and DT efficiencies are summarized in Table 1, where the
efficiency of $\bar{n}$ selections is already corrected with the the data-
driven method Liang:2021nC . The branching fraction is determined to be
$\mathcal{B}(\bar{\Lambda}_{c}^{-}\to\bar{n}+X)=(33.5\pm 0.7\pm 1.2)\%$, where
the first uncertainty is statistical and the second systematic.

The systematic uncertainties for the branching fraction measurement include
those associated with the ST yields, detection efficiencies of the ST
$\Lambda^{+}_{c}$ and the DT selections. As the DT technique is adopted, the
systematic uncertainties associated with the ST detection efficiency cancel
out.

The uncertainty in the ST yields is 0.5%, which arises from the statistical
uncertainty and a systematic component coming from the fit to the
$M_{\mathrm{BC}}$ distribution. The uncertainty is evaluated by floating the
truncation parameter of the ARGUS function and changing the single gaussian
function to a double gaussian function. The uncertainty associated with the
finite size of the signal MC samples is 0.3%. The uncertainty arising from the
signal modeling is 2.7%, which combines two sources. The first is due to
unknown processes in the MC production, which is investigated by generating
alternative signal MC samples only with the known $\bar{n}$ processes in the
PDG PDG:2020 . The second one is the imperfect simulation of the $E_{\bar{n}}$
distribution, which is estimated by comparing the difference in the detection
efficiencies between the results with and without reweighting the MC-simulated
$E_{\bar{n}}$ distribution to data, where all the signal selection criteria in
the analysis are applied except for the $E_{\bar{n}}$ requirement. For each
case, the change of the signal efficiencies is taken as the systematic
uncertainty. The uncertainty in the fit strategy of extracting the signal
yields is assigned to be 0.4%, which is estimated by floating the truncation
parameter of the ARGUS function and changing the single gaussian function to a
double gaussian function. The uncertainty arising from
$\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ background estimation is studied by
generating alternative inclusive MC samples only with the known processes in
the PDG PDG:2020 , and comparing the background yields between the nominal and
alternative MC samples. The difference of signal yields after subtracting the
estimated $\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ background, 1.0%, is assigned
as the corresponding uncertainty. The uncertainty due to $\bar{n}$ selections
is assigned to be 2.0%, as explained in Ref. Liang:2021nC . All other
uncertainties are negligible. Assuming that all the systematic uncertainties
are uncorrelated, the total uncertainty is then taken to be the quadratic sum
of the individual values, which is 3.5%.

In summary, the first measurement of the absolute branching fraction of the
inclusive decay $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$ is reported using 4.5
$\mathrm{fb}^{-1}$ $e^{+}e^{-}$ collision data collected at seven c.m.
energies between 4.600 and 4.699 GeV with the BESIII detector. The absolute
branching fraction is determined to be
$\mathcal{B}(\bar{\Lambda}_{c}^{-}\to\bar{n}+X)=(33.5\pm 0.7\pm 1.2)\%$, where
the first uncertainty is statistical and the second systematic. Neglecting the
effect of $C\\!P$ violation, the inclusive decay $\Lambda^{+}_{c}\to n+X$
should have the same value as $\bar{\Lambda}_{c}^{-}\to\bar{n}+X$. The
measurement significantly improves the precision up to 4%, comparing to the
previous result of this inclusive decay, ($50\pm 16$)%, inferred from the
$B$-meson decays Crawford:1992 . The branching fraction of the inclusive decay
is greater than the sum of the known exclusive decays, that is about 25%,
which means that about one-fourth of the $\Lambda^{+}_{c}$ decays with a
neutron in the final state remain to be explored in experiments. By following
the fact that all $\Lambda^{+}_{c}$ must eventually decay to either proton or
neutron, the measured $\mathcal{B}(\bar{\Lambda}_{c}^{-}\to\bar{n}+X)$ in this
analysis indicates the existence of an asymmetry in the branching fractions
between the decay of $\Lambda^{+}_{c}$ with a proton in the final state and
that with a neutron.

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing
center and the supercomputing center of the University of Science and
Technology of China (USTC) for their strong support. This work is supported in
part by National Key R&D Program of China under Contracts Nos. 2020YFA0406400,
2020YFA0406300; National Natural Science Foundation of China (NSFC) under
Contracts Nos. 11635010, 11735014, 11835012, 11935015, 11935016, 11935018,
11961141012, 12022510, 12025502, 12035009, 12035013, 12192260, 12192261,
12192262, 12192263, 12192264, 12192265, 12005311; the Fundamental Research
Funds for the Central Universities, Sun Yat-sen University, University of
Science and Technology of China; 100 Talents Program of Sun Yat-sen
University; the Chinese Academy of Sciences (CAS) Large-Scale Scientific
Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and
CAS under Contract No. U1832207; the CAS Center for Excellence in Particle
Physics (CCEPP); 100 Talents Program of CAS; The Institute of Nuclear and
Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and
Cosmology; ERC under Contract No. 758462; European Union’s Horizon 2020
research and innovation programme under Marie Sklodowska-Curie grant agreement
under Contract No. 894790; German Research Foundation DFG under Contracts Nos.
443159800, Collaborative Research Center CRC 1044, GRK 2149; Istituto
Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under
Contract No. DPT2006K-120470; National Science and Technology fund; National
Science Research and Innovation Fund (NSRF) via the Program Management Unit
for Human Resources & Institutional Development, Research and Innovation under
Contract No. B16F640076; STFC (United Kingdom); Suranaree University of
Technology (SUT), Thailand Science Research and Innovation (TSRI), and
National Science Research and Innovation Fund (NSRF) under Contract No.
160355; The Royal Society, UK under Contracts Nos. DH140054, DH160214; The
Swedish Research Council; U. S. Department of Energy under Contract No. DE-
FG02-05ER41374

## References

  * (1) F. S. Yu et al., Chin. Phys. C 42, 051001 (2018).
  * (2) R. Dutta, Phys. Rev. D 93, 054003 (2016).
  * (3) W. Detmold et al., Phys. Rev. D 92, 034503 (2015).
  * (4) H. Y. Cheng, Chin. J. Phys. 78 324-362 (2022).
  * (5) G. S. Abrams et al., Phys. Rev. Lett. 44, 10 (1980).
  * (6) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 128, 142001 (2022).
  * (7) J. Adler et al., Phys. Rev. Lett. 62, 1821 (1989).
  * (8) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 118, 112001 (2017).
  * (9) M. Ablikim et al. (BESIII Collaboration), arXiv:2210.03375.
  * (10) M. Ablikim et al. (BESIII Collaboration), Phys. Lett. B 772 388 (2017).
  * (11) R. L. Workman et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022)
  * (12) G. D. Crawford et al. (CLEO), Phys. Rev. D 45, 752 (1992).
  * (13) M. Ablikim et al. (BESIII Collaboration), arXiv:2203.03133.
  * (14) M. Ablikim et al. (BESIII Collaboration), arXiv:2205.04809.
  * (15) M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum. Meth. A 614, 345 (2010).
  * (16) S. Agostinelli et al., Nucl. Instrum. Meth. A 506, 250 (2003).
  * (17) S. Jadach et al., Phys. Rev. D 63, 113009 (2001).
  * (18) D. J. Lange, Nucl. Instrum. Meth. A 462, 152 (2001).
  * (19) R. G. Ping, Chin. Phys. C 32, 599 (2008).
  * (20) J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang, and Y. S. Zhu, Phys. Rev. D 62, 034003 (2000).
  * (21) R. L. Yang, R. G. Ping, and H. Chen, Chin. Phys. Lett. 31, 061301 (2014).
  * (22) B. Richter-Was, Phys. Lett. B 303, 163 (1993).
  * (23) H. Albrecht et al. (ARGUS Collaboration), Phys. Lett. B 241, 278 (1990).
  * (24) L. Liu, X. R. Zhou, and H. P. Peng, Nucl. Instrum. Meth. A 1033, 166672 (2022).


# Ring That Bell: A Corpus and Method for Multimodal Metaphor Detection in
Videos

###### Abstract

We present the first openly available multimodal metaphor annotated corpus.
The corpus consists of videos including audio and subtitles that have been
annotated by experts. Furthermore, we present a method for detecting metaphors
in the new dataset based on the textual content of the videos. The method
achieves a high F1-score (62%) for metaphorical labels. We also experiment
with other modalities and multimodal methods; however, these methods did not
out-perform the text-based model. In our error analysis, we do identify that
there are cases where video could help in disambiguating metaphors, however,
the visual cues are too subtle for our model to capture. Our code, models and
data will be openly released on Github and Zenodo.

Keywords: keyword1, keyword2, keyword3

languageresourceLanguage Resources

Ring That Bell: A Corpus and Method for Multimodal Metaphor Detection in
Videos

Author1, Author2, Author3
---
Affiliation1, Affiliation2, Affiliation3
Address1, Address2, Address3
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
{author1, author5<EMAIL_ADDRESS>

Abstract content

## 1\. Introduction

Figurative language is a challenging topic for computational modeling as the
meaning of a figurative expression is non-compositional and typically very
context dependent (see roberts1994people). Metaphor is one of the most
important figures of language; it is constantly used in every day language
[steen2010metaphor] to draw comparisons or to express something difficult and
foreign in more familiar terms. Metaphors can be conventional
[traugott1985conventional] and they are often found in idioms, but at the same
time metaphors are used to create something new (see runoousoppi).

Given its ubiquitous presence, understanding metaphors is integral in
achieving true natural language understanding (NLU) in the real world. Without
their successful interpretation, our models are bound to make mistakes
whenever anything is expressed in an indirect or creative fashion. Metaphors
are often very contextual and their successful detection and interpretation
requires a wide range of contextual cues that would be captured in audio
(e.g., prosody) and video (e.g., gestures and actions). Therefore, we believe
a multimodal dataset is a great contribution to metaphor research within and
outside of the field of NLP.

Two important parts of a metaphor are a tenor and a vehicle (see Richards36).
For example, in the metaphor life is a journey, life is the tenor and journey
is the vehicle. How metaphors essentially operate is that a vehicle is used to
give some of its attributes to the tenor. In the case above, journeys are long
and full of adventure, which means that these properties are attributed to
life in an indirect fashion. The meaning of a metaphor is never literal nor
compositional, but rather calls for interpretation on the level of pragmatics
(see rosales2016metaphor).

Meanwhile, multimodality is becoming increasingly important for many tasks
(see nlpbt-2020-international,lantern-2020-beyond,mmw-2020-lrec). We believe
the availability of multimodal datasets for a variety of NLP tasks is lacking,
and we hope to contribute to the community with our multimodal metaphor
dataset.

In this paper, we present the first fully open expert annotated multimodal
dataset for metaphor detection111a Zenodo link will be added to the camera
ready version. In addition, we experiment with uni-modal and multimodal
methods for metaphor detection. Our results indicate that the text-based model
achieved the best performance. We discuss the results of our experiments and
conduct an extensive error analysis to shed light on what was learned
successfully by the model and its shortcomings.

Using CC BY licensed videos in our corpus has been the primary design
principle of our data collection so that we can release our corpus without any
restrictions in its entirety. This, we believe, is more useful for research
purposes than a corpus consisting of short video clips to compile with
copyright laws such as the fair use law in the US.

## 2\. Related Work

Metaphors have, thus far, been computationally detected using only text. In
this section, we describe some of the recent approaches for textual metaphor
detection, the corpora used to achieve that and some of the multimodal
research conducted on NLP tasks other than metaphor detection. There are
several takes on metaphor interpretation [xiao2016meta4meaning,
rai2019understanding, bar2020automatic] and generation
[hamalainen2018harnessing, terai2019construction, zheng2019love], but we do
not describe them in detail as interpretation is a very different problem.

There are two corpora currently used for metaphor detection, VU Amsterdam
(VUA) Metaphor Corpus [steen2010method] and Corpus of Non-Native Written
English Annotated for Metaphor [beigman-klebanov-etal-2018-corpus]. Unlike our
corpus, both of these datasets contain textual modality only.

For textual metaphor detection, gao-etal-2018-neural has used a bi-directional
LSTM (long short-term memory) based model with ELMo embeddings. Similarly,
liu-etal-2020-metaphor have used a bi-LSTM model with BERT and XLNet for the
same task. Not unlike the previous approaches, dankers-etal-2020-neighbourly
has also applied bi-LSTM models comparing ELMo and GloVe embeddings to BERT
embeddings with global and hierarchical attention models. Traditional machine
learning methods, Logistic Regression, Linear SVC (Support Vector
Classification) and Random Forest Classifier, have been used recently with
feature engineering to detect metaphors [wan-etal-2020-using]. In DeepMet,
proposed by su-etal-2020-deepmet, a siamese neural network have been utilized,
where textual RoBERTa [liu2019roberta] embeddings are computed from the
context, the token in question and its part-of-speech and fine-grained part-
of-speech. DeepMet was the best performing solution for detecting textual
metaphors in the VUA dataset, based on a recent shared task [leong-
etal-2020-report].

There are several recent works on multimodal detection of a variety of
linguistic phenomena. For example, SVMs (Support Vector Machines) with word
embeddings and feature extraction have been used for multimodal sarcasm
detection [mustard, alnajjar2021que]. mittal2020m3er uses GloVe embeddings,
features extracted from audio and facial recognition system output to predict
emotion in a multimodal dataset. These multimodal features are fused using a
memory fusion network (MFN) [zadeh2018memory]. Similarly, li2021quantum detect
emotion in a multimodal dataset by modeling the problem from the point of view
of the quantum theory. While the field has seen increasing research on
multimodal NLP [tsai2019multimodal, mai2020modality, sahu-
vechtomova-2021-adaptive], no data or model has been proposed for multimodal
metaphor detection.

## 3\. Our Metaphor Corpus

sentence
---
that you can use to really up your <v>game</v>
because while a <t>quick fix</t> can be <v>appetizing</v> and appealing
<t r=”domain name”>That</t>’s <v>the street address</v> for your website
you’re ready to <v>give it a shot</v>
Table 1: Example of the annotations for the metaphor detection corpus.

In this section, we present our video, audio and textual corpus of manually
annotated metaphorical language. Our selection of the video clips includes
only CC-BY licensed videos on YouTube that have human authored closed captions
in English. The content of the videos presents mainly real people talking,
which rules out animations and video game streams. The availability of human
authored closed captioning is important as it speeds up our annotation time
and provides us with subtitles that are already aligned with video and audio.
The CC-BY license was an important selection criterion because it makes it
possible for us to release the dataset openly.

We used the filters provided by YouTube to limit our search to videos that
were marked as CC-BY and had closed captioning. However, the YouTube filter
does not distinguish between automatically generated closed captioning and a
human authored one. Fortunately, it is relatively easy to tell these two apart
from each other. Automated closed captioning tends to appear one word at a
time, whereas human authored closed captioning is visualized more like
traditional subtitles. These criteria greatly reduced the number of eligible
videos to include in our corpus. Apart from these criteria, we also filtered
videos with sensitive and offensive languages. No further restrictions have
been explicitly placed on the genres or types of videos, as we do not want to
introduce biases for which types of contents are more likely to contain
metaphors. Therefore, the availability of the metaphors naturally occurring in
the corpus is the result of the ubiquity of the metaphor in everyday language
use. All Youtube queries were conducted in incognito mode to avoid biased
YouTube suggestions based on our viewing habits.

Figure 1: Metaphors made visible in the video through gestures.

Figure 1 shows real examples from our corpus where video can be useful in
detecting metaphors. On the left, the woman wearing a gray shirt is talking
about sprinkling keywords and showing a sprinkling gesture. On the right, the
woman wearing the wine red shirt says ring that bell and shows a bell ringing
gesture.

Our corpus consists of 27 YouTube videos with a total duration of 3 hours, 53
minutes and 47 seconds of video. For comparison, a recently released
multimodal dataset for sarcasm detection [mustard] has the duration of 3
hours, 40 minutes and 47 seconds. The videos belong mostly to a start-up
domain and many of them deal with issues of online visibility for a start-up
company. This domain was a consequence of our selection criteria for videos.
It turns out that YouTube has plenty of high-quality human close-captioned
videos released under the CC-BY license that relate to this particular domain.

Our corpus provides linguistics researchers with the ability to study the use
of metaphor in a multimodal setting, something that has gained attention in
their field of science as well [MullerCienki]. This can, indeed, foster a
wider interdisciplinary collaboration leading to a deeper understanding of the
phenomenon.

### 3.1. Annotation

Two expert annotators went through the video files and annotated metaphors by
surrounding them with v tags for vehicles and t tags for tenors. The use of
experts is motivated by the fact that previous research has found that non-
expert annotators struggle with metaphors [hamalainen-alnajjar-2019-lets].

The annotators followed a simple procedure in annotating the data:

  * •

Is the meaning literal?

  * •

If the meaning of the word is abstract, is it a dictionary meaning?

  * •

Does the potential metaphor express pragmatic insincerity?

  * •

If the answer to all of the questions is no, annotate it as a metaphor.

In other words, if the meaning of a word or a phrase is not literal, it is
annotated as a metaphor. However, just the mere fact of a word being used in
an abstract way is not enough to mark it as metaphorical. For example, in the
sentence it is tied to revenue, “tied” is not tagged as a metaphor just
because it is used in a more abstract sense than the typical concrete sense of
tying one’s shoes, for example. If the abstract meaning of a word appears in a
dictionary, the word is not considered metaphorical. However, conventional
metaphors that consist of multiple words, and are thus idioms, are tagged as
metaphors. We do not make a distinction between metaphors and similes.

Pragmatic insincerity (see grice1975logic) is a phenomenon related to sarcasm
as one of its preconditions (see kumon1995another). There is a certain overlap
between metaphors and sarcastic expressions in the sense that both use words
in their non-literal meaning. In order to ensure that we do not mix these two
notions with each other, it is important to avoid annotating pragmatically
insincere expressions as metaphorical.

Table 1 shows an example of annotations. The annotations were done directly in
the subtitles The utterances are time stamped and aligned with the video. In
the table, tenors are indicated with $<$t$>$ and vehicles with $<$v$>$. For
deictic tenors, an r attribute is provided to resolve the deixis by indicating
the actual tenor that has appeared earlier in the conversation. In the
examples, game is used metaphorically to talk about marketing, quick fix is
called appetizing as though it was something edible and domain name is
contrasted to a physical street address by direct comparison. Give it a shot
is a conventional metaphor.

All in all, after multiple annotation iterations, the dataset consists of 304
vehicles and 67 tenors. This totals to 371 metaphorical expressions. They vary
in length: the shortest tenor is one word, such as it, while the longest tenor
is several words the discovery of those five noble gases to illuminate like
that. The same goes for vehicles where their length varies form one word such
as dive to multiple words: the history of the internet itself. On a token
level, we have 672 vehicle tokens and 113 tenor tokens, so altogether 785
metaphorical tokens.

In total, 6% of the expressions in the corpus are metaphorical. While this
percentage might appear low, it is natural and more representative of the real
usage of metaphors in typical conversations which makes this corpus suitable
for building metaphor detection models applicable for real-world scenarios.

Around 55% of the vehicles are conventional metaphors and 45% are novel
metaphors. However, it is fairly common that same words appear in the corpus
in a metaphorical and non-metaphorical sense. In our corpus, there are two
videos that deal with actual cooking, in which many food-related metaphors
appear non-metaphorically, such as sprinkle those in, said metaphorically
about keywords and a little sprinkle, said non-metaphorically about sugar.
Another example is the use of house non-metaphorically as in come pick it up
at my house and metaphorically as in think of hosting as your house, where a
metaphorical connection is drawn between hosting and a house.

### 3.2. Data preparation

As YouTube serves files in several different formats such as webm, mkv and mp4
the first step is to use FFmpeg222https://ffmpeg.org/ to convert all videos
into mp4 format. We also use the same tool to clip the video files into
sentence-length clips based on the time stamps in the subtitles and extract
their audio into wav files. This process yielded 6,565 video and audio clips
that are aligned with text.

We split the datset randomly so that 70% of sentences that contain metaphors
and 70% of sentences that don’t contain any metaphors are used for training,
15 % of both types of sentences for validation and 15% of both for testing.
This way we ensure that both metaphorical and non-metaphorical sentences are
divided proportionally with the same ratios. These splits are used for all the
models.

## 4\. Metaphor Detection

We experiment with uni- and multi-modal models for metaphor detection. In this
section, we describe the preprocessing steps applied and the experimental
setups conducted.

### 4.1. Preprocessing

For each modality, we make use of the latest advances in neural network models
to capture important features that have achieved state-of-the-art results in
various NLP tasks. As metaphor detection has been conducted solely based on
text, we follow the DeepMet approach by su-etal-2020-deepmet and process the
entire textual content using spaCy [spacy] to tokenize it and acquire
Universal Dependencies style syntactic trees [nivre2020universal] and Penn
Treebank parts-of-speech tags [santorini1990part]. Similarly to the original
approach, all of our textual models predict metaphors at the token level given
the context surrounding it and its POS tags as input.

We resample the audio to 16kHz. Audio features are extracted using
Wav2Vec2FeatureExtractor provided by the Transoformers Python library [wolf-
etal-2020-transformers].

Video features are obtained by taking equally-distributed 16 frames from a
clip and then resize them into 128x171, followed by normalization and center
cropping to 112x112.

### 4.2. Textual model

We train two text-only models, both follow the architecture and approach of
DeepMet where we obtain textual embeddings using RoBERTa [liu2019roberta] and
feed them into two transformer encoding layers which are then combined by
applying global average pooling and concatenation. A dense fully-connected
layer takes in the combined output of both encoders and predicts whether the
token is metaphorical (c.f., su-etal-2020-deepmet for more details).

In our first textual model, we train the model using our corpus, whereas in
the second one we train it using VUA corpus (with a learning rate of 0.00001,
akin the original paper) and later fine-tune it using our corpus.

### 4.3. Audio model

We extend and fine-tune Facebook’s pretrained multilingual XLSR-Wav2Vec2 large
model [baevski2020wav2vec]. The model is trained on Multilingual LibriSpeech
[Pratap2020MLSAL], CommonVoice [ardila-etal-2020-common] and Babel
[roach1996babel] for speech recognition. We employ this model to encode speech
into vector representations from raw audio.

We replace the classification layer of the original model with a dense fully-
connected layer that produces two outputs, one for each label. Unlike the
textual model, here we classify whether the entire spoken expression contains
a metaphor or not (i.e., not on a word level).

### 4.4. Video model

For our video unimodal model, we incorporate a pretrained model for human
action detection. The model is based on the 18 layer deep R(2+1)D network
[8578773] and it is trained on the Kinetics-400 [46330] dataset. The intuition
behind using this model is that it was able to detect actions (e.g., playing
organ), gestures (e.g., pointing) and movements (e.g., waving). Realizing such
information is crucial in understanding the context, and would provide further
cues for detecting metaphors.

Similar to the audio model, we substitute the original classification layer
with a fully connected layer and fine-tune the pretrained model to predict
whether a scene is metaphorical or not.

### 4.5. Multimodal metaphor detection

We test out three multimodal metaphor detection models; 1) text and audio, 2)
text and video and 3) text, audio and video. The textual model is the fine-
tuned model using the VUA corpus and our textual corpus.

In all of the models, the final classification layer of their sub-models are
removed. Unimodal models are combined by concatenating the weights of their
last layer, which are then fed to a classification layer.

### 4.6. Common configuration

All of the models described above share common configurations, unless we
explicitly indicate otherwise. Prior to the last classification layer of all
of our mono- and multimodal models, we introduce a dropout layer
[JMLR:v15:srivastava14a] (with a probability of 20%) to accelerate training,
and reduce internal covariate shift and overfitting.

We use the cross entropy loss function along with Adam optimizer
[kingma2014adam, loshchilov2019decoupled] to update the weights and train the
models. All the fine-tuned models are trained with a learning rate of 0.0001
and for 3 full epochs.

## 5\. Results

In this section, we follow the evaluation metrics commonly used for the
metaphor detection task by reporting the precision, recall and F1 scores for
the metaphorical label.

Regarding the textual models, we report three sets of results, which are for
the models trained on: 1) VUA corpus, 2) our corpus and 3) both the VUA and
our corpus. All the models predict metaphoricity on the token level. To ensure
that our implementation of the DeepMet approach is correct, we tested the
first model on the VUA test dataset of the metaphor detection shared task and
achieved an F1-score of 0.68 and 0.73 on all POS and verb subsets of the data,
respectively. These results are relatively close to the results reported by
the authors.

Table 2 shows the classification results of all three models on the test set.
The test set contained 90 metaphorical tokens and 6,961 non-metaphorical
tokens. The results indicate that the textual model trained solely on the VUA
dataset performed poorly on our test set. In comparison, training the model
using our metaphor corpus only resulted in a great increase of correct
predictions. Nonetheless, combining both corpora by fine-tuning the first
model with our corpus produced the winning model, which managed to spot 76% of
the metaphorical tokens correctly.

We believe that the huge differences between the first and second textual
models, despite the larger size of VUA’s training dataset, are due to the
differences in domains. The VUA corpus contains academic texts, conversation,
fiction, and news texts, whereas our corpus is dominated by conversations on
the web and start-ups. It is evident that by exposing the model to general
domains (i.e., VUA’s corpus) and, thereafter, concentrating it on the start-up
domain, the model was able to identify the highest number of metaphorical
usages.

Trained on | Precision | Recall | F1-score
---|---|---|---
VUA | 0.04 | 0.33 | 0.07
Ours | 0.38 | 0.63 | 0.47
VUA + Ours | 0.53 | 0.76 | 0.62
Table 2: Classification results of the textual monomodal models on the test
set of our corpus, for the metaphorical label.

Results from the other models (unimodal or multimodal) that involving audio
and video showed that adding these modalities actually did not help improving
the model - rather, they are detrimental to the model performance on metaphor
detection. We extend two possible explanations for this failure. First, it is
possible that because the visual and audio cues of metaphor are subtle, these
models failed to learn from such a small amount of annotated data.

Second, it is unclear that the specific models we are using for audio and
video modalities encode the information relevant for the metaphor detection
task. For instance, whereas it is impossible to completely disentangle what
exactly the Wav2Vec model is encoding, we can conjecture that it encodes
information about phoneme identity considering it is optimized for the speech
recognition task. Therefore, it may not be entirely surprising that the
Wav2Vec encoding is not useful for the metaphor detection task because it is
adding redundant or irrelevant information to the model. It is our future work
(or the future work for the community who utilizes this dataset) to refine our
understanding of the multimodal encoding for the metaphor detection task (for
instance, employing a model that more directly encodes information about
speech prosody from the audio).

### 5.1. Error analysis

When looking at the results of the text only model, we can see that the model
identifies metaphors correctly as metaphors more often than not. There are
some metaphorical tokens in metaphors consisting of multiple words that get
classified wrong, for example, in You could think of hosting as your house,
the tenor hosting and the determinant your of the metaphorical word house are
not identified as metaphorical, while house is correctly identified. Another
example is the conventional metaphor toot their own horn, where all other
words except for own are correctly identified as metaphorical.

There are also a fewer number of cases where all words get identified wrongly
as non-metaphorical, for example, the model did not predict any metaphorical
tokens in It’s where you live, while in reality it is the tenor and where you
live is the vehicle. Also, individual tenors where the vehicle comes later get
often not recognized such as in Yes, malware you could think of like, where
malware is the tenor for a vehicle that appears later in the dialog.

When the tenor and the vehicle co-exist nearby, the model can get all
metaphorical tokens right such as in It’s kinda like real estate right? where
both the tenor it and the vehicle real estate are correctly identified. Also
many tenorless expressions are fully recognized correctly as metaphorical,
such as Spreadin’ the love.

There were plenty of cases (61) where the model predicted a metaphor tag for a
token while there was no metaphor. Curiously, prepositions were often tagged
metaphorical, such as to in ring that bell to see these episodes first. The
actual metaphorical part ring that bell ends before the preposition to that
has a non-metaphorical meaning in order to.

We can also see that the model was indeed fooled by cooking terms that were
used both metaphorically and non-metaphorically. In Yeah a little sprinkle,
both a and sprinkle were classified as metaphors, while the context was about
sprinkling sugar. Another similar case was there’s five noble gases that
illuminate, where noble gases and illuminate were erroneously classified to be
metaphorical. This was clearly due to the tenor in the corpus: the discovery
of those five noble gases to illuminate like that that contained similar
words. It is evident that the model relies on word similarities more than
reaching to a higher pragmatic representation of the phenomenon, however, this
is not an unexpected behavior from a machine learning model.

There are also cases where the model detects a metaphor, that could
theoretically be a metaphor, but is not because of the way it was used in the
corpus. For example, the model predicts Give it a go as metaphorical in the
expression button, ”Give it a go.”, where people are talking about a button
with a particular text rather than using the expression metaphorically.
Another such an example is flying in (money flying). Such an expression might
be used metaphorically, but in this case this was a note for the hearing
impaired as money was actually flying on the video.

## 6\. Discussion and Conclusions

In this work, we have only focused on metaphor as a strictly linguistic
phenomenon and we have built a multimodal dataset where these linguistic
metaphors have been tagged in terms of tenors and vehicles. However, it is
apparent that metaphor is a phenomenon that occurs on a higher level of our
cognitive capacities than mere language. There are several cases in our
corpus, where we can evidence the existence of a metaphor but it is never
expressed verbally. For example in Figure 2, money flying cannot be a metaphor
when inspected purely from the point of view of language and its relation to
the video when money is actually flying in the scene. However, it is a
metaphor on a higher level in the sense that the entire scene where money was
flying was to indicate someone becoming rich. In other words, stating a fact
that is happening is not metaphorical if the fact is literally taking place,
however the fact itself might be metaphorical.

Figure 2: Money actually flying on the video.

At the same time, as evidenced by our error analysis, there are certainly
cases where video modality could help in disambiguating whether something is
said metaphorically or not. For instance, talking about sprinkling in a
kitchen environment (see Figure 3) is a very strong sign that the word is
potentially non-metaphorical. Integrating these weak cues into a multimodal
system is, however, not an easy task given that the current methods for video
processing are limited in their coverage.

Figure 3: Sprinkling used in a kitchen in reference to sugar.

Therefore, in the future, it would be useful to annotate metaphors also in the
other modalities. Money flying can be a visual metaphor, and so can a sound
effect, and they can exist independently from each other in different
modalities. Perhaps the reason why our multimodal attempts failed was that
metaphor can be independent of the other modalities. Producing such a dataset
where these modal specific metaphors are also annotated for video and audio is
definitely a huge undertaking that requires research in its own right.

It is clear that our model can detect metaphors correctly, but also the
mistakes it makes highlight that despite using a large RoBERTa model, the
meaning representation the model has cannot reach to such a nuanced level as
to confidently detect metaphors. Metaphor is a figurative device that cannot
be explained by semantics, but rather requires pragmatic inspection. It is not
clear based on our research and other contemporary approaches whether the
current word or sentence embedding models are sufficient to navigate in the
depths of pragmatics and subjective interpretation in any other way than
learning some irrelevant co-occurring phenomena from a biased corpus. At the
same time there is no such thing as an unbiased corpus, either, given that
bias (and mostly heuristics causing it) is a fundamental part of our cognition
as human beings.

In this paper, we have presented a new open and multimodal dataset for
metaphor detection. Because we have focused strictly on CC-BY licensed videos,
we can make the entire dataset available on Zenodo. In our current work, we
have not taken the context widely into account when predicting metaphoricity,
but rather resorted to a very local context. The fact that the videos can be
published in full length makes it possible for any future work to explore
different ways of including contextual cues freely.

## 7\. Bibliographical References

## 8\. Language Resource References

lrec2022-bib languageresource