This is the accepted manuscript made available via CHORUS. The article has been
published as:
Measurements of Absolute Hadronic Branching Fractions of
the Λ_{c}^{+} Baryon
M. Ablikim et al. (BESIII Collaboration)
Phys. Rev. Lett. 116, 052001 — Published 5 February 2016
DOI:
10.1103/PhysRevLett.116.052001
Measurements of absolute hadronic branching fractions of the
Λ
cbaryon
M. Ablikim1, M. N. Achasov9,e, X. C. Ai1, O. Albayrak5, M. Albrecht4, D. J. Ambrose44, A. Amoroso49A,49C, F. F. An1,
2
Q. An46,a, J. Z. Bai1, R. Baldini Ferroli20A, Y. Ban31, D. W. Bennett19, J. V. Bennett5, M. Bertani20A, D. Bettoni21A,
3
J. M. Bian43, F. Bianchi49A,49C, E. Boger23,c, I. Boyko23, R. A. Briere5, H. Cai51, X. Cai1,a, O. Cakir40A, A. Calcaterra20A,
4
G. F. Cao1, S. A. Cetin40B
, J. F. Chang1,a, G. Chelkov23,c,d, G. Chen1, H. S. Chen1, H. Y. Chen2, J. C. Chen1,
5
M. L. Chen1,a, S. J. Chen29, X. Chen1,a, X. R. Chen26, Y. B. Chen1,a, H. P. Cheng17, X. K. Chu31, G. Cibinetto21A,
6
H. L. Dai1,a, J. P. Dai34, A. Dbeyssi14, D. Dedovich23, Z. Y. Deng1, A. Denig22, I. Denysenko23, M. Destefanis49A,49C,
7
F. De Mori49A,49C, Y. Ding27, C. Dong30, J. Dong1,a, L. Y. Dong1, M. Y. Dong1,a, Z. L. Dou29, S. X. Du53, P. F. Duan1,
8
E. E. Eren40B, J. Z. Fan39, J. Fang1,a, S. S. Fang1, X. Fang46,a, Y. Fang1, R. Farinelli21A,21B, L. Fava49B,49C, O. Fedorov23,
9
F. Feldbauer22, G. Felici20A, C. Q. Feng46,a, E. Fioravanti21A, M. Fritsch14,22, C. D. Fu1, Q. Gao1, X. L. Gao46,a,
10
X. Y. Gao2, Y. Gao39, Z. Gao46,a, I. Garzia21A, K. Goetzen10, L. Gong30, W. X. Gong1,a, W. Gradl22, M. Greco49A,49C,
11
M. H. Gu1,a, Y. T. Gu12, Y. H. Guan1, A. Q. Guo1, L. B. Guo28, Y. Guo1, Y. P. Guo22, Z. Haddadi25, A. Hafner22, S. Han51,
12
X. Q. Hao15, F. A. Harris42, K. L. He1, T. Held4, Y. K. Heng1,a, Z. L. Hou1, C. Hu28, H. M. Hu1, J. F. Hu49A,49C, T. Hu1,a,
13
Y. Hu1, G. S. Huang46,a, J. S. Huang15, X. T. Huang33, Y. Huang29, T. Hussain48, Q. Ji1, Q. P. Ji30, X. B. Ji1, X. L. Ji1,a,
14
L. W. Jiang51, X. S. Jiang1,a
, X. Y. Jiang30, J. B. Jiao33, Z. Jiao17, D. P. Jin1,a
, S. Jin1, T. Johansson50, A. Julin43,
15
N. Kalantar-Nayestanaki25, X. L. Kang1, X. S. Kang30, M. Kavatsyuk25, B. C. Ke5, P. Kiese22, R. Kliemt14, B. Kloss22,
16
O. B. Kolcu40B,h, B. Kopf4, M. Kornicer42, W. Kuehn24, A. Kupsc50, J. S. Lange24,a, M. Lara19, P. Larin14, C. Leng49C,
17
C. Li50, Cheng Li46,a
, D. M. Li53, F. Li1,a
, F. Y. Li31, G. Li1, H. B. Li1, J. C. Li1, Jin Li32, K. Li13, K. Li33, Lei Li3,
18
P. R. Li41, Q. Y. Li33, T. Li33, W. D. Li1, W. G. Li1, X. L. Li33, X. M. Li12, X. N. Li1,a, X. Q. Li30, Z. B. Li38, H. Liang46,a,
19
Y. F. Liang36, Y. T. Liang24, G. R. Liao11, D. X. Lin14, B. J. Liu1, C. X. Liu1, D. Liu46,a, F. H. Liu35, Fang Liu1, Feng Liu6,
20
H. B. Liu12, H. H. Liu1, H. H. Liu16, H. M. Liu1, J. Liu1, J. B. Liu46,a, J. P. Liu51, J. Y. Liu1, K. Liu39, K. Y. Liu27,
21
L. D. Liu31, P. L. Liu1,a, Q. Liu41, S. B. Liu46,a, X. Liu26, Y. B. Liu30, Z. A. Liu1,a, Zhiqing Liu22, H. Loehner25,
22
X. C. Lou1,a,g, H. J. Lu17, J. G. Lu1,a, Y. Lu1, Y. P. Lu1,a, C. L. Luo28, M. X. Luo52, T. Luo42, X. L. Luo1,a, X. R. Lyu41,
23
F. C. Ma27, H. L. Ma1, L. L. Ma33, Q. M. Ma1, T. Ma1, X. N. Ma30, X. Y. Ma1,a, Y. M. Ma33, F. E. Maas14,
24
M. Maggiora49A,49C, Y. J. Mao31, Z. P. Mao1, S. Marcello49A,49C, J. G. Messchendorp25, J. Min1,a, R. E. Mitchell19,
25
X. H. Mo1,a, Y. J. Mo6, C. Morales Morales14, N. Yu. Muchnoi9,e, H. Muramatsu43, Y. Nefedov23, F. Nerling14,
26
I. B. Nikolaev9,e, Z. Ning1,a, S. Nisar8, S. L. Niu1,a, X. Y. Niu1, S. L. Olsen32, Q. Ouyang1,a, S. Pacetti20B, Y. Pan46,a,
27
P. Patteri20A, M. Pelizaeus4, H. P. Peng46,a, K. Peters10, J. Pettersson50, J. L. Ping28, R. G. Ping1, R. Poling43, V. Prasad1,
28
H. R. Qi2, M. Qi29, S. Qian1,a, C. F. Qiao41, L. Q. Qin33, N. Qin51, X. S. Qin1, Z. H. Qin1,a, J. F. Qiu1, K. H. Rashid48,
29
C. F. Redmer22, M. Ripka22, G. Rong1, Ch. Rosner14, X. D. Ruan12, V. Santoro21A, A. Sarantsev23,f, M. Savri´e21B,
30
K. Schoenning50, S. Schumann22, W. Shan31, M. Shao46,a, C. P. Shen2, P. X. Shen30, X. Y. Shen1, H. Y. Sheng1,
31
W. M. Song1, X. Y. Song1, S. Sosio49A,49C, S. Spataro49A,49C, G. X. Sun1, J. F. Sun15, S. S. Sun1, Y. J. Sun46,a, Y. Z. Sun1,
32
Z. J. Sun1,a, Z. T. Sun19, C. J. Tang36, X. Tang1, I. Tapan40C, E. H. Thorndike44, M. Tiemens25, M. Ullrich24, I. Uman40D,
33
G. S. Varner42, B. Wang30, B. L. Wang41, D. Wang31, D. Y. Wang31, K. Wang1,a, L. L. Wang1, L. S. Wang1, M. Wang33,
34
P. Wang1, P. L. Wang1, S. G. Wang31, W. Wang1,a, W. P. Wang46,a, X. F. Wang39, Y. D. Wang14, Y. F. Wang1,a,
35
Y. Q. Wang22, Z. Wang1,a, Z. G. Wang1,a, Z. H. Wang46,a, Z. Y. Wang1, T. Weber22, D. H. Wei11, J. B. Wei31,
36
P. Weidenkaff22, S. P. Wen1, U. Wiedner4, M. Wolke50, L. H. Wu1, Z. Wu1,a, L. Xia46,a, L. G. Xia39, Y. Xia18, D. Xiao1,
37
H. Xiao47, Z. J. Xiao28, Y. G. Xie1,a, Q. L. Xiu1,a, G. F. Xu1, L. Xu1, Q. J. Xu13, Q. N. Xu41, X. P. Xu37, L. Yan49A,49C,
38
W. B. Yan46,a, W. C. Yan46,a, Y. H. Yan18, H. J. Yang34, H. X. Yang1, L. Yang51, Y. X. Yang11, M. Ye1,a, M. H. Ye7,
39
J. H. Yin1, B. X. Yu1,a, C. X. Yu30, J. S. Yu26, C. Z. Yuan1, W. L. Yuan29, Y. Yuan1, A. Yuncu40B,b, A. A. Zafar48,
40
A. Zallo20A, Y. Zeng18, Z. Zeng46,a, B. X. Zhang1, B. Y. Zhang1,a, C. Zhang29, C. C. Zhang1, D. H. Zhang1, H. H. Zhang38,
41
H. Y. Zhang1,a, J. J. Zhang1, J. L. Zhang1, J. Q. Zhang1, J. W. Zhang1,a, J. Y. Zhang1, J. Z. Zhang1, K. Zhang1, L. Zhang1,
42
X. Y. Zhang33, Y. Zhang1, Y. H. Zhang1,a, Y. N. Zhang41, Y. T. Zhang46,a, Yu Zhang41, Z. H. Zhang6, Z. P. Zhang46,
43
Z. Y. Zhang51, G. Zhao1, J. W. Zhao1,a
, J. Y. Zhao1, J. Z. Zhao1,a
, Lei Zhao46,a, Ling Zhao1, M. G. Zhao30, Q. Zhao1,
44
Q. W. Zhao1, S. J. Zhao53, T. C. Zhao1, Y. B. Zhao1,a, Z. G. Zhao46,a, A. Zhemchugov23,c, B. Zheng47, J. P. Zheng1,a,
45
W. J. Zheng33, Y. H. Zheng41, B. Zhong28, L. Zhou1,a, X. Zhou51, X. K. Zhou46,a, X. R. Zhou46,a, X. Y. Zhou1, K. Zhu1,
46
K. J. Zhu1,a, S. Zhu1, S. H. Zhu45, X. L. Zhu39, Y. C. Zhu46,a
, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1,a
, L. Zotti49A,49C, 47 B. S. Zou1, J. H. Zou1 48 (BESIII Collaboration) 49
1 Institute of High Energy Physics, Beijing 100049, People’s Republic of China
50
2 Beihang University, Beijing 100191, People’s Republic of China
51
3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China
52
4 Bochum Ruhr-University, D-44780 Bochum, Germany
53
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
54
6 Central China Normal University, Wuhan 430079, People’s Republic of China
55
7 China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
56
8 COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
57
9 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
58
10GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
59
11 Guangxi Normal University, Guilin 541004, People’s Republic of China
60
12 GuangXi University, Nanning 530004, People’s Republic of China
2
13 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
62
14 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
63
15 Henan Normal University, Xinxiang 453007, People’s Republic of China
64
16 Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
65
17Huangshan College, Huangshan 245000, People’s Republic of China
66
18Hunan University, Changsha 410082, People’s Republic of China
67
19 Indiana University, Bloomington, Indiana 47405, USA
68
20(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia,
69
Italy
70
21 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
71
22Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
72
23 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
73
24 Justus Liebig University Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
74
25 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
75
26Lanzhou University, Lanzhou 730000, People’s Republic of China
76
27Liaoning University, Shenyang 110036, People’s Republic of China
77
28 Nanjing Normal University, Nanjing 210023, People’s Republic of China
78
29 Nanjing University, Nanjing 210093, People’s Republic of China
79
30Nankai University, Tianjin 300071, People’s Republic of China
80
31 Peking University, Beijing 100871, People’s Republic of China
81
32Seoul National University, Seoul, 151-747 Korea
82
33Shandong University, Jinan 250100, People’s Republic of China
83
34Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
84
35 Shanxi University, Taiyuan 030006, People’s Republic of China
85
36 Sichuan University, Chengdu 610064, People’s Republic of China
86
37 Soochow University, Suzhou 215006, People’s Republic of China
87
38Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
88
39Tsinghua University, Beijing 100084, People’s Republic of China
89
40(A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey;
90
(C)Uludag University, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey
91
41 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
92
42 University of Hawaii, Honolulu, Hawaii 96822, USA
93
43University of Minnesota, Minneapolis, Minnesota 55455, USA
94
44University of Rochester, Rochester, New York 14627, USA
95
45 University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China
96
46 University of Science and Technology of China, Hefei 230026, People’s Republic of China
97
47 University of South China, Hengyang 421001, People’s Republic of China
98
48 University of the Punjab, Lahore-54590, Pakistan
99
49 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN,
100
I-10125, Turin, Italy
101
50 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
102
51Wuhan University, Wuhan 430072, People’s Republic of China
103
52Zhejiang University, Hangzhou 310027, People’s Republic of China
104
53Zhengzhou University, Zhengzhou 450001, People’s Republic of China
105
a Also at State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of
106
China
107
bAlso at Bogazici University, 34342 Istanbul, Turkey
108
c Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
109
dAlso at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia
110
e Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
111
f Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
112
g Also at University of Texas at Dallas, Richardson, Texas 75083, USA
113
hAlso at Istanbul Arel University, 34295 Istanbul, Turkey
114
1
115
1
116
We report the first measurement of absolute hadronic branching fractions of Λ+
c baryon at the
117
Λ+
cΛ−c production threshold, in the 30 years since the Λ+c discovery. In total, twelve Cabibbo-favored
118
Λ+
c hadronic decay modes are analyzed with a double-tag technique, based on a sample of 567 pb−1
119
of e+
e− collisions at√s = 4.599 GeV recorded with the BESIII detector. A global least-squares
fitter is utilized to improve the measured precision. Among the measurements for twelve Λ+ c decay
121
modes, the branching fraction for Λ+
c → pK−π+ is determined to be (5.84 ± 0.27 ± 0.23)%, where
122
the first uncertainty is statistical and the second is systematic. In addition, the measurements of
123
the branching fractions of the other eleven Cabibbo-favored hadronic decay modes are significantly
124
improved.
125
PACS numbers: 14.20.Lq, 13.30.Eg, 13.66.Bc
126
Charmed baryon decays provide crucial information 127
for the study of both strong and weak interactions. 128
Hadronic decays of Λ+
c, the lightest charmed baryon
129
with quark configuration udc, provide important input 130
to Λb physics as Λb decays dominantly to Λ+c [1, 2].
131
Improved measurements of the Λ+
c hadronic decays can
132
be used to constrain fragmentation functions of charm 133
and bottom quarks by counting inclusive heavy flavor 134
baryons [3]. Most Λ+
c branching fractions (BF) have until
135
now been obtained by combining measurements of ratios 136
with a single branching fraction of the golden reference 137
mode Λ+
c → pK
−π+, thus introducing strong
correla-138
tions and compounding uncertainties. The experimen-139 tally averaged BF, B(Λ+ c → pK − π+) = (5.0 ± 1.3)% [4], 140
has large uncertainty due to the introduction of mod-141
el assumptions on Λ+
c inclusive decays in these
mea-142
surements [5]. Recently, the Belle experiment reported 143 B(Λ+ c → pK −π+) = (6.84 ± 0.24+0.21 −0.27)% with a preci-144
sion improved by a factor of 5 over previous results [6]. 145
However, most hadronic BFs still have poor precision [4]. 146
In this Letter, we present the first simultaneous determi-147
nation of multiple Λ+
c absolute BFs.
148
Our analysis is based on a data sample with an in-149
tegrated luminosity of 567 pb−1 [7] collected with the 150
BESIII detector [8] at the center-of-mass energy of√s = 151
4.599 GeV. At this energy, no additional hadrons accom-152
panying the Λ+ cΛ
−
c pairs are produced. Previously, the
153
Mark III collaboration measured D hadronic BFs at the 154
D ¯D threshold using a double-tag technique, which re-155
lies on fully reconstructing both D and ¯D decays [9]. 156
This technique obviates the need for knowledge of the 157
luminosity or the production cross section. We em-158
ploy a similar technique [10] using BESIII data near 159
the Λ+ cΛ
−
c threshold, resulting in improved
measure-160
ments of charge-averaged BFs for twelve Cabibbo-favored 161
hadronic decay modes: Λ+
c → pKS0, pK − π+, pK0 Sπ0, 162 pK0 Sπ+π − , pK− π+π0, Λπ+, Λπ+π0, Λπ+π− π+, Σ0π+, 163
Σ+π0, Σ+π+π−, and Σ+ω [11]. Throughout the Letter,
164
charge-conjugate modes are implicitly assumed, unless 165 otherwise stated. 166 To identify the Λ+ cΛ −
c signal candidates, we first
recon-167
struct one Λ−
c baryon [called a single tag (ST)] through
168
the final states of any of the twelve modes. For a given 169
decay mode j, the ST yield is determined to be 170
NjST= NΛ+
cΛ−c · Bj· εj, (1) where NΛ+
cΛ−c is the total number of produced Λ
+ cΛ
− c
171
pairs and εj is the corresponding efficiency. Then we
172
define double-tag (DT) events as those where the partner 173
Λ+
c recoiling against the Λ −
c is reconstructed in one of the
174
twelve modes. That is, in DT events, the Λ+ cΛ
−
c event is
175
fully reconstructed. The DT yield with Λ+c → i (signal
176 mode) and Λ− c → j (tagging mode) is 177 NijDT= NΛ+ cΛ−c · Bi· Bj· εij, (2) where εij is the efficiency for simultaneously
reconstruct-178
ing modes i and j. Hence, the ratio of the DT yield 179
(NDT
ij ) and ST yield (NjST) provides an absolute
mea-180 surement of the BF: 181 Bi= NDT ij NST j εj εij . (3)
Because of the large acceptance of the BESIII detec-182
tor and the low multiplicities of Λc hadronic decays,
183
εij ≈ εiεj. Hence, the ratio εj/εij is insensitive to most
184
systematic effects associated with the decay mode j, and 185
a signal BF Bi obtained using this procedure is
near-186
ly independent of the efficiency of the tagging mode. 187
Therefore, Bi is sensitive to the signal mode efficiency
188
(εi), whose uncertainties dominate the contribution to
189
the systematic error from the efficiencies. According to 190
Eqs. (1) and (2), the total DT yield with Λ+
c → i (signal
191
mode) over the twelve ST modes is determined to be 192 Ni−DT= NΛ+ cΛ−c · X j Bi· Bj· εDTi− , (4) where εDT i− ≡ P jP(Bj·εij)
jBj is the average DT efficiency 193
weighted over the twelve modes. 194
The BESIII detector is an approximately cylindrically 195
symmetric detector with 93% coverage of the solid an-196
gle around the e+e−
interaction point (IP). The com-197
ponents of the apparatus, ordered by distance from the 198
IP, are a 43-layer small-cell main drift chamber (MDC), 199
a time-of-flight (TOF) system based on plastic scintilla-200
tors with two layers in the barrel region and one layer 201
in the end-cap region, a 6240-cell CsI(Tl) crystal electro-202
magnetic calorimeter (EMC), a superconducting solenoid 203
magnet providing a 1.0 T magnetic field aligned with the 204
beam axis, and resistive-plate muon-counter layers inter-205
leaved with steel. The momentum resolution for charged 206
tracks in the MDC is 0.5% for a transverse momen-207
tum of 1 GeV/c. The energy resolution in the EMC is 208
2.5% in the barrel region and 5.0% in the end-cap re-209
gion for 1 GeV photons. Particle identification (PID) for 210
charged tracks combines measurements of the energy de-211
posit dE/dx in MDC and flight time in TOF and forms 212
likelihoods L(h) (h = p, K, π) for a hadron h hypothe-213
sis. More details about the BESIII detector are provided 214
elsewhere [8]. 215
4 High-statistics Monte Carlo (MC) simulations of e+e−
216
annihilations are used to understand backgrounds and to 217
estimate detection efficiencies. The simulation includes 218
the beam-energy spread and initial-state radiation (ISR) 219
of the e+e−
collisions as simulated with KKMC [12]. 220
The inclusive MC sample consists of Λ+ cΛ
−
c events, D(s)
221
production [13], ISR return to lower-mass ψ states, and 222
continuum processes e+e−
→ q¯q (q = u, d, s). Decay 223
modes as specified in the Particle Data Group summary 224
(PDG) [4] are modeled with EVTGEN [14]. For the MC 225
production of e+e−
→ Λ+ cΛ
−
c, the observed cross
sec-226
tions are taken into account, and phase-space-generated 227
Λ+
c decays are reweighted according to the observed
be-228
haviors in data. All final tracks and photons are fed into 229
a GEANT4-based [15] detector simulation package. 230
Charged tracks detected in the MDC must satisfy 231
| cos θ| < 0.93 (where θ is the polar angle with respect 232
to the beam direction) and have a distance of closest ap-233
proach to the IP of less than 10 cm along the beam axis 234
and less than 1 cm in the perpendicular plane, except for 235
those used for reconstructing K0
S and Λ decays. Tracks
236
are identified as protons when the PID determines this 237
hypothesis to have the greatest likelihood (L(p) > L(K) 238
and L(p) > L(π)), while charged kaons and pions are dis-239
criminated based on comparing the likelihoods for these 240
two hypotheses (L(K) > L(π) or L(π) > L(K)). 241
Showers in the EMC not associated with any charged 242
track are identified as photon candidates after fulfill-243
ing the following requirements. The deposited ener-244
gy is required to be larger than 25 MeV in the bar-245
rel (| cos θ| < 0.8) region and 50 MeV in the end-cap 246
region(0.84 < | cos θ| < 0.92). To suppress electronic 247
noise and showers unrelated to the event, the EMC time 248
deviation from the event start time is required to be with-249
in (0, 700) ns. The π0 candidates are reconstructed from
250
photon pairs, and their invariant masses are required to 251
satisfy 115 < M (γγ) < 150 MeV/c2. To improve
momen-252
tum resolution, a mass-constrained fit to the π0nominal
253
mass is applied to the photon pairs and the resulting 254
energy and momentum of the π0 are used for further
255
analysis. 256
Candidates for K0
S and Λ are formed by combining
257
two oppositely charged tracks into the final states π+π−
258
and pπ−. For these two tracks, their distances of
clos-259
est approaches to the IP must be within ±20 cm along 260
the beam direction. No distance constraints in the trans-261
verse plane are required. The charged π is not subject-262
ed to the PID requirements described above, while pro-263
ton PID is implemented in order to improve signal sig-264
nificance. The two daughter tracks are constrained to 265
originate from a common decay vertex by requiring the 266
χ2 of the vertex fit to be less than 100. Furthermore,
267
the decay vertex is required to be separated from the 268
IP by a distance of at least twice the fitted vertex res-269
olution. The fitted momenta of the π+π−
and pπ−
are 270
used in the further analysis. We impose requirements 271 487 < M (π+π− ) < 511 MeV/c2 and 1111 < M (pπ− ) < 272 1121 MeV/c2 to select K0
S and Λ signal candidates,
re-273 ) 2 c (GeV/ BC M 2c Events/2.0 MeV/ 2.26 2.28 2.3 1000 2000 3000 0 S pK 2.26 2.28 2.3 200 400 600 Λπ+ 2.26 2.28 2.3 100 200 300 0π0 S pK 2.26 2.28 2.3 100 200 0π+π -S pK 2.26 2.28 2.3 1000 2000 3000 -π+ pK 2.26 2.28 2.3 200 400 600 Λπ+π0 2.26 2.28 2.3 100 200 300 + π -π + π Λ 2.26 2.28 2.3 100 200 Σ+π0 2.26 2.28 2.3 1000 2000 3000 0 π + π -pK 2.26 2.28 2.3 200 400 600 Σ+π+π -2.26 2.28 2.3 100 200 300 + π 0 Σ 2.26 2.28 2.3 100 200 Σ+ω
FIG. 1. Fits to the ST MBC distributions in data for the
different decay modes. Points with error bars are data, solid lines are the sum of the fit functions, and dashed lines are the background shapes.
spectively, which are within about 3 standard deviations 274
from their nominal masses. To form Σ0, Σ+ and ω
can-275
didates, requirements on the invariant masses of 1179 < 276
M (Λγ) < 1203 MeV/c2, 1176 < M (pπ0) < 1200 MeV/c2
277
and 760 < M (π+π−π0) < 800 MeV/c2, are imposed.
278
When we reconstruct the decay modes pK0 Sπ0, 279 pK0 Sπ+π − and Σ+π+π−
, possible backgrounds from Λ → 280
pπ− in the final states are rejected by requiring M (pπ−)
281
outside the range (1110, 1120) MeV/c2. In addition, for
282
the mode pK0
Sπ0, candidate events within the range
283
1170 < M (pπ0) < 1200 MeV/c2are excluded to suppress
284
Σ+backgrounds. To remove K0
Scandidates in the modes
285
Λπ+π−π+, Σ+π0 and Σ+π+π−, masses of any pairs of
286
π+π− and π0π0 are not allowed to fall in the range (480,
287
520) MeV/c2.
288
To discriminate Λc candidates from background, two
289
variables reflecting energy and momentum conservation 290
are used. First, we calculate the energy difference, 291
∆E ≡ E − Ebeam, where E is the total measured
en-292
ergy of the Λc candidate and Ebeam is the average value
293
of the e+ and e−
beam energies. For each tag mode, 294
candidates are rejected if they fail the ∆E requirements 295
in Table I, which correspond to about 3 times the reso-296
lutions. Second, we define the beam-constrained mass 297
MBC of the Λc candidates by substituting the
beam-298
energy Ebeam for the energy E of the Λc candidates,
299
MBCc2 ≡ pEbeam2 − p2c2, where p is the measured Λc
300
momentum in the center-of-mass system of the e+e−
col-301
lision. Figure 1 shows the MBCdistributions for the ST
302
samples, where evident Λcsignals peak at the nominal Λc
303
mass position (2286.46±0.14) MeV/c2[4]. The MC
sim-304
ulations show that peaking backgrounds and cross feeds 305
among the twelve ST modes are negligible. 306
TABLE I. Requirement on ∆E, ST yields, DT yields and detection efficiencies for each of the decay modes. The un-certainties are statistical only. The quoted efficiencies do not include any subleading BFs.
Mode ∆E (MeV) NjST εj(%) Ni−DT εDTi−(%)
pKS0 (−20, 20) 1243 ± 37 55.9 97 ± 10 16.6 pK−π+ (−20, 20) 6308 ± 88 51.2 420 ± 22 14.1 pKS0π 0 (−30, 20) 558 ± 33 20.6 47 ± 8 6.8 pK0 Sπ+π− (−20, 20) 485 ± 29 21.4 34 ± 6 6.4 pK−π+π0 (−30, 20) 1849 ± 71 19.6 176 ± 14 7.6 Λπ+ (−20, 20) 706 ± 27 42.2 60 ± 8 12.7 Λπ+ π0 (−30, 20) 1497 ± 52 15.7 101 ± 13 5.4 Λπ+ π−π+ (−20, 20) 609 ± 31 12.0 53 ± 7 3.6 Σ0π+ (−20, 20) 522 ± 27 29.9 38 ± 6 9.9 Σ+ π0 (−50, 30) 309 ± 24 23.8 25 ± 5 8.0 Σ+ π+π− (−30, 20) 1156 ± 49 24.2 80 ± 9 8.1 Σ+ ω (−30, 20) 157 ± 22 9.9 13 ± 3 3.8
We perform unbinned extended maximum likelihood 307
fits to the MBC distributions to obtain the ST yields,
308
as illustrated in Fig. 1. In each fit, the signal shape 309
is derived from MC simulations of the signal ST modes 310
convolved with a Gaussian function to account for imper-311
fect modeling of the detector resolution and beam-energy 312
spread. The parameters of the Gaussians are allowed to 313
vary in the fits. Backgrounds for each mode are described 314
with the ARGUS function [16]. The resultant ST yields 315
in the signal region 2276 < MBC< 2300 MeV/c2and the
316
corresponding detection efficiencies are listed in Table I. 317
In the signal candidates of the twelve ST modes, a spe-318
cific mode Λ+
c → i is formed from the remaining tracks
319
and showers recoiling against the ST Λ−
c. We combine
320
the DT signal candidates over the twelve ST modes and 321
plot the distributions of the MBCvariable in Fig. 2. We
322
follow the same fit strategy as in the ST samples to es-323
timate the total DT yield NDT
i− in Eq. (4), except that
324
the DT signal shapes are derived from the DT signal MC 325
samples and convolved with the Gaussian function. The 326
parameters of the Gaussians are also allowed to vary in 327
the fits. The extracted DT yields are listed in Table I. 328
The 12 × 12 DT efficiencies εij are evaluated based on
329
the DT signal MC samples, in order to extract the BFs. 330
Main sources of systematic uncertainties related to the 331
measurement of BFs include tracking, PID, reconstruc-332
tion of intermediate states and intermediate BFs. For 333
the ∆E and MBC requirements, the uncertainties are
334
negligible, as we correct resolutions in MC samples to 335
accord with those in data. Uncertainties associated with 336
the efficiencies of the tracking and PID of charged par-337
ticles are estimated by studying a set of control sam-338
ples of e+e−
→ π+π+π−π−, K+K−π+π− and p¯pπ+π−
339
based on data taken at energies above √s = 4.0 GeV. 340
An uncertainty of 1.0% is assigned to each π0due to the
341
reconstruction efficiency. The uncertainties of detecting 342
K0
S and Λ are determined to be 1.2% and 2.5%,
respec-343 ) 2 c (GeV/ BC M 2c Events/1.0 MeV/ 2.26 2.28 2.3 50 100 pK0S 2.26 2.28 2.3 10 20 Λπ+ 2.26 2.28 2.3 5 10 15 20 0π0 S pK sig_mBC_3 2.26 2.28 2.3 5 10 15 -π + π 0 S pK 2.26 2.28 2.3 50 100 π+ -pK 2.26 2.28 2.3 10 20 Λπ+π0 2.26 2.28 2.3 5 10 15 20 + π -π + π Λ sig_mBC_62 2.26 2.28 2.3 5 10 15 0 π + Σ 2.26 2.28 2.3 50 100 pK-π+π0 2.26 2.28 2.3 10 20 Σ+π+π -2.26 2.28 2.3 5 10 15 20 + π 0 Σ sig_mBC_64 2.26 2.28 2.3 5 10 15 ω + Σ
FIG. 2. Fits to the DT MBCdistributions in data for different
signal modes. Points with error bars are data, solid lines are the sum of fit functions, and dashed lines are background shapes.
TABLE II. Summary of systematic uncertainties, in percent. The total numbers are derived from the least-squares fit, by taking into account correlations among different modes.
Source Tracking PID K0 S Λ π0 Signal MC Quoted Total model stat. BFs pK0 S 1.3 0.3 1.2 0.2 0.4 0.1 2.0 pK−π+ 2.5 3.2 0.2 3.9 pKS0π 0 1.1 1.6 1.2 1.0 1.0 0.5 0.1 2.7 pK0 Sπ+π− 2.8 5.4 1.2 0.5 0.5 0.1 5.9 pK−π+π0 3.3 5.8 1.0 2.0 0.5 6.6 Λπ+ 1.0 1.0 2.5 0.5 0.5 0.8 2.4 Λπ+π0 1.0 1.0 2.5 1.0 0.6 0.6 0.8 2.7 Λπ+ π−π+ 3.0 3.0 2.5 0.8 0.8 0.8 4.7 Σ0 π+ 1.0 1.0 2.5 1.7 0.7 0.8 2.4 Σ+π0 1.3 0.3 2.0 1.7 0.8 0.1 2.5 Σ+ π+π− 3.0 3.7 1.0 0.8 0.4 0.1 4.7 Σ+ ω 3.0 3.2 2.0 7.1 1.0 0.8 4.5
tively. Reweighting factors for the twelve signal models 344
are varied within their statistical uncertainties obtained 345
from the ST data samples. Deviations of the resultant ef-346
ficiencies are taken into account in systematic uncertain-347
ties. Systematic uncertainties due to limited statistics in 348
MC samples are included. Uncertainties on the BFs of 349
intermediate state decays from the PDG [4] are also in-350
cluded. A summary of systematic uncertainties are given 351
in Table II. 352
We use a least-squares fitter, which considers statistical 353
and systematic correlations among the different hadronic 354
modes, to obtain the BFs of the twelve Λ+
c decay modes
355
globally. Details of this fitter are discussed in Ref. [17]. In 356
the fitter, the precisions of the twelve BFs are constrained 357
to a common variable, NΛ+
cΛ−c, according to Eqs. (1) and 358
6
TABLE III. Comparison of the measured BFs in this work with previous results from PDG [4]. For our results, the first uncertainties are statistical and the second are systematic.
Mode This work (%) PDG (%)
pKS0 1.52 ± 0.08 ± 0.03 1.15 ± 0.30 pK−π+ 5.84 ± 0.27 ± 0.23 5.0 ± 1.3 pKS0π0 1.87 ± 0.13 ± 0.05 1.65 ± 0.50 pKS0π + π− 1.53 ± 0.11 ± 0.09 1.30 ± 0.35 pK−π+π0 4.53 ± 0.23 ± 0.30 3.4 ± 1.0 Λπ+ 1.24 ± 0.07 ± 0.03 1.07 ± 0.28 Λπ+ π0 7.01 ± 0.37 ± 0.19 3.6 ± 1.3 Λπ+ π−π+ 3.81 ± 0.24 ± 0.18 2.6 ± 0.7 Σ0 π+ 1.27 ± 0.08 ± 0.03 1.05 ± 0.28 Σ+π0 1.18 ± 0.10 ± 0.03 1.00 ± 0.34 Σ+π+π− 4.25 ± 0.24 ± 0.20 3.6 ± 1.0 Σ+ ω 1.56 ± 0.20 ± 0.07 2.7 ± 1.0
(4). In total, there are thirteen free parameters (twelve Bi
359
and NΛ+
cΛ−c) to be estimated. As peaking backgrounds in 360
ST modes and cross feeds among the twelve ST modes are 361
suppressed to a negligible level, they are not considered 362
in the fit. 363
The extracted BFs of Λ+
c are listed in Table III;
364
the correlation matrix is available in the Supplemental 365
Material [18]. The total number of Λ+cΛ − c pairs produced 366 is obtained to be NΛ+ cΛ−c = (105.9 ± 4.8 ± 0.5) × 10 3. The 367 goodness-of-fit is evaluated as χ2/ndf = 9.9/(24 − 13) = 368 0.9. 369
To summarize, twelve Cabibbo-favored Λ+
c decay rates
370
are measured by employing a double-tag technique, based 371
on a sample of threshold data at √s = 4.599 GeV col-372
lected at BESIII. This is the first absolute measurement 373
of the Λ+
c decay branching fractions at the Λ+cΛ − c
pro-374
duction threshold, in the 30 years since the Λ+
c
discov-375
ery. A comparison with previous results is presented in 376
Table III. For the golden mode B(pK−π+), our result is
377
consistent with that in PDG, but lower than Belle’s with 378
a significance of about 2σ. For the branching fractions of 379
the other modes, the precisions are improved by factors 380
of 3 ∼ 6 compared to the world average values. 381
The BESIII collaboration thanks the staff of BEPCII 382
and the IHEP computing center for their strong 383
support. This work is supported in part by 384
National Key Basic Research Program of China under 385
Contract No. 2015CB856700; National Natural Science 386
Foundation of China (NSFC) under Contracts Nos. 387
11125525, 11235011, 11275266, 11322544, 11335008, 388
11425524; the Chinese Academy of Sciences (CAS) 389
Large-Scale Scientific Facility Program; the CAS 390
Center for Excellence in Particle Physics (CCEPP); 391
the Collaborative Innovation Center for Particles and 392
Interactions (CICPI); Joint Large-Scale Scientific Facility 393
Funds of the NSFC and CAS under Contracts Nos. 394
11179007, U1232201, U1332201; CAS under Contracts 395
Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents 396
Program of CAS; National 1000 Talents Program of 397
China; INPAC and Shanghai Key Laboratory for 398
Particle Physics and Cosmology; German Research 399
Foundation DFG under Contract No. Collaborative 400
Research Center CRC-1044; Istituto Nazionale di Fisica 401
Nucleare, Italy; Koninklijke Nederlandse Akademie van 402
Wetenschappen (KNAW) under Contract No. 530-403
4CDP03; Ministry of Development of Turkey under 404
Contract No. DPT2006K-120470; National Natural 405
Science Foundation of China (NSFC) under Contracts 406
Nos. 11405046, U1332103; Russian Foundation for 407
Basic Research under Contract No. 14-07-91152; 408
The Swedish Resarch Council; U. S. Department of 409
Energy under Contracts Nos. DE-FG02-04ER41291, 410
DE-FG02-05ER41374, DE-SC0012069, DESC0010118; 411
U.S. National Science Foundation; University of 412
Groningen (RuG) and the Helmholtzzentrum fuer 413
Schwerionenforschung GmbH (GSI), Darmstadt; WCU 414
Program of National Research Foundation of Korea un-415
der Contract No. R32-2008-000-10155-0. 416
[1] J. L. Rosner, Phys. Rev. D 86, 014017 (2012).
417
[2] S. A. Dytman et al. [CLEO Collaboration], Phys. Rev.
418
D 66, 091101 (2002).
419
[3] P. Abreu et al. [DELPHI Collaboration], Eur. Phys. J. C
420
12, 225 (2000); R. Barate et al. [ALEPH Collaboration],
421
Eur. Phys. J. C 16, 597 (2000); R. Aaij et al. [LHCb
422
Collaboration], Phys. Rev. D 85, 032008 (2012).
423
[4] K.A. Olive et al. [Particle Data Group], Chin. Phys. C
424
38, 090001 (2014).
425
[5] D. E. Jaffe et al. [CLEO Collaboration], Phys. Rev. D
426
62, 072005 (2000).
427
[6] A. Zupanc et al. [Belle Collaboration], Phys. Rev. Lett.
428
113, 042002 (2014).
429
[7] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C
430
39, no. 9, 093001 (2015)
431
[8] M. Ablikim et al. [BESIII Collaboration], Nucl. Instrum.
432
Meth. A 614, 345 (2010).
433
[9] R.M.Baltrusaitis et al. [MARK-III Collaboration], Phys.
434
Rev. Lett. 56, 2140 (1986); J.Adler et al. [MARK-III
435
Collaboration], Phys. Rev. Lett. 60, 89 (1988).
436
[10] M. Ablikim et al. [BESIII Collaboration], Phys. Rev.
437
Lett. 115, 221805 (2015).
438
[11] The Σ+
π+π−π0 mode suffers from huge combinatorial
439
backgrounds. We restrict π+
π−π0 from ω decays and
440
only measure the resonant component Σ+ω, where the
441
non-resonant final states Σ+
π+π−π0are negligible.
442
[12] S. Jadach et al., Phys. Rev. D 63, 113009 (2001).
443
[13] N. Brambilla et al., Eur. Phys. J. C 71, 1534 (2011).
444
[14] D. J. Lange, Nucl. Instrum. Meth. A 462, 152 (2001);
445
R. G. Ping, Chin. Phys. C 32, 599 (2008).
446
[15] S. Agostinelli et al. [GEANT Collaboration], Nucl.
447
Instrum. Meth. A 506, 250 (2003); J. Allison et al., IEEE
Trans. Nucl. Sci. 53, 270 (2006).
449
[16] H.Albrecht et al. [ARGUS Collaboration], Phys. Rev.
450
Lett. B 241, 278 (1990).
451
[17] Y. Guan, X. R. Lu, Y. Zheng and Y. S. Zhu, Chin. Phys.
452
C 37, 106201 (2013).
453
[18] See Supplemental Material at [URL will be inserted by
454
publisher] for the correlation matrix of the fit.
