# Observation of the Singly Cabibbo-Suppressed Decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$

M. Ablikim1, M. N. Achasov5,b, P. Adlarson74, X. C. Ai80, R. Aliberti35, A.
Amoroso73A,73C, M. R. An39, Q. An70,57, Y. Bai56, O. Bakina36, I.
Balossino29A, Y. Ban46,g, V. Batozskaya1,44, K. Begzsuren32, N. Berger35, M.
Berlowski44, M. Bertani28A, D. Bettoni29A, F. Bianchi73A,73C, E.
Bianco73A,73C, A. Bortone73A,73C, I. Boyko36, R. A. Briere6, A. Brueggemann67,
H. Cai75, X. Cai1,57, A. Calcaterra28A, G. F. Cao1,62, N. Cao1,62, S. A.
Cetin61A, J. F. Chang1,57, T. T. Chang76, W. L. Chang1,62, G. R. Che43, G.
Chelkov36,a, C. Chen43, Chao Chen54, G. Chen1, H. S. Chen1,62, M. L.
Chen1,57,62, S. J. Chen42, S. M. Chen60, T. Chen1,62, X. R. Chen31,62, X. T.
Chen1,62, Y. B. Chen1,57, Y. Q. Chen34, Z. J. Chen25,h, W. S. Cheng73C, S. K.
Choi11A, X. Chu43, G. Cibinetto29A, S. C. Coen4, F. Cossio73C, J. J. Cui49, H.
L. Dai1,57, J. P. Dai78, A. Dbeyssi18, R. E. de Boer4, D. Dedovich36, Z. Y.
Deng1, A. Denig35, I. Denysenko36, M. Destefanis73A,73C, F. De Mori73A,73C, B.
Ding65,1, X. X. Ding46,g, Y. Ding40, Y. Ding34, J. Dong1,57, L. Y. Dong1,62,
M. Y. Dong1,57,62, X. Dong75, M. C. Du1, S. X. Du80, Z. H. Duan42, P.
Egorov36,a, Y.H. Y. Fan45, Y. L. Fan75, J. Fang1,57, S. S. Fang1,62, W. X.
Fang1, Y. Fang1, R. Farinelli29A, L. Fava73B,73C, F. Feldbauer4, G. Felici28A,
C. Q. Feng70,57, J. H. Feng58, K Fischer68, M. Fritsch4, C. Fritzsch67, C. D.
Fu1, J. L. Fu62, Y. W. Fu1, H. Gao62, Y. N. Gao46,g, Yang Gao70,57, S.
Garbolino73C, I. Garzia29A,29B, P. T. Ge75, Z. W. Ge42, C. Geng58, E. M.
Gersabeck66, A Gilman68, K. Goetzen14, L. Gong40, W. X. Gong1,57, W. Gradl35,
S. Gramigna29A,29B, M. Greco73A,73C, M. H. Gu1,57, C. Y Guan1,62, Z. L.
Guan22, A. Q. Guo31,62, L. B. Guo41, M. J. Guo49, R. P. Guo48, Y. P. Guo13,f,
A. Guskov36,a, T. T. Han49, W. Y. Han39, X. Q. Hao19, F. A. Harris64, K. K.
He54, K. L. He1,62, F. H H.. Heinsius4, C. H. Heinz35, Y. K. Heng1,57,62, C.
Herold59, T. Holtmann4, P. C. Hong13,f, G. Y. Hou1,62, X. T. Hou1,62, Y. R.
Hou62, Z. L. Hou1, H. M. Hu1,62, J. F. Hu55,i, T. Hu1,57,62, Y. Hu1, G. S.
Huang70,57, K. X. Huang58, L. Q. Huang31,62, X. T. Huang49, Y. P. Huang1, T.
Hussain72, N Hüsken27,35, W. Imoehl27, J. Jackson27, S. Jaeger4, S. Janchiv32,
J. H. Jeong11A, Q. Ji1, Q. P. Ji19, X. B. Ji1,62, X. L. Ji1,57, Y. Y. Ji49, X.
Q. Jia49, Z. K. Jia70,57, H. J. Jiang75, P. C. Jiang46,g, S. S. Jiang39, T. J.
Jiang16, X. S. Jiang1,57,62, Y. Jiang62, J. B. Jiao49, Z. Jiao23, S. Jin42, Y.
Jin65, M. Q. Jing1,62, T. Johansson74, X. K.1, S. Kabana33, N. Kalantar-
Nayestanaki63, X. L. Kang10, X. S. Kang40, M. Kavatsyuk63, B. C. Ke80, A.
Khoukaz67, R. Kiuchi1, R. Kliemt14, O. B. Kolcu61A, B. Kopf4, M. Kuessner4, A.
Kupsc44,74, W. Kühn37, J. J. Lane66, P. Larin18, A. Lavania26, L.
Lavezzi73A,73C, T. T. Lei70,57, Z. H. Lei70,57, H. Leithoff35, M. Lellmann35,
T. Lenz35, C. Li43, C. Li47, C. H. Li39, Cheng Li70,57, D. M. Li80, F. Li1,57,
G. Li1, H. Li70,57, H. B. Li1,62, H. J. Li19, H. N. Li55,i, Hui Li43, J. R.
Li60, J. S. Li58, J. W. Li49, K. L. Li19, Ke Li1, L. J Li1,62, L. K. Li1, Lei
Li3, M. H. Li43, P. R. Li38,j,k, Q. X. Li49, S. X. Li13, T. Li49, W. D.
Li1,62, W. G. Li1, X. H. Li70,57, X. L. Li49, Xiaoyu Li1,62, Y. G. Li46,g, Z.
J. Li58, C. Liang42, H. Liang70,57, H. Liang34, H. Liang1,62, Y. F. Liang53,
Y. T. Liang31,62, G. R. Liao15, L. Z. Liao49, Y. P. Liao1,62, J. Libby26, A.
Limphirat59, D. X. Lin31,62, T. Lin1, B. J. Liu1, B. X. Liu75, C. Liu34, C. X.
Liu1, F. H. Liu52, Fang Liu1, Feng Liu7, G. M. Liu55,i, H. Liu38,j,k, H. M.
Liu1,62, Huanhuan Liu1, Huihui Liu21, J. B. Liu70,57, J. L. Liu71, J. Y.
Liu1,62, K. Liu1, K. Y. Liu40, Ke Liu22, L. Liu70,57, L. C. Liu43, Lu Liu43,
M. H. Liu13,f, P. L. Liu1, Q. Liu62, S. B. Liu70,57, T. Liu13,f, W. K. Liu43,
W. M. Liu70,57, X. Liu38,j,k, Y. Liu38,j,k, Y. Liu80, Y. B. Liu43, Z. A.
Liu1,57,62, Z. Q. Liu49, X. C. Lou1,57,62, F. X. Lu58, H. J. Lu23, J. G.
Lu1,57, X. L. Lu1, Y. Lu8, Y. P. Lu1,57, Z. H. Lu1,62, C. L. Luo41, M. X.
Luo79, T. Luo13,f, X. L. Luo1,57, X. R. Lyu62, Y. F. Lyu43, F. C. Ma40, H. L.
Ma1, J. L. Ma1,62, L. L. Ma49, M. M. Ma1,62, Q. M. Ma1, R. Q. Ma1,62, R. T.
Ma62, X. Y. Ma1,57, Y. Ma46,g, Y. M. Ma31, F. E. Maas18, M. Maggiora73A,73C,
S. Malde68, Q. A. Malik72, A. Mangoni28B, Y. J. Mao46,g, Z. P. Mao1, S.
Marcello73A,73C, Z. X. Meng65, J. G. Messchendorp14,63, G. Mezzadri29A, H.
Miao1,62, T. J. Min42, R. E. Mitchell27, X. H. Mo1,57,62, N. Yu. Muchnoi5,b,
J. Muskalla35, Y. Nefedov36, F. Nerling18,d, I. B. Nikolaev5,b, Z. Ning1,57,
S. Nisar12,l, W. D. Niu54, Y. Niu 49, S. L. Olsen62, Q. Ouyang1,57,62, S.
Pacetti28B,28C, X. Pan54, Y. Pan56, A. Pathak34, P. Patteri28A, Y. P.
Pei70,57, M. Pelizaeus4, H. P. Peng70,57, K. Peters14,d, J. L. Ping41, R. G.
Ping1,62, S. Plura35, S. Pogodin36, V. Prasad33, F. Z. Qi1, H. Qi70,57, H. R.
Qi60, M. Qi42, T. Y. Qi13,f, S. Qian1,57, W. B. Qian62, C. F. Qiao62, J. J.
Qin71, L. Q. Qin15, X. P. Qin13,f, X. S. Qin49, Z. H. Qin1,57, J. F. Qiu1, S.
Q. Qu60, C. F. Redmer35, K. J. Ren39, A. Rivetti73C, M. Rolo73C, G. Rong1,62,
Ch. Rosner18, S. N. Ruan43, N. Salone44, A. Sarantsev36,c, Y. Schelhaas35, K.
Schoenning74, M. Scodeggio29A,29B, K. Y. Shan13,f, W. Shan24, X. Y. Shan70,57,
J. F. Shangguan54, L. G. Shao1,62, M. Shao70,57, C. P. Shen13,f, H. F.
Shen1,62, W. H. Shen62, X. Y. Shen1,62, B. A. Shi62, H. C. Shi70,57, J. L.
Shi13, J. Y. Shi1, Q. Q. Shi54, R. S. Shi1,62, X. Shi1,57, J. J. Song19, T. Z.
Song58, W. M. Song34,1, Y. J. Song13, Y. X. Song46,g, S. Sosio73A,73C, S.
Spataro73A,73C, F. Stieler35, Y. J. Su62, G. B. Sun75, G. X. Sun1, H. Sun62,
H. K. Sun1, J. F. Sun19, K. Sun60, L. Sun75, S. S. Sun1,62, T. Sun1,62, W. Y.
Sun34, Y. Sun10, Y. J. Sun70,57, Y. Z. Sun1, Z. T. Sun49, Y. X. Tan70,57, C.
J. Tang53, G. Y. Tang1, J. Tang58, Y. A. Tang75, L. Y Tao71, Q. T. Tao25,h, M.
Tat68, J. X. Teng70,57, V. Thoren74, W. H. Tian51, W. H. Tian58, Y. Tian31,62,
Z. F. Tian75, I. Uman61B, S. J. Wang 49, B. Wang1, B. L. Wang62, Bo Wang70,57,
C. W. Wang42, D. Y. Wang46,g, F. Wang71, H. J. Wang38,j,k, H. P. Wang1,62, J.
P. Wang 49, K. Wang1,57, L. L. Wang1, M. Wang49, Meng Wang1,62, S. Wang13,f,
S. Wang38,j,k, T. Wang13,f, T. J. Wang43, W. Wang58, W. Wang71, W. P.
Wang70,57, X. Wang46,g, X. F. Wang38,j,k, X. J. Wang39, X. L. Wang13,f, Y.
Wang60, Y. D. Wang45, Y. F. Wang1,57,62, Y. H. Wang47, Y. N. Wang45, Y. Q.
Wang1, Yaqian Wang17,1, Yi Wang60, Z. Wang1,57, Z. L. Wang71, Z. Y. Wang1,62,
Ziyi Wang62, D. Wei69, D. H. Wei15, F. Weidner67, S. P. Wen1, C. W. Wenzel4,
U. Wiedner4, G. Wilkinson68, M. Wolke74, L. Wollenberg4, C. Wu39, J. F.
Wu1,62, L. H. Wu1, L. J. Wu1,62, X. Wu13,f, X. H. Wu34, Y. Wu70, Y. H. Wu54,
Y. J. Wu31, Z. Wu1,57, L. Xia70,57, X. M. Xian39, T. Xiang46,g, D. Xiao38,j,k,
G. Y. Xiao42, S. Y. Xiao1, Y. L. Xiao13,f, Z. J. Xiao41, C. Xie42, X. H.
Xie46,g, Y. Xie49, Y. G. Xie1,57, Y. H. Xie7, Z. P. Xie70,57, T. Y. Xing1,62,
C. F. Xu1,62, C. J. Xu58, G. F. Xu1, H. Y. Xu65, Q. J. Xu16, Q. N. Xu30, W.
Xu1,62, W. L. Xu65, X. P. Xu54, Y. C. Xu77, Z. P. Xu42, Z. S. Xu62, F.
Yan13,f, L. Yan13,f, W. B. Yan70,57, W. C. Yan80, X. Q. Yan1, H. J. Yang50,e,
H. L. Yang34, H. X. Yang1, Tao Yang1, Y. Yang13,f, Y. F. Yang43, Y. X.
Yang1,62, Yifan Yang1,62, Z. W. Yang38,j,k, Z. P. Yao49, M. Ye1,57, M. H. Ye9,
J. H. Yin1, Z. Y. You58, B. X. Yu1,57,62, C. X. Yu43, G. Yu1,62, J. S. Yu25,h,
T. Yu71, X. D. Yu46,g, C. Z. Yuan1,62, L. Yuan2, S. C. Yuan1, X. Q. Yuan1, Y.
Yuan1,62, Z. Y. Yuan58, C. X. Yue39, A. A. Zafar72, F. R. Zeng49, X. Zeng13,f,
Y. Zeng25,h, Y. J. Zeng1,62, X. Y. Zhai34, Y. C. Zhai49, Y. H. Zhan58, A. Q.
Zhang1,62, B. L. Zhang1,62, B. X. Zhang1, D. H. Zhang43, G. Y. Zhang19, H.
Zhang70, H. H. Zhang34, H. H. Zhang58, H. Q. Zhang1,57,62, H. Y. Zhang1,57, J.
Zhang80, J. J. Zhang51, J. L. Zhang20, J. Q. Zhang41, J. W. Zhang1,57,62, J.
X. Zhang38,j,k, J. Y. Zhang1, J. Z. Zhang1,62, Jianyu Zhang62, Jiawei
Zhang1,62, L. M. Zhang60, L. Q. Zhang58, Lei Zhang42, P. Zhang1,62, Q. Y.
Zhang39,80, Shuihan Zhang1,62, Shulei Zhang25,h, X. D. Zhang45, X. M. Zhang1,
X. Y. Zhang49, Xuyan Zhang54, Y. Zhang71, Y. Zhang68, Y. T. Zhang80, Y. H.
Zhang1,57, Yan Zhang70,57, Yao Zhang1, Z. H. Zhang1, Z. L. Zhang34, Z. Y.
Zhang43, Z. Y. Zhang75, G. Zhao1, J. Zhao39, J. Y. Zhao1,62, J. Z. Zhao1,57,
Lei Zhao70,57, Ling Zhao1, M. G. Zhao43, S. J. Zhao80, Y. B. Zhao1,57, Y. X.
Zhao31,62, Z. G. Zhao70,57, A. Zhemchugov36,a, B. Zheng71, J. P. Zheng1,57, W.
J. Zheng1,62, Y. H. Zheng62, B. Zhong41, X. Zhong58, H. Zhou49, L. P.
Zhou1,62, X. Zhou75, X. K. Zhou7, X. R. Zhou70,57, X. Y. Zhou39, Y. Z.
Zhou13,f, J. Zhu43, K. Zhu1, K. J. Zhu1,57,62, L. Zhu34, L. X. Zhu62, S. H.
Zhu69, S. Q. Zhu42, T. J. Zhu13,f, W. J. Zhu13,f, Y. C. Zhu70,57, Z. A.
Zhu1,62, J. H. Zou1, J. Zu70,57 (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 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
17 Hebei University, Baoding 071002, People’s Republic of China
18 Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
19 Henan Normal University, Xinxiang 453007, People’s Republic of China
20 Henan University, Kaifeng 475004, People’s Republic of China
21 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
22 Henan University of Technology, Zhengzhou 450001, People’s Republic of
China
23 Huangshan College, Huangshan 245000, People’s Republic of China
24 Hunan Normal University, Changsha 410081, People’s Republic of China
25 Hunan University, Changsha 410082, People’s Republic of China
26 Indian Institute of Technology Madras, Chennai 600036, India
27 Indiana University, Bloomington, Indiana 47405, USA
28 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
29 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara,
Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
30 Inner Mongolia University, Hohhot 010021, People’s Republic of China
31 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
32 Institute of Physics and Technology, Peace Avenue 54B, Ulaanbaatar 13330,
Mongolia
33 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica
1000000, Chile
34 Jilin University, Changchun 130012, People’s Republic of China
35 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
36 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
37 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
38 Lanzhou University, Lanzhou 730000, People’s Republic of China
39 Liaoning Normal University, Dalian 116029, People’s Republic of China
40 Liaoning University, Shenyang 110036, People’s Republic of China
41 Nanjing Normal University, Nanjing 210023, People’s Republic of China
42 Nanjing University, Nanjing 210093, People’s Republic of China
43 Nankai University, Tianjin 300071, People’s Republic of China
44 National Centre for Nuclear Research, Warsaw 02-093, Poland
45 North China Electric Power University, Beijing 102206, People’s Republic of
China
46 Peking University, Beijing 100871, People’s Republic of China
47 Qufu Normal University, Qufu 273165, People’s Republic of China
48 Shandong Normal University, Jinan 250014, People’s Republic of China
49 Shandong University, Jinan 250100, People’s Republic of China
50 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
51 Shanxi Normal University, Linfen 041004, People’s Republic of China
52 Shanxi University, Taiyuan 030006, People’s Republic of China
53 Sichuan University, Chengdu 610064, People’s Republic of China
54 Soochow University, Suzhou 215006, People’s Republic of China
55 South China Normal University, Guangzhou 510006, People’s Republic of China
56 Southeast University, Nanjing 211100, People’s Republic of China
57 State Key Laboratory of Particle Detection and Electronics, Beijing 100049,
Hefei 230026, People’s Republic of China
58 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
59 Suranaree University of Technology, University Avenue 111, Nakhon
Ratchasima 30000, Thailand
60 Tsinghua University, Beijing 100084, People’s Republic of China
61 Turkish Accelerator Center Particle Factory Group, (A)Istinye University,
34010, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus,
99138, Mersin 10, Turkey
62 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
63 University of Groningen, NL-9747 AA Groningen, The Netherlands
64 University of Hawaii, Honolulu, Hawaii 96822, USA
65 University of Jinan, Jinan 250022, People’s Republic of China
66 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
67 University of Muenster, Wilhelm-Klemm-Strasse 9, 48149 Muenster, Germany
68 University of Oxford, Keble Road, Oxford OX13RH, United Kingdom
69 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
70 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
71 University of South China, Hengyang 421001, People’s Republic of China
72 University of the Punjab, Lahore-54590, Pakistan
73 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
74 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
75 Wuhan University, Wuhan 430072, People’s Republic of China
76 Xinyang Normal University, Xinyang 464000, 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 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

(May 9, 2023)

###### Abstract

The singly Cabibbo-suppressed decay $\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$
is observed for the first time with a statistical significance of $6.4\sigma$
by using 4.5 $\mathrm{fb}^{-1}$ of $e^{+}e^{-}$ collision data collected at
center-of-mass energies between 4.600 and 4.699 GeV with the BESIII detector
at BEPCII. The absolute branching fraction of
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ is measured to be $(3.8\pm 1.3_{\rm
stat}\pm 0.2_{\rm syst})\times 10^{-4}$ in a model-independent approach. This
is the first observation of a Cabibbo-suppressed $\Lambda^{+}_{c}$ decay
involving $\Sigma^{-}$ in the final state. The ratio of branching fractions
between $\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ and the Cabibbo-favored
decay $\Lambda^{+}_{c}{}\to\Sigma^{-}\pi^{+}\pi^{+}$ is calculated to be
$(0.4\pm 0.1)s_{c}^{2}$, where $s_{c}\equiv\sin\theta_{c}=0.2248$ with
$\theta_{c}$ the Cabibbo mixing angle. This ratio significantly deviates from
$1.0s_{c}^{2}$ and provides important information for the understanding of
nonfactorization contributions in $\Lambda^{+}_{c}$ decays.

Understanding the nonfactorization contribution is critically challenging for
advancing our knowledge of the hadronic weak decays of charmed baryons, as
$W$-exchange and inner $W$-emission are no longer subject to helicity and
color suppression PhysRevD.44.2799 . The evaluation of nonfactorizable terms
is far more difficult than that of factorizable contributions. In recent
years, SU(3) flavor (SU(3)F) symmetry has become popular and has been
demonstrated to be a powerful tool for predicting the hadronic weak decays of
charmed baryons PhysRevD.55.7067 ; PhysRevD.93.056008 ; Geng:2017JHEP .
Nevertheless, there are still some open points to be understood, e.g. the
ratio
$\mathcal{B}(\Xi_{c}^{0}\to\Xi^{-}K^{+})/\mathcal{B}(\Xi_{c}^{0}\to\Xi^{-}\pi^{+})\simeq(0.6\pm
0.2)s_{c}^{2}$ as quoted from the Particle Data Group (PDG) PDG:2022 ;
GENG2018593 , where $s_{c}\equiv\sin\theta_{c}=0.2248$ with $\theta_{c}$ the
Cabibbo mixing angle GENG2018593 , hints at a deviation from $1.0s_{c}^{2}$.
Under SU(3)F symmetry, such a deviation is explained with SU(3)F-symmetry
breaking effects arising from $m_{s}\gg m_{u,d}$. However, in
$\Lambda^{+}_{c}$ decays, there seems to be no such large effects, since the
ratios $\mathcal{B}(\Lambda^{+}_{c}\to\Lambda
K^{+})/\mathcal{B}(\Lambda^{+}_{c}\to\Lambda\pi^{+})\simeq(1.0\pm
0.1)s_{c}^{2}$ BESIII:lambdak  and
$\mathcal{B}(\Lambda^{+}_{c}\to\Sigma^{0}K^{+})/\mathcal{B}(\Lambda^{+}_{c}\to\Sigma^{0}\pi^{+})\simeq(0.8\pm
0.1)s_{c}^{2}$ PDG:2022  are consistent with $1.0s_{c}^{2}$. Furthermore, the
discrepancy between the experimental results and the theoretical prediction
for the branching fraction of the decay $\Lambda^{+}_{c}\to p\pi^{0}$ can not
be explained by this breaking effect, and is instead probably due to the
significant contribution of a nonfactorization component and the interference
between nonfactorization and factorization contributions Geng:2018 ; Geng:2019
. Extensive studies of charmed baryons in both experiment and theory have been
conducted for two-body decays Cheng:2015Front ; Cheng:2021qpd , while the
situation becomes much more complicated in three-body decays. The decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ is the simplest singly Cabibbo-
suppressed (CS) process with a $\Sigma^{-}$ directly in the final state. Here
the $W$-exchange and inner $W$-emission diagrams are expected to play the
dominant role, as shown in Fig. 1. Therefore, the observation of the CS decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ and the comparison with the Cabbibo
favored (CF) decay $\Lambda^{+}_{c}\to\Sigma^{-}\pi^{+}\pi^{+}$ will open a
new window for probing SU(3)F breaking effects and the nonfactorization
contribution in $\Lambda^{+}_{c}$ decays.

Figure 1: Feynman diagrams for the CS decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$: (a) internal $W$-emission, (b)
$W$-exchange.

Although several noteworthy achievements have been made by BESIII and Belle
since 2014 PhysRevLett.113.042002 ; PhysRevLett.129.231803 ;
PhysRevLett.116.052001 ; PhysRevLett.120.132001 , such as the significant
improvements in the measurement of the branching fraction of the golden
channel $\Lambda^{+}_{c}\to pK^{-}\pi^{+}$, the improved measurement of the
semi-leptonic decay $\Lambda^{+}_{c}\to\Lambda e^{+}\nu$, and the cross-
section measurements for the process
$e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$, results on CS
$\Lambda^{+}_{c}$ decays, which are driven by both factorizable and
nonfactorizable contributions, are still limited by the available data
PDG:2022 . Additionally, few results on channels containing a neutron have
been reported due to the challenge of identifying neutron signals in
detectors. In 2022, BESIII observed the decay $\Lambda^{+}_{c}\to n\pi^{+}$
BESIII:npi , which is the first CS $\Lambda^{+}_{c}$ decay to be discovered
with a neutron in the final state. However, the measured branching fraction
$\mathcal{B}(\Lambda^{+}_{c}\to n\pi^{+})=(6.6\pm 1.3)\times 10^{-4}$ differs
from the majority of the theoretical predictions Sharma:1997 ; Lu:2016 ;
Uppal:1994 ; Cheng:2018 ; Geng:2018 ; Geng:2019 ; Zhao:2020 , which motivates
further efforts in both experiment and theory to further understand the
nonfactorization contribution. According to recent constraints provided by the
reported branching fraction of the inclusive decay $\Lambda^{+}_{c}\to n+X$
BESIII:nx , there is a large room to probe experimentally for decays with a
neutron in the final state, including the $\Lambda^{+}_{c}$ decays to
$\Sigma^{-}$, as $\Sigma^{-}\to n\pi^{-}$ almost saturates the branching
fraction. At present, CS processes involving the lighter baryons ($p$
PhysRevLett.117.232002 ; JHEP03(2018)043 , $n$ BESIII:nx , $\Lambda$
PhysRevD.75.052002 ; BESIII:lambdak ) or $\Sigma^{+/0}$ hyperon
PhysRevD.75.052002 ; ABE200233 ) from $\Lambda^{+}_{c}$ decays have already
been confirmed and studied extensively in experiment. However, no CS decays
with a $\Sigma^{-}$ have been observed. With the threshold data samples of
$\Lambda^{+}_{c}$-pair production around 4.6 GeV, processes with $\Sigma^{-}$
can be investigated by reconstructing the neutron signal through its missing
energy under energy-momentum conservation at BESIII.

In this Letter, the first observation of the singly CS decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ is reported using 4.5
$\mathrm{fb}^{-1}$ of $e^{+}e^{-}$ collision data collected with the BESIII
detector at seven center-of-mass (c.m.) energies between 4.600 and 4.699 GeV.
Throughout this Letter, charge-conjugate modes are implicitly included.

Details about 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 Kaixuan:2022  of the BESIII detector. Signal MC samples of
$e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ with
$\bar{\Lambda}^{-}_{c}$ decaying into ten hadronic modes and $\Lambda^{+}_{c}$
to $\Sigma^{-}K^{+}\pi^{+}$, $\Xi^{-}K^{+}\pi^{+}$, and $\Xi^{*0}K^{+}$ are
used to determine the detection efficiencies, where the intermediate states
are required to be $\Sigma^{-}\to n\pi^{-}$ and $\Xi^{\ast
0}\to\Xi^{-}\pi^{+}$ with $\Xi^{-}$ subsequently decaying through any allowed
process. The ten hadronic decay modes are presented in Table 1. These samples
are generated for the individual c.m. energy by the generator kkmc
Jadach:2000ir  incorporating initial-state radiation effects and the beam-
energy spread. The inclusive MC samples, consisting of open-charm states,
radiative return to charmonium (like) $\psi$ states, 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 BFs taken from the Particle Data Group (PDG) PDG:2022 ,
when available, or otherwise estimated with lundcharm Chen:2000tv ;
PhysRevLett.31.061301 . Final-state radiation from charged final-state
particles is incorporated using photos Richter-Was:1992hxq .

The double-tag (DT) approach is employed to measure the absolute branching
fraction of $\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$. A data sample of
$\bar{\Lambda}^{-}_{c}$ baryons, referred to as the single-tag (ST) sample, is
reconstructed with ten exclusive hadronic decay modes, as the aforementioned
and listed in Table 1. The procedure of selecting the ST
$\bar{\Lambda}^{-}_{c}$ baryon decays is described in Refs. BESIII:npi ;
PhysRevD.106.072002 ; PhysRevD.106.072008 , where $105249\pm 386$ ST events
are reconstructed in data. Those events in which the signal decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ is reconstructed in the system
recoiling against the $\bar{\Lambda}^{-}_{c}$ candidates of the ST sample are
denoted as DT candidates.

The decay $\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ with $\Sigma^{-}\to
n\pi^{-}$ is searched for among the remaining tracks recoiling against the ST
$\bar{\Lambda}^{-}_{c}$ candidates. Particle identification (PID) is
implemented by combining measurements of the ionization energy loss in the
helium-based multilayer drift chamber (MDC) ($d$E/d$x$) and the flight time in
the time-of-flight system. Only three charged tracks, detected in the MDC and
reconstructed within a polar angle ($\theta$) range of $|\\!\cos\theta|<0.93$,
are allowed for a DT signal candidate event, where $\theta$ is defined with
respect to the $z$ axis, which is the symmetry axis of the MDC. Two of the
charged tracks, whose distances of closest approach to the interaction point
(IP) must be less than 10 cm along the $z$ axis ($|V_{z}|<10$ cm) and less
than 1 cm in the transverse plane ($|V_{r}|<1$ cm), are assigned to be $K^{+}$
and $\pi^{+}$, according to the PID probability. A vertex fit is performed to
the $K^{+}$ and $\pi^{+}$ candidates, and the momenta updated by the fit are
used in the subsequent analysis. Then, another charged track is assigned to be
the $\pi^{-}$ from the decay of the long-lived $\Sigma^{-}$ based on the PID
information, whose distance of the closest approach to the IP is required to
be within $\pm 20$ cm along the $z$ axis ($|V_{z}|<20$ cm). To suppress
background events containing other long-lived particles in the final state,
the candidate events are further required to have no extra charged tracks with
$|\\!\cos\theta|<0.93$, $|V_{r}|<1$ cm and $|V_{z}|<20$ cm.

To suppress the continuum hadron background (denoted as $q\bar{q}$ hereafter),
the recoiling mass against the ST $\bar{\Lambda}^{-}_{c}$ in the center-of-
mass frame, defined as

$\displaystyle M_{\rm
rec}(\bar{\Lambda}^{-}_{c})=\sqrt{(2E_{\mathrm{beam}}-E_{\bar{\Lambda}^{-}_{c}})^{2}/c^{4}-|\vec{p}_{\bar{\Lambda}^{-}_{c}}|^{2}/c^{2}},$
(1)

is required to fall inside the range (2.275, 2.310) GeV/$c^{2}$, where
$E_{\mathrm{beam}}$ is the beam energy, and $E_{\bar{\Lambda}^{-}_{c}}$ and
$\vec{p}_{\bar{\Lambda}^{-}_{c}}$ are the energy and momentum of the ST
$\bar{\Lambda}^{-}_{c}$, respectively. To remove the peaking background due to
the process $\Lambda^{+}_{c}\to\Sigma^{+}K^{+}\pi^{-}$, we exclude events with
$M_{\rm rec}({K^{+}}{\pi^{-}})\in(1.15,1.24)$ GeV/c2, where the recoiling mass
$M_{\rm rec}({K^{+}}{\pi^{-}})$ is calculated as:

$\displaystyle\left[M_{\rm
rec}(K^{+}\pi^{-})\right]^{2}=\left[E_{\mathrm{beam}}-\sum_{i}E_{i}\right]^{2}/c^{4}$
(2)
$\displaystyle-\left|\rho\cdot\vec{p}_{0}-\sum_{i}\vec{p}_{i}\right|^{2}/c^{2}.$

Here $E_{i}$ and $\vec{p}_{i}$ represent the energy and momentum,
respectively, of particle $i$ ($K^{+}$ or $\pi^{-}$),
$\rho=\sqrt{E_{\mathrm{beam}}^{2}/c^{2}-m_{\Lambda^{+}_{c}}^{2}c^{2}}$, and
$\hat{p}_{0}=-\vec{p}_{\bar{\Lambda}^{-}_{c}}/|\vec{p}_{\bar{\Lambda}^{-}_{c}}|$
is the unit direction opposite to the ST $\bar{\Lambda}^{-}_{c}$, where
$m_{\Lambda^{+}_{c}}$ is the known $\Lambda^{+}_{c}$ mass PDG:2022 .
Additionally, to suppress the potential background from $\Lambda^{+}_{c}\to
nK_{S}^{0}K^{+}$ decays, events satisfying $M(\pi^{+}\pi^{-})\in(0.48,0.52)$
$\mathrm{GeV}/c^{2}$ are vetoed where $M(\pi^{+}\pi^{-})$ is the invariant
mass of the $\pi^{+}\pi^{-}$ pair. The requirement $M_{\rm
rec}(K^{+}\pi^{+})>1.15$ $\mathrm{GeV}/c^{2}$ is imposed to suppress
backgrounds due to the $q\bar{q}$ and non-signal
$\Lambda^{+}_{c}$$\bar{\Lambda}^{-}_{c}$ processes. Here, the variable $M_{\rm
rec}(K^{+}\pi^{+})$ is the recoiling mass against the ST
$\bar{\Lambda}^{-}_{c}$, $K^{+}$ and $\pi^{+}$, and expressed as in Equation
2, but with the subscript $i$ now denoting the $K^{+}$ and $\pi^{+}$
particles. With all the above selection criteria, the $\Sigma^{-}$ signal is
reconstructed through the $M_{\rm rec}(K^{+}\pi^{+})$, while the neutron
signal, the daughter particle of the $\Sigma^{-}$ decay, is reconstructed
through $M_{\rm rec}(K^{+}\pi^{+}\pi^{-})$, which is the mass recoiling
against the ST $\bar{\Lambda}^{-}_{c}$, $K^{+}$, $\pi^{+}$ and $\pi^{-}$. This
recoil mass is as defined in Equation 2, with the subscript $i$ now
representing the $K^{+}$, $\pi^{+}$ and $\pi^{-}$ particles.

The two-dimensional (2D) distribution of $M_{\rm rec}(K^{+}\pi^{+})$ and
$M_{\rm rec}(K^{+}\pi^{+}\pi^{-})$ is shown in Fig. 2, where the events
containing both a $\Sigma^{-}$ and a neutron are clustered close to the left-
bottom corner, indicating the existence of the singly CS decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ with $\Sigma^{-}\to n\pi^{-}$. A
large number of events containing a $\Lambda$ and $\Xi^{-}$ appear in the
central region of the 2D distribution, which originate from the CF decay
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{-}$ with $\Xi^{-}\to\Lambda\pi^{-}$ and
$\Lambda$ decaying into neutral particles. These resonances are also observed
in the projected distributions of $M_{\rm rec}(K^{+}\pi^{+}\pi^{-})$ and
$M_{\rm rec}(K^{+}\pi^{+})$, as shown in Fig. 2 and 2, respectively.
Furthermore, by selecting the events in the $\Xi^{-}$ signal region $M_{\rm
rec}(K^{+}\pi^{+})\in(1.294,1.340)$ GeV/$c^{2}$, the $\Xi^{\ast 0}$ signal is
observed, originating from the process $\Lambda^{+}_{c}\to\Xi^{\ast 0}K^{+}$
with $\Xi^{\ast 0}\to\Xi^{-}\pi^{+}$, in the distribution of $M_{\rm
rec}(K^{+})$ as shown in Fig. 2. Here the variable $M_{\rm rec}(K^{+})$ is
also determined according to Equation 2, with the subscript $i$ labeling only
the $K^{+}$ particle.

Figure 2: The 2D distribution of $M_{\mathrm{rec}}(K^{+}\pi^{+})$ versus
$M_{\mathrm{rec}}(K^{+}\pi^{+}\pi^{-})$ (a), the distributions of
$M_{\mathrm{rec}}(K^{+}\pi^{+}\pi^{-})$ (b), $M_{\mathrm{rec}}(K^{+}\pi^{+})$
(c), and $M_{\mathrm{rec}}(K^{+})$ (d) of the accepted DT candidate events
from data for all energy points. The black points with error bars are data.
The curves represent the fit results, including the signal and background
components, respectively.

Potential backgrounds are classified into two categories: $q\bar{q}$
processes, and $e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ events
excluding signal contributions of $\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$,
$\Xi^{-}K^{+}\pi^{+}$, and $\Xi^{*0}K^{+}$ (referred to as
$\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ background hereafter) . The $q\bar{q}$
and $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ backgrounds are investigated with
the inclusive MC samples, which are normalized to the same integrated
luminosity as the data. No peaking background is observed in these samples.

The signal yields ($N_{\rm obs}$) of the
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ and $\Xi^{-}K^{+}\pi^{+}$ decays
are obtained by performing an unbinned maximum-likelihood fit to the 2D
distribution of $M_{\rm rec}(K^{+}\pi^{+})$ and $M_{\rm
rec}(K^{+}\pi^{+}\pi^{-})$, where the 2D signal shapes are modeled by the
simulated shapes for the two decays, respectively, convolved with the same
Gaussian function accounting for the resolution difference between data and MC
simulation. The 2D shapes of $q\bar{q}$ and
$\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ backgrounds are modeled as a whole by
the inclusive MC samples, where the individual cross sections are taken into
account, and their magnitude is a free parameter in the fit. Additionally, a
fit to the distribution of $M_{\rm rec}(K^{+})$ is performed simultaneously to
determine the yield of the decay $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$, where
its shape is also described from the simulation convolved with an individual
Gaussian function. Here, the $q\bar{q}$ and
$\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ backgrounds are described individually
by two third-order Chebyshev polynomials, whose shape parameters are obtained
from fits to the corresponding inclusive MC samples, and whose magnitudes are
determined from the fit to the data. In addition, the non-resonant three-body
decay $\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ has a smooth distribution in
$M_{\rm rec}(K^{+})$, and is also modeled by a third-order Chebyshev
polynomial with its shape parameters obtained from the MC simulation, and its
magnitude determined from the fit to data. The yield of
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ decays in the 2D fit is constrained to
be equal to the sum of those of the decay
$\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ and the three-body decay
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ in the fit to the distribution of
$M_{\rm rec}(K^{+})$. The yield of $q\bar{q}$ and
$\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ backgrounds in the region $M_{\rm
rec}(K^{+}\pi^{+})\in(1.294,1.340)$ $\rm{GeV}/c^{2}$ is fixed to the numbers
obtained from the fit to the distribution of $M_{\rm rec}(K^{+})$. The
resultant fit is depicted in Fig. 2, and the signal yields are determined to
be $12\pm 4$, $128\pm 13$, and $55\pm 8$ for
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$, $\Xi^{-}K^{+}\pi^{+}$ and
$\Xi^{*0}K^{+}$, respectively, where the uncertainties are statistical. The
statistical significance of the $\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$
signal is $6.4\sigma$, which is calculated from the change of the likelihood
values between fits with and without the signal component, accounting for the
change in the number of degrees of freedom.

Table 1: The DT detection efficiencies (%) for $\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$/$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$/$\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ for each ST mode at c.m. energies between $\sqrt{s}=$ 4.600 and 4.699 GeV. channel / $\sqrt{s}$ (GeV) | 4.600 | 4.612 | 4.628 | 4.641 | 4.661 | 4.682 | 4.699
---|---|---|---|---|---|---|---
$\bar{p}K^{+}\pi^{-}$ |  16.5$/$ |  8.5 $/$ | 8.2 |  15.6$/$ |  8.0 $/$ | 7.8 |  15.1$/$ |  7.7 $/$ | 7.6 |  15.0$/$ |  7.7 $/$ | 7.7 |  14.8$/$ |  7.4 $/$ | 7.6 |  14.1$/$ |  7.4 $/$ | 7.3 |  14.0$/$ |  7.2 $/$ | 7.3
$\bar{p}K_{S}^{0}$ |  18.7$/$ |  9.7 $/$ | 9.7 |  17.5$/$ |  9.0 $/$ | 9.1 |  16.9$/$ |  8.5 $/$ | 8.2 |  16.5$/$ |  8.5 $/$ | 8.6 |  15.7$/$ |  8.3 $/$ | 8.3 |  15.7$/$ |  8.0 $/$ | 8.1 |  15.1$/$ |  7.8 $/$ | 7.9
$\bar{p}K^{+}\pi^{-}\pi^{0}$ |  4.6$/$ |  1.9 $/$ | 1.9 |  4.2$/$ |  2.3 $/$ | 2.0 |  4.1$/$ |  2.2 $/$ | 2.0 |  4.4$/$ |  2.2 $/$ | 1.8 |  3.9$/$ |  2.1 $/$ | 1.7 |  4.3$/$ |  1.9 $/$ | 1.6 |  4.2$/$ |  2.1 $/$ | 1.7
$\bar{p}K_{S}^{0}\pi^{0}$ |  6.5$/$ |  3.3 $/$ | 3.3 |  6.0$/$ |  3.0 $/$ | 2.8 |  5.2$/$ |  2.7 $/$ | 2.6 |  5.3$/$ |  2.9 $/$ | 2.8 |  5.2$/$ |  2.8 $/$ | 2.7 |  5.3$/$ |  2.8 $/$ | 2.6 |  5.2$/$ |  2.6 $/$ | 2.5
$\bar{p}K_{S}^{0}\pi^{+}\pi^{-}$ |  6.2$/$ |  3.1 $/$ | 3.1 |  5.5$/$ |  2.8 $/$ | 2.8 |  5.2$/$ |  2.8 $/$ | 2.6 |  5.5$/$ |  2.7 $/$ | 2.7 |  5.2$/$ |  2.9 $/$ | 2.9 |  5.0$/$ |  2.6 $/$ | 2.6 |  4.9$/$ |  2.6 $/$ | 2.5
$\bar{\Lambda}\pi^{-}$ |  14.5$/$ |  7.1 $/$ | 7.1 |  12.7$/$ |  7.1 $/$ | 7.2 |  12.3$/$ |  6.4 $/$ | 6.6 |  12.1$/$ |  6.5 $/$ | 6.7 |  12.5$/$ |  6.0 $/$ | 6.0 |  11.0$/$ |  6.1 $/$ | 6.0 |  11.7$/$ |  5.4 $/$ | 5.5
$\bar{\Lambda}\pi^{-}\pi^{0}$ |  5.7$/$ |  2.8 $/$ | 2.8 |  5.1$/$ |  2.5 $/$ | 2.5 |  4.7$/$ |  2.4 $/$ | 2.4 |  4.7$/$ |  2.4 $/$ | 2.4 |  4.7$/$ |  2.3 $/$ | 1.8 |  4.5$/$ |  2.3 $/$ | 1.6 |  4.3$/$ |  2.1 $/$ | 1.8
$\bar{\Lambda}\pi^{+}\pi^{-}\pi^{-}$ |  4.0$/$ |  1.9 $/$ | 1.9 |  3.6$/$ |  1.9 $/$ | 1.8 |  3.7$/$ |  1.7 $/$ | 1.7 |  3.6$/$ |  1.7 $/$ | 1.6 |  3.3$/$ |  1.9 $/$ | 1.8 |  3.6$/$ |  1.8 $/$ | 1.6 |  3.6$/$ |  1.8 $/$ | 1.8
$\bar{\Sigma}^{0}\pi^{-}$ |  8.2$/$ |  4.0 $/$ | 4.0 |  7.3$/$ |  3.7 $/$ | 3.6 |  6.4$/$ |  3.2 $/$ | 3.1 |  7.1$/$ |  3.3 $/$ | 3.1 |  6.8$/$ |  3.1 $/$ | 3.2 |  6.8$/$ |  3.1 $/$ | 3.2 |  6.0$/$ |  2.9 $/$ | 2.7
$\bar{\Sigma}^{-}\pi^{+}\pi^{-}$ |  6.6$/$ |  3.3 $/$ | 3.3 |  6.3$/$ |  3.1 $/$ | 3.0 |  6.1$/$ |  3.1 $/$ | 3.0 |  5.4$/$ |  2.8 $/$ | 2.9 |  5.5$/$ |  2.9 $/$ | 2.6 |  5.5$/$ |  2.7 $/$ | 2.6 |  5.5$/$ |  2.6 $/$ | 2.6

The branching fractions ($\mathcal{B}$) are determined as

$\mathcal{B}=\frac{N_{\mathrm{obs}}}{\sum_{ij}N_{ij}^{\mathrm{ST}}\cdot(\epsilon_{ij}^{\mathrm{DT}}/\epsilon_{ij}^{\mathrm{ST}})},$
(3)

where the subscripts $i$ and $j$ label the ST modes and the data samples at
individual c.m. energies, respectively. The parameters $N_{ij}^{\mathrm{ST}}$,
$\epsilon_{ij}^{\mathrm{ST}}$ and $\epsilon_{ij}^{\mathrm{DT}}$ are the ST
yields, and ST and DT efficiencies, respectively. The detection efficiencies
$\epsilon_{ij}^{\mathrm{ST}}$ and $\epsilon_{ij}^{\mathrm{DT}}$ are estimated
from signal MC samples, where the key distributions of the ST modes have been
reweighted to agree with those of data. Since the decay
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ has two major components, i.e.
$\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ and the non-resonant three-body decay
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$, its detection efficiencies combine
the contributions from both these two components. To take into account
potential intermediate-resonance effects, the signal MC sample of
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ is reweighted to match the data
together with the $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ component, and the DT
efficiencies of the decay $\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ are derived.
The ST efficiencies can be found in Ref. BESIII:npi , whereas the DT
efficiencies are summarized in Table 1. The BFs are determined to be
$\mathcal{B}(\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+})=(3.8\pm 1.3\pm
0.2)\times 10^{-4}$,
$\mathcal{B}(\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+})=(7.76\pm 0.77\pm
0.54)\times 10^{-3}$, and
$\mathcal{B}(\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+})=(5.08\pm 0.78\pm
0.20)\times 10^{-3}$, where the first uncertainties are statistical and the
second are systematic.

Benefiting from the DT approach, the systematic uncertainties associated with
the ST selection efficiency cancel out in the branching-fraction measurements.
Thus, the systematic uncertainties for this measurements comprise those
associated with the ST yields, the $K^{+}$ and $\pi^{\pm}$ tracking and PID
efficiencies, the requirement on the number of tracks, the determination of
the DT signal yields, the branching fraction of the intermediate-state decays
and the statistical uncertainties from the signal MC samples.

The uncertainty in the total ST yields is 0.5% PhysRevD.106.072002 ;
PhysRevD.106.072008 , which arises from the statistical uncertainty and
fitting strategy for extracting these yields. The uncertainties associated
with the $K^{+}$ and $\pi^{\pm}$ tracking and PID efficiencies are both
assigned to be 1.0%, from studies performed with control samples of $J/\psi\to
K^{0}_{S}K^{\pm}\pi^{\mp}$, $K^{0}_{S}\to\pi^{+}\pi^{-}$ PhysRevD.99.012003
and $J/\psi\to\pi^{+}\pi^{-}\pi^{0}$ BESIII:jpsi  decays. The uncertainty due
to the no extra charged track requirement is 2.2%, which is assigned from
studies of a control sample of
$e^{+}e^{-}\to\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ decays, with
$\Lambda^{+}_{c}\to pK^{-}\pi^{+}$ and the $\bar{\Lambda}^{-}_{c}$ decaying
into the ten tagged decay modes. The uncertainties from the determination of
the DT yields are 2.0%, 2.0% and 2.2% for the decays
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$, $\Xi^{-}K^{+}\pi^{+}$, and
$\Xi^{*0}K^{+}$, respectively, including those from the modeling of $q\bar{q}$
and $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ backgrounds, which are estimated by
considering the uncertainty of the scale-factor for the $q\bar{q}$ estimation
and implementing alternative Chebyshev polynomial functions for the $q\bar{q}$
and $\Lambda^{+}_{c}\bar{\Lambda}^{-}_{c}$ backgrounds. The uncertainties in
the quoted branching fractions of $\Xi^{-}$ and $\Xi^{*0}$ are both 1.4% for
the decays $\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ and $\Xi^{*0}K^{+}$,
respectively. The uncertainty arising from the MC modeling for
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ is investigated by reweighting the MC
distribution to data, and comparing with the results obtained between the
original and reweighted samples. The resultant uncertainty in the MC modeling
is 5.9%. The uncertainties associated with the finite size of the signal MC
samples are 0.5%. Assuming that all the sources of bias are uncorrelated, the
total uncertainties are then taken to be the quadratic sum of the individual
contributions, which are 3.8%, 6.9% and 4.0% for
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$, $\Xi^{-}K^{+}\pi^{+}$, and
$\Xi^{*0}K^{+}$, respectively.

In summary, the singly Cabibbo-suppressed decay
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ is observed for the first time with
a statistical significance of $6.4\sigma$ by analyzing $e^{+}e^{-}$ collision
data samples corresponding to a total integrated luminosity of 4.5
$\mathrm{fb}^{-1}$ collected at c.m. energies between 4.600 and 4.699 GeV with
the BESIII detector. The branching fraction of
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ is measured to be $(3.8\pm 1.3_{\rm
stat}\pm 0.2_{\rm syst})\times 10^{-4}$ with a model-independent approach.
This is the first observation of the CS $\Lambda^{+}_{c}$ decay containing a
$\Sigma^{-}$ in the final state. The ratio of branching fractions between
$\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+}$ and the CF decay
$\Lambda^{+}_{c}{}\to\Sigma^{-}\pi^{+}\pi^{+}$ PDG:2022  is calculated to be
$(2.03\pm 0.73)\%\simeq(0.4\pm 0.1)s_{c}^{2}$, which is close to the ratio
$\mathcal{B}(\Xi_{c}^{0}\to\Xi^{-}K^{+})/\mathcal{B}(\Xi_{c}^{0}\to\Xi^{-}\pi^{+})$
and deviates significantly from $1.0s_{c}^{2}$. This result indicates the
nonfactorization components have an important role in three-body decays
involving a $\Sigma^{-}$ baryon. A prediction based on SU(3)F symmetry gave
$\mathcal{B}^{\rm pred}(\Lambda^{+}_{c}\to\Sigma^{-}K^{+}\pi^{+})=(3.3\pm
2.3)\times 10^{-4}$ PhysRevD.99.073003 , which has a larger uncertainty than
our measurement due to the limited sample sizes of the channels used as inputs
to the calculation. Our measurement provides direct information to improve the
understanding of the $\Lambda^{+}_{c}$ decay mechanisms. Meanwhile, the
branching fractions of CF decays $\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ and
$\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$ are measured to be $(7.76\pm 0.77_{\rm
stat}\pm 0.54_{\rm syst})\times 10^{-3}$ and $(5.08\pm 0.78_{\rm stat}\pm
0.20_{\rm syst})\times 10^{-3}$, respectively, which are consistent with
previous results PDG:2022 . The measured
$\Lambda^{+}_{c}\to\Xi^{-}K^{+}\pi^{+}$ is the sum of nonresonant three-body
decay and $\Lambda^{+}_{c}\to\Xi(1530)^{0}K^{+}$.

The BESIII collaboration thanks the staff of BEPCII, the IHEP computing center
and the supercomputing center of the University of Science and Technology of
China (USTC) for their strong support. Authors are grateful to Hai-Yang Cheng,
Fanrong Xu and Yu-Kuo Hsiao for enlightening discussions. 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. 11335008, 11625523, 11635010, 11735014, 11822506,
11835012, 11935015, 11935016, 11935018, 11961141012, 12022510, 12025502,
12035009, 12035013, 12061131003, 12005311, 11805086, 11705192, 11950410506;
the Fundamental Research Funds for the Central Universities, University of
Science and Technology of China, Sun Yat-sen University; 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 Contracts Nos. U1732263, U1832207, U1832103, U2032111;
CAS Key Research Program of Frontier Sciences under Contract No. QYZDJ-SSW-
SLH040; 100 Talents Program of CAS; China Postdoctoral Science Foundation
under Contracts Nos. 2019M662152, 2020T130636; INPAC and Shanghai Key
Laboratory for Particle Physics and Cosmology; ERC under Contract No. 758462;
European Union Horizon 2020 research and innovation programme under Contract
No. Marie Sklodowska-Curie grant agreement No 894790; German Research
Foundation DFG under Contracts Nos. 443159800, Collaborative Research Center
CRC 1044, FOR 2359, FOR 2359, GRK 214; Istituto Nazionale di Fisica Nucleare,
Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470;
National Science and Technology fund; Olle Engkvist Foundation under Contract
No. 200-0605; STFC (United Kingdom); The Knut and Alice Wallenberg Foundation
(Sweden) under Contract No. 2016.0157; The Royal Society, UK under Contracts
Nos. DH140054, DH160214; The Swedish Research Council; U. S. Department of
Energy under Contracts Nos. DE-FG02-05ER41374, DE-SC-0012069.

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