# Measurement of the absolute branching fraction of the three-body decay
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ and search for $\Lambda^{+}_{c}\to
nK^{+}\pi^{0}{}$, $\Sigma^{0}K^{+}\pi^{0}$ and $\Lambda K^{+}\pi^{0}$

M. Ablikim1, M. N. Achasov5,c, P. Adlarson75, O. Afedulidis4, X. C. Ai80, R.
Aliberti36, A. Amoroso74A,74C, M. R. An40, Q. An71,58,a, Y. Bai57, O.
Bakina37, I. Balossino30A, Y. Ban47,h, V. Batozskaya1,45, K. Begzsuren33, N.
Berger36, M. Berlowski45, M. Bertani29A, D. Bettoni30A, F. Bianchi74A,74C, E.
Bianco74A,74C, A. Bortone74A,74C, I. Boyko37, R. A. Briere6, A. Brueggemann68,
H. Cai76, X. Cai1,58, A. Calcaterra29A, G. F. Cao1,63, N. Cao1,63, S. A.
Cetin62A, J. F. Chang1,58, G. R. Che44, G. Chelkov37,b, C. Chen44, Chao
Chen55, G. Chen1, H. S. Chen1,63, M. L. Chen1,58,63, S. J. Chen43, S. L.
Chen46, S. M. Chen61, T. Chen1,63, X. R. Chen32,63, X. T. Chen1,63, Y. B.
Chen1,58, Y. Q. Chen35, Z. J. Chen26,i, Z. Y. Chen1,63, S. K. Choi11A, X.
Chu44, G. Cibinetto30A, S. C. Coen4, F. Cossio74C, J. J. Cui50, H. L. Dai1,58,
J. P. Dai78, A. Dbeyssi19, R. E. de Boer4, D. Dedovich37, Z. Y. Deng1, A.
Denig36, I. Denysenko37, M. Destefanis74A,74C, F. De Mori74A,74C, B. Ding66,1,
X. X. Ding47,h, Y. Ding35, Y. Ding41, J. Dong1,58, L. Y. Dong1,63, M. Y.
Dong1,58,63, X. Dong76, M. C. Du1, S. X. Du80, Z. H. Duan43, P. Egorov37,b, Y.
H. Fan46, Y. L. Fan76, J. Fang1,58, S. S. Fang1,63, W. X. Fang1, Y. Fang1, R.
Farinelli30A, L. Fava74B,74C, F. Feldbauer4, G. Felici29A, C. Q. Feng71,58, J.
H. Feng59, K. Fischer69, M. Fritsch4, C. D. Fu1, J. L. Fu63, Y. W. Fu1,63, H.
Gao63, Y. N. Gao47,h, Yang Gao71,58, S. Garbolino74C, I. Garzia30A,30B, L.
Ge80, P. T. Ge76, Z. W. Ge43, C. Geng59, E. M. Gersabeck67, A. Gilman69, K.
Goetzen14, L. Gong41, W. X. Gong1,58, W. Gradl36, S. Gramigna30A,30B, M.
Greco74A,74C, M. H. Gu1,58, Y. T. Gu16, C. Y. Guan1,63, Z. L. Guan23, A. Q.
Guo32,63, L. B. Guo42, M. J. Guo50, R. P. Guo49, Y. P. Guo13,g, A. Guskov37,b,
T. T. Han50, W. Y. Han40, X. Q. Hao20, F. A. Harris65, K. K. He55, K. L.
He1,63, F. H. Heinsius4, C. H. Heinz36, Y. K. Heng1,58,63, C. Herold60, T.
Holtmann4, P. C. Hong13,g, G. Y. Hou1,63, X. T. Hou1,63, Y. R. Hou63, Z. L.
Hou1, B. Y. Hu59, H. M. Hu1,63, J. F. Hu56,j, T. Hu1,58,63, Y. Hu1, G. S.
Huang71,58, K. X. Huang59, L. Q. Huang32,63, X. T. Huang50, Y. P. Huang1, T.
Hussain73, F. Hölzken4, N Hüsken28,36, W. Imoehl28, J. Jackson28, S. Jaeger4,
S. Janchiv33, J. H. Jeong11A, Q. Ji1, Q. P. Ji20, X. B. Ji1,63, X. L. Ji1,58,
Y. Y. Ji50, X. Q. Jia50, Z. K. Jia71,58, H. B. Jiang76, P. C. Jiang47,h, S. S.
Jiang40, T. J. Jiang17, X. S. Jiang1,58,63, Y. Jiang63, J. B. Jiao50, Z.
Jiao24, S. Jin43, Y. Jin66, M. Q. Jing1,63, T. Johansson75, S. Kabana34, N.
Kalantar-Nayestanaki64, X. L. Kang10, X. S. Kang41, R. Kappert64, M.
Kavatsyuk64, B. C. Ke80, A. Khoukaz68, R. Kiuchi1, R. Kliemt14, O. B.
Kolcu62A, B. Kopf4, M. Kuessner4, X. Kui1,63, N. Kumar27, A. Kupsc45,75, W.
Kühn38, J. J. Lane67, P. Larin19, A. Lavania27, L. Lavezzi74A,74C, T. T.
Lei71,58, Z. H. Lei71,58, M. Lellmann36, T. Lenz36, C. Li44, C. Li48, C. H.
Li40, Cheng Li71,58, D. M. Li80, F. Li1,58, G. Li1, H. B. Li1,63, H. J. Li20,
H. N. Li56,j, Hui Li44, J. R. Li61, J. S. Li59, J. W. Li50, K. L. Li20, Ke
Li1, L. J Li1,63, L. K. Li1, Lei Li3, M. H. Li44, P. R. Li39,l, Q. X. Li50, S.
X. Li13, T. Li50, W. D. Li1,63, W. G. Li1,a, X. H. Li71,58, X. L. Li50, Xiaoyu
Li1,63, Y. G. Li47,h, Z. J. Li59, Z. X. Li16, C. Liang43, H. Liang1,63, H.
Liang35, H. Liang71,58, Y. F. Liang54, Y. T. Liang32,63, G. R. Liao15, L. Z.
Liao50, J. Libby27, A. Limphirat60, D. X. Lin32,63, T. Lin1, B. J. Liu1, B. X.
Liu76, C. Liu35, C. X. Liu1, F. H. Liu53, Fang Liu1, Feng Liu7, G. M. Liu56,j,
H. Liu39,k,l, H. B. Liu16, H. M. Liu1,63, Huanhuan Liu1, Huihui Liu22, J. B.
Liu71,58, J. L. Liu72, J. Y. Liu1,63, K. Liu1, K. Y. Liu41, Ke Liu23, L.
Liu71,58, L. C. Liu44, Lu Liu44, M. H. Liu13,g, P. L. Liu1, Q. Liu63, S. B.
Liu71,58, T. Liu13,g, W. K. Liu44, W. M. Liu71,58, X. Liu39,k,l, Y. Liu39,k,l,
Y. Liu80, Y. B. Liu44, Z. A. Liu1,58,63, Z. Q. Liu50, X. C. Lou1,58,63, F. X.
Lu59, H. J. Lu24, J. G. Lu1,58, X. L. Lu1, Y. Lu8, Y. P. Lu1,58, Z. H. Lu1,63,
C. L. Luo42, M. X. Luo79, T. Luo13,g, X. L. Luo1,58, X. R. Lyu63, Y. F. Lyu44,
F. C. Ma41, H. L. Ma1, J. L. Ma1,63, L. L. Ma50, M. M. Ma1,63, Q. M. Ma1, R.
Q. Ma1,63, R. T. Ma63, X. Y. Ma1,58, Y. Ma47,h, Y. M. Ma32, F. E. Maas19, M.
Maggiora74A,74C, S. Malde69, A. Mangoni29B, Y. J. Mao47,h, Z. P. Mao1, S.
Marcello74A,74C, Z. X. Meng66, J. G. Messchendorp14,64, G. Mezzadri30A, H.
Miao1,63, T. J. Min43, R. E. Mitchell28, X. H. Mo1,58,63, N. Yu. Muchnoi5,c,
J. Muskalla36, Y. Nefedov37, F. Nerling19,e, I. B. Nikolaev5,c, Z. Ning1,58,
S. Nisar12,m, Y. Niu 50, S. L. Olsen63, Q. Ouyang1,58,63, S. Pacetti29B,29C,
X. Pan55, Y. Pan57, A. Pathak35, P. Patteri29A, Y. P. Pei71,58, M. Pelizaeus4,
H. P. Peng71,58, K. Peters14,e, J. L. Ping42, R. G. Ping1,63, S. Plura36, S.
Pogodin37, V. Prasad34, F. Z. Qi1, H. Qi71,58, H. R. Qi61, M. Qi43, T. Y.
Qi13,g, S. Qian1,58, W. B. Qian63, C. F. Qiao63, X. K. Qiao80, J. J. Qin72, L.
Q. Qin15, X. P. Qin13,g, X. S. Qin50, Z. H. Qin1,58, J. F. Qiu1, S. Q. Qu61,
C. F. Redmer36, K. J. Ren40, A. Rivetti74C, V. Rodin64, M. Rolo74C, G.
Rong1,63, Ch. Rosner19, S. N. Ruan44, N. Salone45, A. Sarantsev37,d, Y.
Schelhaas36, K. Schoenning75, M. Scodeggio30A, K. Y. Shan13,g, W. Shan25, X.
Y. Shan71,58, J. F. Shangguan55, L. G. Shao1,63, M. Shao71,58, C. P. Shen13,g,
H. F. Shen1,9, W. H. Shen63, X. Y. Shen1,63, B. A. Shi63, H. C. Shi71,58, J.
L. Shi13,g, J. Y. Shi1, Q. Q. Shi55, X. Shi1,58, J. J. Song20, T. Z. Song59,
W. M. Song35,1, Y. J. Song13,g, Y. X. Song47,h,n, S. Sosio74A,74C, S.
Spataro74A,74C, F. Stieler36, Y. J. Su63, G. B. Sun76, G. X. Sun1, H. Sun63,
H. K. Sun1, J. F. Sun20, K. Sun61, L. Sun76, S. S. Sun1,63, T. Sun1,63, T.
Sun51,f, W. Y. Sun35, Y. Sun10, Y. J. Sun71,58, Y. Z. Sun1, Z. T. Sun50, C. J.
Tang54, G. Y. Tang1, J. Tang59, Y. A. Tang76, L. Y. Tao72, Q. T. Tao26,i, M.
Tat69, J. X. Teng71,58, V. Thoren75, W. H. Tian59, W. H. Tian52, Y. Tian32,63,
Z. F. Tian76, I. Uman62B, S. J. Wang 50, B. Wang1, B. L. Wang63, Bo Wang71,58,
C. W. Wang43, D. Y. Wang47,h, F. Wang72, H. J. Wang39,k,l, H. P. Wang1,63, J.
P. Wang 50, K. Wang1,58, L. L. Wang1, M. Wang50, Meng Wang1,63, S. Wang39,k,l,
S. Wang13,g, T. Wang13,g, T. J. Wang44, W. Wang72, W. Wang59, W. P.
Wang36,71,o, X. Wang47,h, X. F. Wang39,k,l, X. J. Wang40, X. L. Wang13,g, Y.
Wang61, Y. D. Wang46, Y. F. Wang1,58,63, Y. H. Wang48, Y. N. Wang46, Y. Q.
Wang1, Yaqian Wang18, Yi Wang61, Z. Wang1,58, Z. L. Wang72, Z. Y. Wang1,63,
Ziyi Wang63, D. H. Wei15, F. Weidner68, S. P. Wen1, C. Wenzel4, U. Wiedner4,
G. Wilkinson69, M. Wolke75, L. Wollenberg4, C. Wu40, J. F. Wu1,9, L. H. Wu1,
L. J. Wu1,63, X. Wu13,g, X. H. Wu35, Y. Wu71,58, Y. J. Wu32, Z. Wu1,58, L.
Xia71,58, X. M. Xian40, T. Xiang47,h, D. Xiao39,k,l, G. Y. Xiao43, S. Y.
Xiao1, Y. L. Xiao13,g, Z. J. Xiao42, C. Xie43, X. H. Xie47,h, Y. Xie50, Y. G.
Xie1,58, Y. H. Xie7, Z. P. Xie71,58, T. Y. Xing1,63, C. F. Xu1,63, C. J. Xu59,
G. F. Xu1, H. Y. Xu66, M. Xu71,58, Q. J. Xu17, Q. N. Xu31, W. Xu1, W. L. Xu66,
X. P. Xu55, Y. C. Xu77, Z. P. Xu43, Z. S. Xu63, F. Yan13,g, L. Yan13,g, W. B.
Yan71,58, W. C. Yan80, X. Q. Yan1, H. J. Yang51,f, H. L. Yang35, H. X. Yang1,
Tao Yang1, Y. Yang13,g, Y. F. Yang44, Y. X. Yang1,63, Yifan Yang1,63, Z. W.
Yang39,k,l, Z. P. Yao50, M. Ye1,58, M. H. Ye9, J. H. Yin1, Z. Y. You59, B. X.
Yu1,58,63, C. X. Yu44, G. Yu1,63, J. S. Yu26,i, T. Yu72, X. D. Yu47,h, Y. C.
Yu80, C. Z. Yuan1,63, L. Yuan2, S. C. Yuan1, X. Q. Yuan1, Y. Yuan1,63, Z. Y.
Yuan59, C. X. Yue40, A. A. Zafar73, F. R. Zeng50, X. Zeng13,g, Y. Zeng26,i, X.
Y. Zhai35, Y. C. Zhai50, Y. H. Zhan59, A. Q. Zhang1,63, B. L. Zhang1,63, B. X.
Zhang1, D. H. Zhang44, G. Y. Zhang20, H. Zhang71,58, H. H. Zhang35, H. H.
Zhang59, H. Q. Zhang1,58,63, H. Y. Zhang1,58, J. Zhang80, J. J. Zhang52, J. L.
Zhang21, J. Q. Zhang42, J. W. Zhang1,58,63, J. X. Zhang39,k,l, J. Y. Zhang1,
J. Z. Zhang1,63, Jianyu Zhang63, Jiawei Zhang1,63, L. M. Zhang61, Lei Zhang43,
P. Zhang1,63, Q. Y. Zhang40,80, Shuihan Zhang1,63, Shulei Zhang26,i, X. D.
Zhang46, X. M. Zhang1, X. Y. Zhang50, Xuyan Zhang55, Y. Zhang72, Y. T.
Zhang80, Y. H. Zhang1,58, Yan Zhang71,58, Yao Zhang1, Z. H. Zhang1, Z. L.
Zhang35, Z. Y. Zhang44, Z. Y. Zhang76, G. Zhao1, J. Zhao40, J. Y. Zhao1,63, J.
Z. Zhao1,58, Lei Zhao71,58, Ling Zhao1, M. G. Zhao44, S. J. Zhao80, Y. B.
Zhao1,58, Y. X. Zhao32,63, Z. G. Zhao71,58, A. Zhemchugov37,b, B. Zheng72, J.
P. Zheng1,58, W. J. Zheng1,63, Y. H. Zheng63, B. Zhong42, X. Zhong59, H.
Zhou50, L. P. Zhou1,63, S. Zhou7, X. Zhou76, X. K. Zhou7, X. R. Zhou71,58, X.
Y. Zhou40, Y. Z. Zhou13,g, J. Zhu44, K. Zhu1, K. J. Zhu1,58,63, L. Zhu35, L.
X. Zhu63, S. H. Zhu70, S. Q. Zhu43, T. J. Zhu13,g, W. J. Zhu13,g, Y. C.
Zhu71,58, Z. A. Zhu1,63, J. H. Zou1, J. Zu71,58
(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 Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
6 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
7 Central China Normal University, Wuhan 430079, People’s Republic of China
8 Central South University, Changsha 410083, People’s Republic of China
9 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
10 China University of Geosciences, Wuhan 430074, People’s Republic of China
11 Chung-Ang University, Seoul, 06974, Republic of Korea
12 COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind
Road, 54000 Lahore, Pakistan
13 Fudan University, Shanghai 200433, People’s Republic of China
14 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
15 Guangxi Normal University, Guilin 541004, People’s Republic of China
16 Guangxi University, Nanning 530004, People’s Republic of China
17 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
18 Hebei University, Baoding 071002, People’s Republic of China
19 Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
20 Henan Normal University, Xinxiang 453007, People’s Republic of China
21 Henan University, Kaifeng 475004, People’s Republic of China
22 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
23 Henan University of Technology, Zhengzhou 450001, People’s Republic of
China
24 Huangshan College, Huangshan 245000, People’s Republic of China
25 Hunan Normal University, Changsha 410081, People’s Republic of China
26 Hunan University, Changsha 410082, People’s Republic of China
27 Indian Institute of Technology Madras, Chennai 600036, India
28 Indiana University, Bloomington, Indiana 47405, USA
29 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
30 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara,
Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
31 Inner Mongolia University, Hohhot 010021, People’s Republic of China
32 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
33 Institute of Physics and Technology, Peace Avenue 54B, Ulaanbaatar 13330,
Mongolia
34 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica
1000000, Chile
35 Jilin University, Changchun 130012, People’s Republic of China
36 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
37 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
38 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
39 Lanzhou University, Lanzhou 730000, People’s Republic of China
40 Liaoning Normal University, Dalian 116029, People’s Republic of China
41 Liaoning University, Shenyang 110036, People’s Republic of China
42 Nanjing Normal University, Nanjing 210023, People’s Republic of China
43 Nanjing University, Nanjing 210093, People’s Republic of China
44 Nankai University, Tianjin 300071, People’s Republic of China
45 National Centre for Nuclear Research, Warsaw 02-093, Poland
46 North China Electric Power University, Beijing 102206, People’s Republic of
China
47 Peking University, Beijing 100871, People’s Republic of China
48 Qufu Normal University, Qufu 273165, People’s Republic of China
49 Shandong Normal University, Jinan 250014, People’s Republic of China
50 Shandong University, Jinan 250100, People’s Republic of China
51 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
52 Shanxi Normal University, Linfen 041004, People’s Republic of China
53 Shanxi University, Taiyuan 030006, People’s Republic of China
54 Sichuan University, Chengdu 610064, People’s Republic of China
55 Soochow University, Suzhou 215006, People’s Republic of China
56 South China Normal University, Guangzhou 510006, People’s Republic of China
57 Southeast University, Nanjing 211100, People’s Republic of China
58 State Key Laboratory of Particle Detection and Electronics, Beijing 100049,
Hefei 230026, People’s Republic of China
59 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
60 Suranaree University of Technology, University Avenue 111, Nakhon
Ratchasima 30000, Thailand
61 Tsinghua University, Beijing 100084, People’s Republic of China
62 Turkish Accelerator Center Particle Factory Group, (A)Istinye University,
34010, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus,
99138, Mersin 10, Turkey
63 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
64 University of Groningen, NL-9747 AA Groningen, The Netherlands
65 University of Hawaii, Honolulu, Hawaii 96822, USA
66 University of Jinan, Jinan 250022, People’s Republic of China
67 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
68 University of Muenster, Wilhelm-Klemm-Strasse 9, 48149 Muenster, Germany
69 University of Oxford, Keble Road, Oxford OX13RH, United Kingdom
70 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
71 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
72 University of South China, Hengyang 421001, People’s Republic of China
73 University of the Punjab, Lahore-54590, Pakistan
74 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
75 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
76 Wuhan University, Wuhan 430072, People’s Republic of China
77 Yantai University, Yantai 264005, People’s Republic of China
78 Yunnan University, Kunming 650500, People’s Republic of China
79 Zhejiang University, Hangzhou 310027, People’s Republic of China
80 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 MOE 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 75270,
Pakistan
m Also at Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne,
Switzerland
n Also at Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany

###### Abstract

The Cabbibo-favored decay $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$ is studied
for the first time using 6.1 $\mathrm{fb}^{-1}{}$ of $e^{+}e^{-}{}$ collision
data at center-of-mass energies between 4.600 and 4.840 GeV, collected with
the BESIII detector at the BEPCII collider. With a double-tag method, the
branching fraction of the three-body decay
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$ is measured to be $(7.79\pm 1.46\pm
0.71)\times 10^{-3}$, where the first and second uncertainties are statistical
and systematic, respectively. The branching fraction of the two-body decay
$\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}{}$ is $(5.99\pm 1.04\pm 0.29)\times
10^{-3}$, which is consistent with the previous result of $(5.02\pm 0.99\pm
0.31)\times 10^{-3}$. In addition, the upper limit on the branching fraction
of the doubly Cabbibo-suppressed decay $\Lambda^{+}_{c}\to nK^{+}\pi^{0}{}$ is
$7.1\times 10^{-4}$ at the 90$\%$ confidence level. The upper limits on the
branching fractions of $\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$ and $\Lambda
K^{+}\pi^{0}$ are also determined to be $1.8\times 10^{-3}$ and $2.0\times
10^{-3}$, respectively.

##  I Introduction

Fig. 1: The dominant Feynman diagram of the decay (a)
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ and (b) $nK^{+}\pi^{0}$.

Hadronic decays of charmed baryons provide an ideal laboratory to understand
the interplay of weak and strong interactions in the charm system [1, 2, 3, 4,
5, 6, 7, 8, 9], and the measured branching fractions of charmed baryons play
an important role in constraining models of charmed hadronic decays [10, 11].
However, no reliable phenomenological model of charmed baryon decays currently
exists. The $\Lambda^{+}_{c}$ baryon is the lightest charmed baryon, thus it
is often a decay product in many charmed baryon decays. Hence, an
investigation of the $\Lambda^{+}_{c}$ decay is essential for understanding
excited charmed baryons [12]. In charmed baryon decays, the non-factorizable
contributions from W-exchange diagrams play an essential role. In contrast,
these effects are negligible in heavy meson decays [13]. Therefore,
measurements of the absolute branching fractions of $\Lambda^{+}_{c}$ decays
are important to understanding the internal dynamics of charmed baryon decays
[14].

In recent years, great progress has been made in the experimental study of the
$\Lambda^{+}_{c}$ baryon at the Belle [15], LHCb [16] and BESIII experiments
[18, 19, 17, 20]. First, a breakthrough was achieved with the measurement of
the absolute branching fraction of $\Lambda^{+}_{c}\to pK^{-}\pi^{+}$ [21,
22]. Next, BESIII directly measured the absolute branching fractions of twelve
decay modes for the first time [21]. However, precise measurements for several
Cabbibo-favored (CF) decays of $\Lambda^{+}_{c}$ are currently unavailable.
Furthermore, a large number of the singly Cabbibo-suppressed (SCS) decays and
the doubly Cabbibo-suppressed (DCS) decays of $\Lambda^{+}_{c}$ have not yet
been studied. Based on the data sets at BESIII, measurements of the branching
fractions of $\Lambda^{+}_{c}$ decays of currently known decay modes could
potentially reach a sensitivity of $10^{-4}$. In particular, the branching
fraction of $\Lambda_{c}^{+}\to n\pi^{+}$ was recently measured to be $(6.6\pm
1.3)\times 10^{-4}$ [17]. In addition, the data allows for a search of many
rare $\Lambda^{+}_{c}$ decays.

The three-body CF decay $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ is expected to
have a large decay rate. Figure 1 presents a typical Feynman diagram of this
decay. Some phenomenological models have predicted different branching
fractions for the $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ decay, which are
$(4.5\pm 0.8)\times{10^{-2}}$ [23] and $(3.2\pm 0.6)\times{10^{-2}}$ [24] by
assuming SU(3) flavor symmetry and isospin asymmetry, respectively.
Experimentally, there are only a few studies of $\Lambda^{+}_{c}$ decays with
a $\Xi^{0}$ baryon in the final state, and the three-body decay
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ has not yet been studied. Measurement
of the branching fraction will help us further understand the underlying
dynamics of $\Lambda^{+}_{c}$ decays and distinguish among the different
theoretical models [23].

The three-body DCS decay $\Lambda^{+}_{c}\to nK^{+}\pi^{0}$ is also of great
interest, and phenomenological models of this decay mode have been proposed
[23, 24]. SU(3) flavor symmetry predicts the branching fraction of
$\Lambda^{+}_{c}\to nK^{+}\pi^{0}$ to be $(5.0\pm 0.5)\times{10^{-5}}$ [23].
Figure 1 shows a typical Feynman diagram of $\Lambda^{+}_{c}\to
nK^{+}\pi^{0}$. Experimental measurements of DCS decays of $\Lambda^{+}_{c}$
are limited due to the suppressed branching fractions. Currently, the only
study of a DCS $\Lambda^{+}_{c}$ decay is ${\Lambda^{+}_{c}\to
pK^{+}\pi^{-}}$. The relative branching fraction
${\mathcal{B}}({\Lambda^{+}_{c}\to pK^{+}\pi^{-}})$/
${\mathcal{B}}({\Lambda^{+}_{c}\to pK^{-}\pi^{+}})$ is measured to be $(2.4\pm
0.4)\times 10^{-3}$ [25].

In this paper, the three-body decays $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$,
$\Lambda^{+}_{c}\to nK^{+}\pi^{0}$,
$\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$, $\Lambda^{+}_{c}\to\Lambda
K^{+}\pi^{0}$, and the two-body decay $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$
are studied experimentally with a double-tag (DT) method [26]. This analysis
is performed using a data sample with an integrated luminosity of 6.1
$\mathrm{fb}^{-1}$ collected at center-of-mass (CM) energies between 4.600 and
4.840 GeV, listed in Table 1, by the BESIII detector at the BEPCII collider.
Throughout the text, the charge conjugate states are always implied.

Table 1: The CM energy and the integrated luminosity ($\mathcal{L}_{\rm int}$) for each energy point. The first and the second uncertainties are statistical and systematic, respectively. Dataset | CM energy (MeV) |  $\mathcal{L}_{\rm int}$ ($\mathrm{pb}^{-1}$)
---|---|---
4.600 | 4599.53 $\pm$ 0.07 $\pm$ 0.74 | 586.90 $\pm$ 0.10 $\pm$ 3.90
4.612 | 4611.84 $\pm$ 0.12 $\pm$ 0.28 | 103.45 $\pm$ 0.05 $\pm$ 0.64
4.620 | 4628.00 $\pm$ 0.06 $\pm$ 0.31 | 519.93 $\pm$ 0.11 $\pm$ 3.22
4.640 | 4640.67 $\pm$ 0.06 $\pm$ 0.36 | 548.15 $\pm$ 0.12 $\pm$ 3.40
4.660 | 4661.22 $\pm$ 0.06 $\pm$ 0.29 | 527.55 $\pm$ 0.12 $\pm$ 3.27
4.680 | 4681.84 $\pm$ 0.08 $\pm$ 0.29 | 1664.34 $\pm$ 0.21 $\pm$ 10.32
4.700 | 4698.57 $\pm$ 0.10 $\pm$ 0.32 | 534.40 $\pm$ 0.12 $\pm$ 3.31
4.740 | 4739.70 $\pm$ 0.20 $\pm$ 0.30 | 164.27 $\pm$ 0.07 $\pm$ 0.87
4.750 | 4750.05 $\pm$ 0.12 $\pm$ 0.29 | 367.21 $\pm$ 0.10 $\pm$ 1.95
4.780 | 4780.54 $\pm$ 0.12 $\pm$ 0.33 | 512.78 $\pm$ 0.12 $\pm$ 2.72
4.840 | 4843.07 $\pm$ 0.20 $\pm$ 0.31 | 527.29 $\pm$ 0.12 $\pm$ 2.79

##  II BESIII detector and Monte Carlo

The BESIII detector [29] records symmetric $e^{+}e^{-}$ collisions provided by
the BEPCII [30] storage ring, which operates in the CM energy range from 2.0
to 4.95 GeV, with a peak luminosity of $1.1\times
10^{33}\;\text{cm}^{-2}\text{s}^{-1}$ achieved at $\sqrt{s}=3.77\;\text{GeV}$
[31]. The cylindrical core of the BESIII detector covers 93% of the full solid
angle and consists of a helium-based multilayer drift chamber (MDC), a plastic
scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic
calorimeter (EMC), which are all enclosed in a superconducting solenoidal
magnet providing a 1.0 T magnetic field. The solenoid is supported by an
octagonal flux-return yoke with resistive plate counter muon identification
modules interleaved with steel [32]. The charged-particle momentum resolution
at $1~{}{\rm GeV}/c$ is $0.5\%$, and resolution of the ionization energy loss
in the MDC ($\mathrm{d}E/\mathrm{d}x$) is $6\%$ for electrons from Bhabha
scattering. The EMC measures photon energies with a resolution of $2.5\%$
($5\%$) at $1$ GeV in the barrel (end-cap) region. The time resolution in the
TOF barrel region is 68 ps. The end-cap TOF system was upgraded in 2015 using
multi-gap resistive plate chamber technology, providing a time resolution of
60 ps [33].

Simulated samples produced with geant4-based [34] Monte Carlo software, which
includes the geometric description [35, 36] of the BESIII detector and the
detector response, are used to determine the detection efficiency and to
estimate backgrounds. Exclusive simulation samples of
$e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ are produced with
$\bar{\Lambda}^{-}_{c}$ decaying into ten specific tag modes and
$\Lambda^{+}_{c}$ decaying into $\Xi^{0}K^{+}\pi^{0}$ and $nK^{+}\pi^{0}$. The
simulation includes the beam-energy spread and initial-state radiation (ISR)
in the $e^{+}e^{-}$ annihilations with the specific tag modes [37] modeled
with the generator kkmc [38, 39]. The signal events are modeled with a phase-
space generator. The $e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ line-
shape implements the description from Ref. [18]. The inclusive simulation
sample, which consists of $\Lambda_{c}^{+}\bar{\Lambda}_{c}^{-}$ events,
$D_{(s)}$ production, ISR return to lower-mass $\psi$ states, and continuum
processes ($e^{+}e^{-}\rightarrow u\bar{u},d\bar{d}$ and $s\bar{s}$) is used
to estimate the potential background. All the known decay modes of charmed
hadrons and charmonia are modeled with evtgen [40, 41] using branching
fractions either taken from the Particle Data Group [42], when available, or
otherwise estimated with lundcharm [43, 44]. Final state radiation from
charged final state particles is incorporated using photos [45].

##  III Methodology

The $\bar{\Lambda}_{c}^{-}$ baryons are fully reconstructed by their hadronic
decays to $\bar{p}K^{+}\pi^{-}$, $\bar{p}K^{0}_{S}$,
$\bar{p}K^{+}\pi^{-}\pi^{0}$, $\bar{p}K^{0}_{S}\pi^{0}$,
$\bar{p}K^{0}_{S}\pi^{+}\pi^{-}$, $\bar{\Lambda}\pi^{-}$,
$\bar{\Lambda}\pi^{-}\pi^{-}\pi^{+}$, $\bar{\Lambda}\pi^{-}\pi^{0}$,
$\bar{\Sigma}^{0}\pi^{-}$ and $\bar{\Sigma}^{-}\pi^{+}\pi^{-}$. These
reconstructed decays are referred to as single-tag (ST)
$\bar{\Lambda}^{-}_{c}$ baryons, where the intermediate particles $K^{0}_{S}$,
$\bar{\Lambda}$, $\bar{\Sigma}^{0}$, $\bar{\Sigma}^{-}$, and $\pi^{0}$ are
reconstructed via $K^{0}_{S}\to\pi^{+}\pi^{-}$,
$\bar{\Lambda}\to\bar{p}\pi^{+}$, $\bar{\Sigma}^{0}\to\gamma\bar{\Lambda}$,
$\bar{\Sigma}^{-}\to\bar{p}\pi^{0}$ and $\pi^{0}\to\gamma\gamma$,
respectively. From the remaining tracks and showers, the three-body decays
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$ and $nK^{+}\pi^{0}$ are selected to
form $\Lambda_{c}^{+}$ candidates, which will be referred to as the recoiling
system. Together with the $\bar{\Lambda}^{-}_{c}$ candidates, these form a
sample of DT events.

The branching fraction is expressed as:

${\mathcal{B}}=\frac{N_{\mathrm{sig}}}{{\mathcal{B}}_{\mathrm{inter}}\cdot\Sigma_{i}\,N^{\rm
ST}_{i}\cdot(\epsilon^{\rm DT}_{i}/\epsilon^{\rm ST}_{i})},$ (1)

where $N_{\mathrm{sig}}$ is the signal yield of the DT candidates and
${\mathcal{B}}_{\mathrm{inter}}$ is the product of branching fractions of
intermediate $\Xi^{0}$ and $\pi^{0}$ decays on the signal side from the PDG
[42]. $N^{\rm ST}_{i}$ denotes the yields of the ST candidates observed in
data, and $\epsilon^{\rm ST}_{i}$ and $\epsilon^{\rm DT}_{i}$ are the ST and
DT efficiencies, respectively.

##  IV Event selection

The selection criteria in this analysis follow that of Ref. [17]. Charged
tracks are required to have a polar angle ($\theta$) within
$|\\!\cos\theta|<0.93$, where $\theta$ is defined with respect to the
$z$-axis, which is the symmetry axis of the MDC. Tracks, except for those from
$K^{0}_{S}$ and $\bar{\Lambda}$ decays, are required to originate from an
interaction region defined by $|V_{xy}|<1$ cm and $|V_{z}|<10$ cm (referred as
a tight track hereafter), where $|V_{xy}|$ and $|V_{z}|$ refer to the
distances of closest approach of the reconstructed track to the interaction
point (IP) in the $xy$ plane and the $z$ direction, respectively.

Particle identification (PID) for charged tracks combines measurements of the
energy deposited in the MDC (d$E$/d$x$) and the flight time in the TOF to form
likelihoods $\mathcal{L}(h)~{}(h=p,K,\pi)$ for each hadron $h$ hypothesis.
Tracks are identified as protons when the proton hypothesis has the greatest
likelihood ($\mathcal{L}(p)>\mathcal{L}(K)$ and
$\mathcal{L}(p)>\mathcal{L}(\pi)$), while charged kaons and pions are
identified by comparing the likelihoods for the kaon and pion hypotheses,
$\mathcal{L}(K)>\mathcal{L}(\pi)$ and $\mathcal{L}(\pi)>\mathcal{L}(K)$,
respectively.

The selection of tracks from $K^{0}_{S}$ and $\bar{\Lambda}$ is different from
those of other tracks. Candidates of $K^{0}_{S}$ and $\bar{\Lambda}$ mesons
are reconstructed from their decays to $\pi^{+}\pi^{-}$ and $\bar{p}\pi^{+}$,
respectively, where the charged tracks must satisfy $|V_{z}|<20$ cm (referred
as a loose track hereafter). The PID selection criteria are imposed on the
antiproton candidate, while the charged pion is not subject to any PID
requirement. A secondary vertex fit is performed for each $K^{0}_{S}$ or
$\bar{\Lambda}$ candidate, and the momentum obtained from the fit is used in
the subsequent analysis. The $K^{0}_{S}$ or $\bar{\Lambda}$ candidate is
retained if the $\chi^{2}$ of the secondary vertex fit is less than 100.
Furthermore, the decay vertex is required to be separated from the IP by a
distance of at least twice the vertex resolution. For $K^{0}_{S}$ and
$\bar{\Lambda}$, the invariant masses of $\pi^{+}\pi^{-}$ and $\bar{p}\pi^{+}$
pairs are required to be within (0.487, 0.511) GeV/$c^{2}$ and (1.111, 1.121)
GeV/$c^{2}$, respectively. The $\pi^{+}\pi^{-}$ and $\bar{p}\pi^{-}$ invariant
mass resolutions determined through simulations, are 2.9 MeV$/c^{2}$ and 1.2
MeV$/c^{2}$, respectively. Similarly, the $\bar{\Sigma}^{0}$ and
$\bar{\Sigma}^{-}$ candidates are reconstructed from the $\gamma\bar{\Lambda}$
and $\bar{p}\pi^{0}$ final states with invariant masses within the ranges of
(1.179, 1.203) GeV/$c^{2}$ and (1.176, 1.200) GeV/$c^{2}$, respectively. The
mass resolutions for $\bar{\Sigma}^{0}$ and $\bar{\Sigma}^{-}$ are found,
using simulation, to be 3.6 MeV$/c^{2}$ and 4.3 MeV$/c^{2}$, respectively.

Photon candidates are identified using showers in the EMC. The deposited
energy of each shower must be more than 25 MeV in the barrel region
($|\\!\cos\theta|\leq 0.80$) or more than 50 MeV in the end-cap region
($0.86\leq|\\!\cos\theta|\leq 0.92$). 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.

A $\pi^{0}$ candidate is reconstructed with a photon pair, and their invariant
mass is required to be within the range (0.115, 0.150) GeV/$c^{2}$. To improve
the resolution, a kinematic fit is performed, where the diphoton invariant
mass is constrained to the known $\pi^{0}$ mass [42], and the $\chi^{2}$ of
the kinematic fit is required to be less than 200. The momenta obtained from
the kinematic fit are used in the subsequent analysis.

To distinguish the ST $\bar{\Lambda}^{-}_{c}$ baryons from combinatorial
backgrounds, the distributions of the energy difference $\Delta E$ are used,
defined as

$\Delta E\equiv E_{\bar{\Lambda}^{-}_{c}}-E_{\mathrm{beam}},$ (2)

where $E_{\rm beam}$ is the beam energy, and $E_{\bar{\Lambda}^{-}_{c}}$ is
the total energy of the ST candidate, calculated in the $e^{+}e^{-}$ rest
frame. The signal events are expected to peak around zero in the $\Delta E$
distribution. If an event has multiple $\bar{\Lambda}^{-}_{c}$ candidates, the
one with the smallest $|\Delta E|$ is retained, and the $\Delta E$
requirements are listed in Table 2.

The beam-constrained mass $M_{\rm BC}$ of the selected ST candidates is
defined as

$M_{\rm
BC}\equiv\sqrt{E_{\mathrm{beam}}^{2}/c^{4}-|\vec{p}_{\bar{\Lambda}^{-}_{c}}|^{2}/c^{2}},$
(3)

where $\vec{\mkern 1.0mup}_{\bar{\Lambda}^{-}_{c}}$ is the total momentum of
the ST candidate and $M_{\rm BC}$ peaks at the $\bar{\Lambda}_{c}^{-}$ mass.
For each tag mode, the ST yield is determined by fitting the $M_{\rm BC}$
distribution. In the fit, the $\bar{\Lambda}_{c}^{-}$ signal is described by
the MC simulated shape convolved with a Gaussian function to compensate for
the resolution difference between data and MC. The parameters of the Gaussian
function are free in the fit and different for each energy and tag mode. The
combinatorial background is described by an ARGUS function [46], with the end-
point parameter fixed to the nominal beam energy. The fits to the $M_{\rm BC}$
distributions of the various tag modes for the 4.600 - 4.700 datasets are the
same as Ref. [37]. The fits to the $M_{\rm BC}$ distributions for the 4.740,
4.750, 4.780, and 4.840 datasets are shown in Fig. 2. Candidates in the
$M_{\rm BC}$ signal region, $(2.275,2.310)$ GeV$/c^{2}$, are kept for further
analysis. The ST yields in data and the ST efficiencies for individual tags
are listed in Table 2. The total ST yield, obtained by summing the ST yield of
all tag modes and all energies, is found to be $N^{\rm tot}_{\rm ST}=130439\pm
425$, where the uncertainty is statistical.

Fig. 2:  The $M_{\rm BC}$ distributions of ST channels of $\bar{\Lambda}_{c}^{-}$ at (a) 4.740 GeV, (b) 4.750 GeV, (c) 4.780 GeV and (d) 4.840 GeV. The signal shape of the $\bar{\Lambda}_{c}^{-}$ is described by the simulated shape convolved with a Gaussian resolution function, and the background is modeled with an ARGUS function. The points with error bars represent data. The (red) solid curves indicate the fit results and the (blue) dashed curves describe the background shapes. The vertical dashed lines show the $M_{\rm BC}$ selection requirements.  Table 2: The $\Delta E$ requirements, the ST yields, and the ST detection efficiencies of each tag mode for the data samples between 4.740 and 4.840 $\rm\,GeV$. The uncertainties of the ST yields are statistical only.  |  | 4.740 | 4.750 | 4.780 | 4.840
---|---|---|---|---|---
Tag mode |  $\Delta E$ (MeV) | $N_{i}^{\mathrm{ST}}$ |  $\epsilon_{i}^{\mathrm{ST}}$(%) | $N_{i}^{\mathrm{ST}}$ |  $\epsilon_{i}^{\mathrm{ST}}$(%) | $N_{i}^{\mathrm{ST}}$ |  $\epsilon_{i}^{\mathrm{ST}}$(%) | $N_{i}^{\mathrm{ST}}$ |  $\epsilon_{i}^{\mathrm{ST}}$(%)
$\bar{p}K^{+}\pi^{-}$ | $(-34,~{}20)$ |  $1201$ $\pm$ |  40 | 48.4 | 2782 $\pm$ |  60 | 48.1 | 3689 $\pm$ |  67 | 47.1 | 2676 $\pm$ |  61 | 43.8
$\bar{p}K_{S}$ | $(-20,~{}20)$ |  $256$ $\pm$ |  17 | 48.5 | 525 $\pm$ |  24 | 46.9 | 629 $\pm$ |  26 | 44.2 | 475 $\pm$ |  23 | 42.4
$\bar{\Lambda}\pi^{-}$ | $(-20,~{}20)$ |  $144$ $\pm$ |  12 | 36.6 | 336 $\pm$ |  19 | 37.0 | 383 $\pm$ |  21 | 35.5 | 265 $\pm$ |  17 | 32.8
$\bar{p}K^{+}\pi^{-}\pi^{0}$ | $(-30,~{}20)$ |  $246$ $\pm$ |  25 | 17.8 | 607 $\pm$ |  40 | 18.3 | 845 $\pm$ |  37 | 17.3 | 583 $\pm$ |  39 | 15.7
$\bar{p}K_{S}\pi^{0}$ | $(-30,~{}20)$ |  $76$ $\pm$ |  12 | 18.7 | 212 $\pm$ |  20 | 18.8 | 269 $\pm$ |  22 | 18.3 | 185 $\pm$ |  20 | 10.9
$\bar{\Lambda}\pi^{-}\pi^{0}$ | $(-30,~{}20)$ |  $239$ $\pm$ |  18 | 18.1 | 529 $\pm$ |  30 | 17.8 | 723 $\pm$ |  33 | 18.0 | 513 $\pm$ |  28 | 16.9
$\bar{p}K_{S}\pi^{+}\pi^{-}$ | $(-20,~{}20)$ |  $89$ $\pm$ |  13 | 20.1 | 192 $\pm$ |  20 | 19.3 | 292 $\pm$ |  24 | 19.7 | 202 $\pm$ |  20 | 17.6
$\bar{\Lambda}\pi^{-}\pi^{+}\pi^{-}$ | $(-20,~{}20)$ |  $152$ $\pm$ |  14 | 13.6 | 326 $\pm$ |  21 | 14.7 | 453 $\pm$ |  25 | 17.5 | 348 $\pm$ |  22 | 13.2
$\bar{\Sigma}^{0}\pi^{-}$ | $(-20,~{}20)$ |  $58$ $\pm$ |  8 | 22.5 | 152 $\pm$ |  13 | 22.0 | 196 $\pm$ |  15 | 20.9 | 145 $\pm$ |  13 | 20.5
$\bar{\Sigma}^{-}\pi^{+}\pi^{-}$ | $(-30,~{}20)$ |  $136$ $\pm$ |  16 | 19.9 | 362 $\pm$ |  32 | 19.6 | 500 $\pm$ |  32 | 19.9 | 373 $\pm$ |  26 | 17.5

Fig. 3:  The schematic diagrams of the two analysis strategies, which are denoted (a) Cat-1 and (b) Cat-2 in the text. Table 3: The DT detection efficiency(%) of $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ in Cat-1/Cat-2 for each tag mode and each energy point. | 4.600 | 4.612 | 4.620 | 4.640 | 4.660 | 4.680 | 4.700 | 4.740 | 4.750 | 4.780 | 4.840
---|---|---|---|---|---|---|---|---|---|---|---
$pK^{-}\pi^{+}$ | 20.3/ |  8.3 | 19.3/ |  7.4 | 19.0/ |  6.7 | 18.6/ |  6.7 | 18.1/ |  6.5 | 17.8/ |  6.5 | 17.4/ |  6.5 | 15.7/ |  6.5 | 15.4/ |  6.4 | 14.9/ |  6.5 | 13.8/ |  6.1
$pK_{\mathrm{S}}^{0}$ | 22.1/ |  9.0 | 20.4/ |  7.6 | 18.7/ |  8.0 | 18.9/ |  8.1 | 18.4/ |  6.7 | 17.4/ |  8.2 | 17.5/ |  7.5 | 17.3/ |  7.1 | 16.8/ |  7.1 | 17.0/ |  6.6 | 14.0/ |  6.6
$\Lambda\pi^{+}$ | 16.9/ |  7.9 | 15.6/ |  6.9 | 14.5/ |  6.2 | 14.5/ |  6.0 | 13.3/ |  6.1 | 13.0/ |  5.6 | 13.6/ |  4.9 | 13.9/ |  5.3 | 13.4/ |  5.4 | 12.1/ |  5.1 | 12.1/ |  4.6
$pK^{-}\pi^{+}\pi^{0}$ | 5.3/ |  1.6 | 4.8/ |  1.4 | 4.6/ |  1.5 | 4.5/ |  1.3 | 4.4/ |  1.3 | 4.3/ |  1.3 | 4.1/ |  1.3 | 3.6/ |  1.4 | 3.5/ |  1.4 | 3.5/ |  1.5 | 3.3/ |  1.4
$pK_{\mathrm{S}}^{0}\pi^{0}$ | 8.0/ |  2.9 | 7.1/ |  2.3 | 7.1/ |  2.0 | 6.8/ |  2.1 | 6.5/ |  2.2 | 6.6/ |  2.5 | 6.0/ |  2.1 | 5.6/ |  2.1 | 5.3/ |  2.2 | 5.1/ |  2.1 | 4.8/ |  2.0
$\Lambda\pi^{+}\pi^{0}$ | 6.7/ |  2.0 | 6.0/ |  1.7 | 5.8/ |  1.8 | 5.7/ |  1.8 | 5.4/ |  1.6 | 5.2/ |  1.7 | 5.1/ |  1.7 | 4.5/ |  1.8 | 4.7/ |  1.7 | 4.4/ |  1.7 | 4.1/ |  1.8
$pK_{\mathrm{S}}^{0}\pi^{+}\pi^{-}$ | 9.0/ |  2.9 | 8.7/ |  2.4 | 8.1/ |  2.0 | 7.9/ |  2.2 | 7.9/ |  2.2 | 7.4/ |  2.2 | 7.4/ |  2.6 | 6.7/ |  2.5 | 7.0/ |  2.7 | 6.7/ |  2.8 | 6.1/ |  2.5
$\Lambda\pi^{+}\pi^{+}\pi^{-}$ | 6.2/ |  1.7 | 5.7/ |  1.3 | 5.4/ |  1.6 | 5.3/ |  1.3 | 5.1/ |  1.4 | 5.3/ |  1.4 | 5.2/ |  1.4 | 4.7/ |  1.6 | 4.5/ |  1.7 | 4.2/ |  1.6 | 4.4/ |  1.8
$\Sigma^{0}\pi^{+}$ | 8.8/ |  3.7 | 7.8/ |  3.0 | 7.8/ |  2.4 | 7.3/ |  2.8 | 6.4/ |  2.4 | 6.6/ |  3.4 | 6.9/ |  2.6 | 5.8/ |  2.5 | 6.0/ |  2.3 | 5.4/ |  2.4 | 5.0/ |  2.3
$\Sigma^{+}\pi^{+}\pi^{-}$ | 3.2/ |  2.5 | 3.2/ |  2.3 | 3.0/ |  2.3 | 3.0/ |  2.4 | 2.6/ |  2.0 | 2.8/ |  1.9 | 2.7/ |  2.2 | 2.3/ |  1.0 | 2.4/ |  1.0 | 2.2/ |  1.1 | 2.0/ |  0.8
Table 4: The DT detection efficiency(%) of $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ in Cat-1/Cat-2 for each tag mode and each energy point. | 4.600 | 4.612 | 4.620 | 4.640 | 4.660 | 4.680 | 4.700 | 4.740 | 4.750 | 4.780 | 4.840
---|---|---|---|---|---|---|---|---|---|---|---
$pK^{-}\pi^{+}$ | 7.7/ |  3.3 | 7.4/ |  2.8 | 7.3/ |  2.8 | 7.2/ |  2.7 | 7.0/ |  2.6 | 7.1/ |  2.7 | 6.8/ |  2.8 | 6.3/ |  2.6 | 6.3/ |  2.8 | 5.9/ |  2.8 | 5.7/ |  2.4
$pK_{\mathrm{S}}^{0}$ | 8.6/ |  3.7 | 8.5/ |  3.2 | 7.6/ |  3.1 | 7.7/ |  2.8 | 7.7/ |  2.9 | 7.7/ |  3.2 | 7.3/ |  2.5 | 6.5/ |  3.3 | 6.7/ |  2.9 | 6.6/ |  3.2 | 6.3/ |  2.4
$\Lambda\pi^{+}$ | 6.3/ |  2.4 | 6.0/ |  2.0 | 6.1/ |  2.2 | 6.1/ |  2.1 | 5.1/ |  2.1 | 5.5/ |  1.9 | 5.9/ |  2.4 | 5.3/ |  2.2 | 5.5/ |  2.3 | 5.2/ |  2.5 | 4.7/ |  2.1
$pK^{-}\pi^{+}\pi^{0}$ | 1.9/ |  0.8 | 2.0/ |  0.7 | 2.0/ |  0.7 | 1.9/ |  0.6 | 2.0/ |  0.6 | 1.8/ |  0.7 | 1.8/ |  0.6 | 1.5/ |  0.6 | 1.4/ |  0.6 | 1.5/ |  0.6 | 1.3/ |  0.6
$pK_{\mathrm{S}}^{0}\pi^{0}$ | 2.9/ |  1.1 | 2.5/ |  1.1 | 2.5/ |  1.0 | 2.3/ |  1.0 | 2.5/ |  1.1 | 2.6/ |  0.9 | 2.4/ |  1.0 | 2.1/ |  0.7 | 2.1/ |  0.8 | 2.0/ |  0.9 | 2.2/ |  0.8
$\Lambda\pi^{+}\pi^{0}$ | 2.5/ |  0.9 | 2.2/ |  0.8 | 2.1/ |  0.8 | 2.1/ |  0.8 | 2.1/ |  0.7 | 2.0/ |  0.8 | 2.0/ |  0.8 | 1.8/ |  0.7 | 1.7/ |  0.7 | 1.9/ |  0.8 | 1.8/ |  0.7
$pK_{\mathrm{S}}^{0}\pi^{+}\pi^{-}$ | 3.2/ |  1.4 | 2.7/ |  1.0 | 3.0/ |  1.0 | 3.1/ |  1.0 | 2.6/ |  1.1 | 2.7/ |  0.9 | 3.0/ |  1.1 | 2.4/ |  0.9 | 2.8/ |  1.0 | 2.7/ |  1.0 | 2.5/ |  1.1
$\Lambda\pi^{+}\pi^{+}\pi^{-}$ | 2.2/ |  0.8 | 2.0/ |  0.6 | 1.8/ |  0.6. | 2.0/ |  0.6 | 1.9/ |  0.6 | 1.9/ |  0.6 | 1.9/ |  0.7 | 1.8/ |  0.7 | 1.6/ |  0.6 | 1.6/ |  0.6 | 1.8/ |  0.6
$\Sigma^{0}\pi^{+}$ | 3.2/ |  1.3 | 2.8/ |  1.3 | 2.9/ |  1.1 | 2.5/ |  1.3 | 2.8/ |  1.3 | 2.9/ |  1.1 | 2.5/ |  1.0 | 2.7/ |  1.1 | 2.4/ |  1.2 | 2.2/ |  1.0 | 2.2/ |  1.0
$\Sigma^{+}\pi^{+}\pi^{-}$ | 1.3/ |  0.7 | 1.2/ |  0.4 | 1.1/ |  0.4. | 1.1/ |  0.5 | 1.1/ |  0.4 | 1.0/ |  0.5 | 1.0/ |  0.4 | 0.8/ |  0.5 | 0.8/ |  0.4 | 0.8/ |  0.4 | 0.9/ |  0.3
Table 5: The DT detection efficiency(%) of $\Lambda^{+}_{c}\to nK^{+}\pi^{0}$ in Cat-1 for each tag mode and each energy point. | 4.600 | 4.612 | 4.620 | 4.640 | 4.660 | 4.680 | 4.700 | 4.740 | 4.750 | 4.780 | 4.840
---|---|---|---|---|---|---|---|---|---|---|---
$pK^{-}\pi^{+}$ | 13.4 | 12.9 | 12.2 | 12.0 | 11.7 | 11.4 | 11.2 | 10.4 | 10.2 | 9.9 | 9.2
$pK_{\mathrm{S}}^{0}$ | 14.3 | 13.8 | 13.3 | 12.9 | 12.1 | 12.5 | 11.5 | 11.2 | 11.6 | 11.1 | 9.9
$\Lambda\pi^{+}$ | 11.3 | 10.6 | 9.7 | 10.0 | 9.3 | 9.4 | 9.5 | 9.3 | 8.2 | 7.9 | 8.1
$pK^{-}\pi^{+}\pi^{0}$ | 3.7 | 3.6 | 3.5 | 3.3 | 3.3 | 3.2 | 3.2 | 2.7 | 2.7 | 2.8 | 2.5
$pK_{\mathrm{S}}^{0}\pi^{0}$ | 4.8 | 4.5 | 4.3 | 4.5 | 4.2 | 4.0 | 3.8 | 3.1 | 3.4 | 3.4 | 3.0
$\Lambda\pi^{+}\pi^{0}$ | 4.2 | 4.0 | 3.6 | 3.7 | 3.5 | 3.4 | 3.4 | 3.2 | 3.1 | 3.0 | 2.7
$pK_{\mathrm{S}}^{0}\pi^{+}\pi^{-}$ | 5.8 | 5.2 | 4.8 | 4.9 | 4.6 | 4.5 | 4.8 | 4.3 | 3.8 | 4.3 | 4.2
$\Lambda\pi^{+}\pi^{+}\pi^{-}$ | 3.9 | 3.3 | 3.5 | 3.2 | 3.4 | 3.4 | 2.9 | 2.7 | 2.8 | 2.7 | 2.8
$\Sigma^{0}\pi^{+}$ | 6.7 | 5.8 | 6.2 | 5.5 | 5.2 | 5.5 | 6.0 | 4.3 | 5.0 | 4.0 | 4.1
$\Sigma^{+}\pi^{+}\pi^{-}$ | 2.4 | 2.3 | 2.1 | 2.3 | 2.2 | 2.2 | 2.0 | 1.8 | 1.9 | 1.9 | 1.6
Table 6: The DT detection efficiency(%) of $\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$ in Cat-1/Cat-2 for each tag mode and each energy point. | 4.600 | 4.612 | 4.620 | 4.640 | 4.660 | 4.680 | 4.700 | 4.740 | 4.750 | 4.780 | 4.840
---|---|---|---|---|---|---|---|---|---|---|---
$pK^{-}\pi^{+}$ | 10.2/ |  5.7 | 9.7/ |  5.3 | 9.0/ |  4.9 | 9.3/ |  4.9 | 9.2/ |  4.9 | 8.7/ |  4.8 | 8.6/ |  4.7 | 8.3/ |  4.5 | 8.1/ |  4.6 | 7.7/ |  4.5 | 7.5/ |  4.2
$pK_{\mathrm{S}}^{0}$ | 11.4/ |  6.1 | 10.0/ |  5.5 | 9.7/ |  5.3 | 9.9/ |  5.6 | 10.0/ |  5.5 | 9.0/ |  5.0 | 9.4/ |  4.6 | 8.8/ |  5.5 | 8.6/ |  5.4 | 8.5/ |  4.9 | 8.2/ |  4.8
$\Lambda\pi^{+}$ | 8.5/ |  4.8 | 8.5/ |  3.6 | 7.3/ |  3.9 | 7.4/ |  4.3 | 7.7/ |  3.9 | 7.0/ |  4.0 | 6.8/ |  3.3 | 6.9/ |  3.9 | 6.9/ |  4.2 | 6.2/ |  3.7 | 6.0/ |  3.5
$pK^{-}\pi^{+}\pi^{0}$ | 2.7/ |  1.2 | 2.4/ |  1.1 | 2.5/ |  1.1 | 2.4/ |  1.1 | 2.3/ |  1.1 | 2.2/ |  0.9 | 2.4/ |  1.0 | 2.0/ |  0.9 | 2.0/ |  1.0 | 1.9/ |  1.0 | 1.9/ |  1.0
$pK_{\mathrm{S}}^{0}\pi^{0}$ | 4.1/ |  1.7 | 3.3/ |  2.0 | 3.4/ |  1.7 | 3.2/ |  1.8 | 3.0/ |  1.7 | 3.4/ |  1.6 | 3.1/ |  1.8 | 3.3/ |  1.5 | 2.7/ |  1.4 | 2.7/ |  1.7 | 2.4/ |  1.3
$\Lambda\pi^{+}\pi^{0}$ | 3.1/ |  1.7 | 2.9/ |  1.3 | 2.7/ |  1.4 | 2.8/ |  1.4 | 2.8/ |  1.2 | 2.8/ |  1.3 | 2.5/ |  1.2 | 2.3/ |  1.3 | 2.3/ |  1.3 | 2.4/ |  1.2 | 2.1/ |  1.2
$pK_{\mathrm{S}}^{0}\pi^{+}\pi^{-}$ | 4.5/ |  2.1 | 4.1/ |  1.8 | 3.6/ |  1.9 | 3.8/ |  1.9 | 3.8/ |  1.5 | 3.4/ |  1.7 | 3.8/ |  1.7 | 3.7/ |  1.6 | 3.0/ |  1.5 | 3.5/ |  1.6 | 3.4/ |  1.8
$\Lambda\pi^{+}\pi^{+}\pi^{-}$ | 3.1/ |  1.4 | 2.6/ |  1.2 | 2.5/ |  1.1 | 2.7/ |  1.2 | 2.7/ |  1.3 | 2.5/ |  1.1 | 2.5/ |  1.2 | 2.2/ |  1.1 | 2.2/ |  1.2 | 2.2/ |  1.2 | 2.2/ |  1.2
$\Sigma^{0}\pi^{+}$ | 4.4/ |  2.1 | 4.6/ |  2.1 | 3.7/ |  2.2 | 3.6/ |  1.9 | 3.9/ |  1.6 | 3.8/ |  1.8 | 3.6/ |  1.9 | 3.4/ |  2.0 | 3.5/ |  1.7 | 3.2/ |  1.7 | 3.1/ |  1.7
$\Sigma^{+}\pi^{+}\pi^{-}$ | 1.8/ |  1.0 | 1.6/ |  0.8 | 1.5/ |  0.8 | 1.5/ |  0.8 | 1.5/ |  0.8 | 1.4/ |  0.9 | 1.6/ |  0.7 | 1.2/ |  0.7 | 1.2/ |  0.7 | 1.3/ |  0.8 | 1.2/ |  0.8
Table 7: The DT detection efficiency(%) of $\Lambda^{+}_{c}\to\Lambda K^{+}\pi^{0}$ in Cat-1/Cat-2 for each tag mode and each energy point. | 4.600 | 4.612 | 4.620 | 4.640 | 4.660 | 4.680 | 4.700 | 4.740 | 4.750 | 4.780 | 4.840
---|---|---|---|---|---|---|---|---|---|---|---
$pK^{-}\pi^{+}$ | 11.0/ |  6.4 | 10.5/ |  6.0 | 10.0/ |  5.6 | 10.0/ |  5.4 | 10.1/ |  5.4 | 9.9/ |  5.5 | 9.5/ |  5.4 | 8.7/ |  5.0 | 8.6/ |  5.1 | 8.2/ |  5.0 | 7.9/ |  4.6
$pK_{\mathrm{S}}^{0}$ | 11.9/ |  7.2 | 10.9/ |  6.7 | 10.9/ |  6.2 | 11.1/ |  6.1 | 10.5/ |  6.0 | 9.9/ |  5.6 | 9.6/ |  5.6 | 9.6/ |  5.8 | 9.4/ |  5.9 | 9.3/ |  5.9 | 8.5/ |  5.3
$\Lambda\pi^{+}$ | 9.8/ |  4.9 | 9.0/ |  4.8 | 7.9/ |  4.5 | 8.6/ |  5.0 | 8.0/ |  4.5 | 7.1/ |  4.6 | 7.8/ |  4.3 | 7.6/ |  4.3 | 7.3/ |  4.8 | 8.2/ |  4.3 | 7.4/ |  3.7
$pK^{-}\pi^{+}\pi^{0}$ | 3.0/ |  1.4 | 2.9/ |  1.3 | 2.8/ |  1.3 | 2.8/ |  1.2 | 2.6/ |  1.2 | 2.6/ |  1.2 | 2.7/ |  1.1 | 2.3/ |  1.2 | 2.2/ |  1.2 | 2.2/ |  1.1 | 2.1/ |  1.1
$pK_{\mathrm{S}}^{0}\pi^{0}$ | 4.6/ |  2.3 | 3.6/ |  1.9 | 3.9/ |  1.7 | 3.5/ |  1.8 | 3.2/ |  1.8 | 3.4/ |  1.9 | 3.5/ |  1.5 | 2.7/ |  1.7 | 3.2/ |  1.6 | 2.9/ |  1.6 | 2.5/ |  1.6
$\Lambda\pi^{+}\pi^{0}$ | 3.5/ |  1.9 | 3.2/ |  1.7 | 3.1/ |  1.6 | 3.1/ |  1.6 | 3.1/ |  1.5 | 3.0/ |  1.5 | 2.7/ |  1.5 | 2.6/ |  1.4 | 2.4/ |  1.3 | 2.4/ |  1.3 | 2.3/ |  1.3
$pK_{\mathrm{S}}^{0}\pi^{+}\pi^{-}$ | 4.7/ |  2.4 | 4.1/ |  2.1 | 4.0/ |  1.9 | 4.4/ |  1.9 | 4.2/ |  1.8 | 3.8/ |  2.0 | 4.1/ |  1.8 | 3.8/ |  2.0 | 3.4/ |  2.0 | 4.1/ |  2.1 | 3.5/ |  1.9
$\Lambda\pi^{+}\pi^{+}\pi^{-}$ | 3.0/ |  1.7 | 2.7/ |  1.3 | 2.7/ |  1.4 | 2.7/ |  1.4 | 2.7/ |  1.3 | 2.8/ |  1.4 | 2.9/ |  1.4 | 2.4/ |  1.4 | 2.8/ |  1.3 | 2.5/ |  1.3 | 2.3/ |  1.4
$\Sigma^{0}\pi^{+}$ | 5.1/ |  2.8 | 4.5/ |  2.4 | 4.4/ |  2.7 | 4.6/ |  2.4 | 4.2/ |  2.4 | 4.4/ |  2.1 | 4.0/ |  2.2 | 3.8/ |  2.6 | 3.4/ |  2.5 | 3.3/ |  2.2 | 3.0/ |  2.1
$\Sigma^{+}\pi^{+}\pi^{-}$ | 2.1/ |  1.4 | 1.9/ |  1.1 | 1.8/ |  1.1 | 1.6/ |  1.0 | 1.8/ |  1.1 | 1.6/ |  1.0 | 1.5/ |  0.9 | 1.6/ |  0.8 | 1.5/ |  0.9 | 1.3/ |  0.8 | 1.3/ |  0.8

After the ST selection, we want to determine the number of
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ and $nK^{+}\pi^{0}$ candidates on the
opposite side of the ST $\bar{\Lambda}_{c}^{-}$. The $K^{+}$ and $\pi^{0}$ are
reconstructed, as described above, from the remaining showers and tracks.
Using total four-momentum conservation, the $\Xi^{0}$ signal is obtained from
the distribution of recoil mass,

$\displaystyle
M^{2}_{\mathrm{recoil}}(\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}})=(E_{\mathrm{beam}}-E_{K^{+}}-E_{\pi^{0}})^{2}/c^{4}$
(4)
$\displaystyle-|\rho\cdot\vec{p}_{0}-\vec{p}_{K^{+}}-\vec{p}_{\pi^{0}}|^{2}/c^{2},$

where $E_{K^{+}}$, $E_{\pi^{0}}$, $\vec{p}_{K^{+}}$ and $\vec{p}_{\pi^{0}}$
are the energies and momenta of ${K^{+}}$ and $\pi^{0}$ candidates,
respectively,
$\rho=\sqrt{E_{\mathrm{beam}}^{2}/c^{2}-m_{\Lambda^{+}_{c}}^{2}c^{2}}$ is the
magnitude of the $\Lambda^{+}_{c}$ momentum, constrained by the beam energy,
and
$\vec{p}_{0}=-\vec{p}_{\bar{\Lambda}_{c}^{-}}/|\vec{p}_{\bar{\Lambda}_{c}^{-}}|$
is its direction. Similarly, the yield of the two-body decay
$\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ is obtained using the recoil mass.

$M^{2}_{\mathrm{recoil}}(\Lambda_{c}^{\mathrm{ST}}{K^{+}})=(E_{\mathrm{beam}}-E_{K^{+}})^{2}/c^{4}-|\rho\cdot\vec{p}_{0}-\vec{p}_{K^{+}}|^{2}/c^{2}.$
(5)

The $\Xi^{0}$ predominant decay mode is $\Xi^{0}\to\Lambda\pi^{0}$ [42]. The
$\Lambda$ baryon has two main decay modes, which are studied in this analysis:
the neutral decay mode $\Lambda\to n\pi^{0}$, which will be referred to as
Cat-1, and the charged decay mode $\Lambda\to p\pi^{-}$, which will be
referred to as Cat-2. The Cat-1 and Cat-2 decays are shown schematically in
Fig. 3. Four variables
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$,
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$,
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
are defined by Eqs. 4 and 5. For Cat-1, a single tight track is reconstructed
and identified as a $K^{+}$ meson. In Cat-2, three charged tracks are
reconstructed as a $K^{+}$, $p$, and $\pi^{-}$. The $K^{+}$ is a tight track,
while the other two are loose tracks from the $\Lambda\to p\pi^{-}$ decay. The
$p$ and $\pi^{-}$ are constrained to originate from a common vertex to form
the $\Lambda$ candidates by a vertex fit [47]. The invariant mass of the
$\Lambda$ candidate is required to fall inside the range (1.111, 1.121)
GeV/${c^{2}}$.

The $\pi^{0}$ candidate is reconstructed via the process
$\pi^{0}\to\gamma\gamma$. If there are multiple $\pi^{0}$ candidates, the one
with the minimum kinematic-fit $\chi^{2}$ is assumed to originate from the
$\Lambda^{+}_{c}$ baryon.

To suppress sources of background due to neutral hyperon decays from the
decays $\Lambda^{+}_{c}\to\Lambda K^{+}$, $\Sigma^{0}K^{+}$ and
$\Xi^{0}K^{+}$, the events falling inside the corresponding intervals of these
three decays of the variable
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
are rejected. This requirement suppresses 95% of these backgrounds.
Furthermore, electron mis-PID backgrounds are suppressed using PID and EMC
information. To suppress contaminations from long-lived particles in the final
state, any event with additional tracks, either loose or tight, is rejected.
The DT efficiencies of each signal decay for Cat-1 and Cat-2 are summarized in
Tables 3-7.

##  V Background analysis

Potential sources of background are classified into two categories: those from
$e^{+}e^{-}$ $\to$ $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ (denoted as
$\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ background) and those directly
originating from continuum hadron production in $e^{+}e^{-}$ annihilation
(denoted as $q\bar{q}$ background).

The $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ background is investigated for both
categories with the $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ inclusive MC
samples, after removing the signal processes. The
$\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ background distributions are the blue-
shaded histograms in Figs. 4 and 5, and they have been normalized to the same
luminosity as data.

For the CAT-1 $q\bar{q}$ background, the data events in the $M_{\rm BC}$
sideband region, defined as $M_{\rm BC}\in(2.200,2.265)$ GeV/$c^{2}$, are
used. Since $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ background is present in
the sideband region, it is estimated using inclusive simulation samples and
subtracted from the total sideband yield to determine the $q\bar{q}$
background in the sideband. The $q\bar{q}$ background in the signal region is
extrapolated from the yield in the sideband using information from the
simulation. In Cat-2, the simulated $q\bar{q}$ samples are used.

Due to fake photons in the EMC, there exists a contamination from mismatched
$\pi^{0}$ candidates (denoted as $\pi^{0}$ mismatch). It has a wide shape and
will not contribute to the narrow resonances in the distributions of
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$.
The $\pi^{0}$ mismatch background is estimated using simulation samples.
Events containing showers where the angular separation between the true and
reconstructed $\pi^{0}$ directions is greater than $20^{\circ}$ are considered
$\pi^{0}$ mismatch background, and the background is normalized according to
the branching fractions of $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ and
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$ in the distributions of
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$.

##  VI Branching fraction measurement

For the two-body decay $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$, a simultaneous
fit is performed by combining the Cat-1 and Cat-2 distributions of
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$.
The signal shapes are modeled with the simulation shapes convolved with a
Gaussian function representing the resolution difference between data and
simulation samples. The background shapes are described by third-order
polynomial functions, and the background yields are floating. The fitted
curves with distributions of
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
are shown in Fig. 4. The signal yields are $30\pm 6$ and $20\pm 5$ events for
Cat-1 and Cat-2, respectively. The DT efficiencies in Cat-1 and Cat-2 are
summarized in Table 3. From Eq. 1, the branching fraction is determined to be
$(5.99\pm 1.04)\times 10^{-3}$, where the uncertainty is statistical. It is
consistent with the previous result [48]. The significance, at $6.9\sigma$, is
determined by evaluating the difference in likelihood values between fits that
include and exclude the signal component, while considering the change in the
number of degrees of freedom.

For the three-body decay $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$, the
simultaneous fit shares the same branching fraction and takes into account the
different detection efficiencies of the individual processes. The fit
projections of
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
are shown in Fig. 5, and the total signal yields of
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ are $57\pm 9$ and $40\pm 7$ events for
Cat-1 and Cat-2, respectively.

The DT efficiencies of Cat-1 and Cat-2 for
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$ are summarized in Table 4. The
simulation samples use a flat phase space model, but intermediate resonances
could affect the momentum and angular distributions of the final state
particles, which would affect DT efficiencies. Therefore, the simulation
samples are reweighted to match data. The two variables,
${M}\left({K^{+}}{\pi^{0}}\right)$ and
${M_{\mathrm{recoil}}}\left({\Lambda_{c}^{\mathrm{ST}}{\pi^{0}}}\right)$, are
selected for the reweighting procedure using a 6$\times$6 binning scheme with
uniformly spaced bins. The overall efficiency is 3.44% before the procedure
and 3.61% after.

Using the results of fits to
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
and correcting for the differences in efficiency, the contributions to the
three-body decays $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$ are calculated.
After subtracting them, the yields of the three-body decay
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ are $48\pm 9$ and $31\pm 7$ for Cat-1
and Cat-2, respectively. Using Eq. 1 and the corrected efficiency, the
branching fraction is determined to be $(7.79\pm 1.46)\times 10^{-3}$, where
the uncertainty is statistical, and the statistical significance is
$8.6\sigma$.

Fig. 4: The fit projections of (a)
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
and
(b)${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}}\right)$
distributions. The black points with error bars are data. The black line is
the sum of all the components in the fit. The blue-shaded histograms are the
$\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ backgrounds. The green-shaded
histograms are from the data sideband (in Cat-1) or hadron sample (in Cat-2).

Fig. 5: Fit projections of (a)
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
and (b)
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
distributions. The black points with error bars are data. The black line is
the sum of all the components in the fit. The blue-shaded histograms are the
$\Lambda^{+}_{c}\bar{\Lambda}_{c}^{-}$ background. The green-shaded histograms
are from the data sideband (in Cat-1) or hadron sample (in Cat-2). The purple
line represents the signal shape of the three-body decay
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$. The dashed blue line represents the
one-dimensional histogram PDF that describes the background distributions of
${M_{\mathrm{recoil}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$,
which are modeled with an ARGUS function.

Fig. 6: Fit projections on (a)
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
distribution and (b) Likelihood distribution over the branching fractions of
$\Lambda^{+}_{c}\to nK^{+}\pi^{0}$.

Fig. 7: Fit projections on (a)
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$,
(b)
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
distributions and (c) Likelihood distributions over the branching fractions of
$\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$. The black curve denotes the fit
result with systematic uncertainty. The blue arrows show the results
corresponding to 90% confidence level.

Fig. 8: Fit projections on (a)
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$,
(b)
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
distributions and (c) Likelihood distributions over the branching fractions of
$\Lambda^{+}_{c}\to\Lambda K^{+}\pi^{0}$.

For the three-body decays $\Lambda^{+}_{c}\to nK^{+}\pi^{0}$,
$\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$ and $\Lambda K^{+}\pi^{0}$,
simultaneous fits are made to the
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
distributions as shown in Figs. 6, 7 and 8. For the three-body decay
$\Lambda^{+}_{c}\to nK^{+}\pi^{0}$, the signal yield is $10\pm 6$ events and
DT efficiencies in Cat-1 are summarized in Table 5. The upper limit on the
branching fraction of this decay at the 90$\%$ confidence level is
${\mathcal{B}}(\Lambda^{+}_{c}\to nK^{+}\pi^{0})<7.1\times 10^{-4}$. For the
three-body decays $\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$ and $\Lambda
K^{+}\pi^{0}$, the signal yields of $\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$
are $7\pm 5$ and $6\pm 4$ events for Cat-1 and Cat-2, respectively. The signal
yields of $\Lambda^{+}_{c}\to\Lambda K^{+}\pi^{0}$ are $10\pm 4$ and $10\pm 4$
events for Cat-1 and Cat-2, respectively. The DT efficiencies in are
summarized in Tables 6 and 7, and the upper limits are
${\mathcal{B}}(\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0})<1.8\times 10^{-3}$
and ${\mathcal{B}}(\Lambda^{+}_{c}\to\Lambda K^{+}\pi^{0})<2.0\times 10^{-3}$,
respectively. The black solid curves in Figs. 6, 7 and 8 show the resulting
likelihood distributions for these three decays.

##  VII Systematic uncertainties

Table 8: Systematic uncertainties.  Sources | $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ | $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ | $\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$ | $\Lambda^{+}_{c}\to\Lambda K^{+}\pi^{0}$ | $\Lambda^{+}_{c}\to nK^{+}\pi^{0}$
---|---|---|---|---|---
Cat-1 | Cat-2 | Cat-1 | Cat-2 | Cat-1 | Cat-2 | Cat-1 | Cat-2 | Cat-1
No extra charged track | 2.20
$K^{+}$ tracking | 1.00
$K^{+}$ PID | 1.00
$\pi^{0}$ reconstruction | 1.00
ST yield | 0.40
Statistics | 0.14 | 0.13 | 0.14 | 0.14 | 0.14 | 0.14 | 0.14 | 0.14 | 0.14
Background PDF | 1.17 | 1.17 | 2.05 | 2.05 | 2.41 | 2.41 | 1.37 | 1.37 | 2.06
$\Lambda$ reconstruction | — | 2.70 | — | 2.70 | — | 2.70 | — | 2.70 | —
$\pi^{0}$ selection | — | — | 1.00 | 1.00 | — | — | — | — | —
$\pi^{0}$ mismatch | 2.00 | — | 5.13 | — | — | — | — | — |
Reweighting | — | — | 4.95 | 2.43 | — | — | — | — | —
Sum | 3.66 | 3.12 | 8.00 | 4.41 | 3.72 | 3.77 | 3.15 | 3.20 | 3.50

The systematic uncertainties for the branching fraction measurements include
those associated with the ST yields ($N^{\rm ST}_{i}$), detection efficiencies
of the ST $\bar{\Lambda}_{c}^{-}$ ($\epsilon^{\rm ST}_{i}$), detection
efficiencies of the DT events ($\epsilon^{\rm DT}_{i}$) and signal yield
($N_{\mathrm{sig}}$). Since Eq. 1 contains a ratio of ST and DT efficiencies,
any systematic uncertainty on the tag side is canceled to first order. Each of
them is evaluated relative to the measured branching fraction.

The numbers of charged tracks are required to be only one (Cat-1) or three
(Cat-2) without any extra charged tracks. This difference between data and MC
simulation for this selection is studied with control sample of
$\Lambda^{+}_{c}\to pK^{-}\pi^{+}$ (the other $\bar{\Lambda}_{c}^{-}$ goes to
the 10 tag modes). The uncertainty on the requirement of the number of charged
tracks is assigned to be 2.2%, which is denoted as “No extra charged track” in
Table 8.

The tracking efficiencies for $K$ as a function of transverse momentum has
been studied with the process $J/\psi\to K^{0}_{S}K^{+}\pi^{-}\to
K\pi^{+}\pi^{-}\pi^{-}$. The efficiency differences between data and MC
simulation are both 1% for $K^{+}$ tracking and PID efficiencies, which are
taken as the systematic uncertainties [49].

The uncertainties of the background and fits of the distributions of
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
arise from the sideband range and background estimation. First, the
uncertainty for the data sideband and $q\bar{q}$ background estimation is
derived from the statistical uncertainty of the background estimate in the
$M_{\rm BC}$ sideband region and the variation of the sideband range. Second,
the background shape is changed from a polynomial function to an ARGUS
function. The differences between the new and nominal results are taken as the
systematic uncertainties.

The uncertainty due to the $\Lambda$ reconstruction efficiency, which is
estimated by a weighted root-mean-square of the statistical uncertainties for
different ($p$, $\cos\theta$) intervals, is assigned to be 0.6% using a sample
of $J/\psi\to\bar{p}K^{+}\Lambda$ decays [50].

The uncertainty due to the $\pi^{0}$ selection with the minimum kinematic-fit
$\chi^{2}$ is studied with control sample of
$\Lambda^{+}_{c}\to\Sigma^{+}\omega$ and
$\Lambda^{+}_{c}\to\Sigma^{+}\pi^{0}$. The difference between data and MC
simulation is assigned as 1%.

The uncertainty due to the $\pi^{0}$ mismatch component in the fit is
evaluated using simulation samples with an alternative $\pi^{0}$ matching
approach, where the $\pi^{0}$ candidate closest to the true $\pi^{0}$ is
chosen to be the reconstructed $\pi^{0}$ candidate. The fit is performed on
the simulation samples, using both the nominal and alternative $\pi^{0}$
matching, and the difference in the fitted branching fraction between them is
taken as the systematic uncertainty.

The uncertainty in reweighting the $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$
simulation samples is derived using different 2D variables and different
choices of 2D binning, for instance 6 bins $\times$ 6 bins to 7 bins $\times$
7 bins. The uncertainty is determined in a similar manner as the uncertainty
from the background shape.

The total systematic uncertainty for the two strategies is obtained by taking
the quadratic sum of the individual values. Some systematic uncertainties are
the same between two strategies, e.g. tracking and PID of the charged kaon, so
they are assumed to be fully correlated in the combination. Other systematic
uncertainties are independent between two strategies, e.g. $\Lambda$
reconstruction, background estimation in the fits on the distributions of
${M_{\mathrm{recoil}}^{\mathrm{Cat-1}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$
and
${M_{\mathrm{recoil}}^{\mathrm{Cat-2}}}\left({\Lambda_{c}^{\mathrm{ST}}{K^{+}}{\pi^{0}}}\right)$,
and they are treated without any correlation in the combination. The different
systematic sources are listed in Table 8, where the two categories have been
separated explicitly.

Table 9: The comparison between the measurement and theoretical predictions
($\times{10^{-3}}$).

| $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ | $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}$ | $\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}$ | $\Lambda^{+}_{c}\to\Lambda K^{+}\pi^{0}$ | $\Lambda^{+}_{c}\to nK^{+}\pi^{0}$
---|---|---|---|---|---
This measurement | $5.99\pm 1.04\pm 0.29$ | $7.79\pm 1.46\pm 0.71$ | $<{1.8}$ | $<{2.0}$ | $<{0.71}$
K. K. Sharma et al . [23] | $-$ | $45\pm 8$ | ${1.2\pm 0.3}$ | ${4.5\pm 0.8}$ | $0.05\pm 0.005$
Jian-Yong Cen et al . [24] | $-$ | $32\pm 6$ | ${0.7\pm 0.2}$ | ${3.5\pm 0.6}$ | $0.05\pm 0.006$
$\mathcal{B}$(previous results) [48] | ${5.02\pm 0.99\pm 0.31}$ | $-$ | $-$ | $-$ | $-$

##  VIII Summary

With ${6.1}~{}\mathrm{fb}^{-1}{}$ of $e^{+}e^{-}{}$ collision data collected
at eleven CM energy points between 4.600 and 4.840 GeV with the BESIII
detector at BEPCII, the CF decays $\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$
and $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}{}$ are observed with significances
of 8.6$\sigma$ and 6.9$\sigma$, respectively. The branching fraction of
$\Lambda^{+}_{c}\to\Xi^{0}K^{+}\pi^{0}{}$ is measured to be $(7.79\pm 1.46\pm
0.71)\times 10^{-3}$, where the first and second uncertainties are statistical
and systematic, respectively. It is smaller than the theoretical predictions
$(4.5\pm 0.8)\times{10^{-2}}$ [23] and $3.2\pm 0.6\times{10^{-2}}$ [24].
Comparisons of theory and experiment are shown in Table 9. The branching
fraction of $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}{}$ is $(5.99\pm 1.04\pm
0.29)\times 10^{-3}$, which is consistent with the previous result $(5.02\pm
0.99\pm 0.31)\times 10^{-3}$ [48].

The upper limits on the branching fractions at the 90$\%$ confidence level of
the SCS or DCS decays $\Lambda^{+}_{c}\to nK^{+}\pi^{0}$,
$\Sigma^{0}K^{+}\pi^{0}$ and $\Lambda K^{+}\pi^{0}$ are $7.1\times 10^{-4}$,
$1.8\times 10^{-3}$ and $2.0\times 10^{-3}$, respectively. The upper limit of
the branching fraction of $\Lambda^{+}_{c}\to\Lambda K^{+}\pi^{0}{}$ is
incompatible with the theory predictions [23, 24]. The upper limits of the
branching fractions of $\Lambda^{+}_{c}\to\Sigma^{0}K^{+}\pi^{0}{}$ and
$\Lambda^{+}_{c}\to nK^{+}\pi^{0}$are consistent with the theoretical
predictions [23, 24]. These results are essential for the understanding of the
dynamics in the charmed baryon decays.

##  IX Acknowledgement

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing
center 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, 12221005, 12225509, 12235017, 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 diFisica 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; Olle Engkvist Foundation under Contract No. 200-0605;
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.

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