Study of $J/\psi$ and $\psi(3686)$ decay to $\Lambda\bar{\Lambda}$ and $\Sigma^0\bar{\Sigma}^0$ final states

0.3 MB·

by  BESIII Collaboration

Study of J/ψ and ψ(3686) decay to ΛΛ¯ and Σ0Σ¯0 final states
M. Ablikim1, M. N. Achasov9,e, S. Ahmed14, M. Albrecht4, A. Amoroso53A,53C, F. F. An1, Q. An50,a,
J. Z. Bai1, Y. Bai39, O. Bakina24, R. Baldini Ferroli20A, Y. Ban32, D. W. Bennett19, J. V. Bennett5,
N. Berger23, M. Bertani20A, D. Bettoni21A, J. M. Bian47, F. Bianchi53A,53C, E. Boger24,c, I. Boyko24,
R. A. Briere5, H. Cai55, X. Cai1,a, O. Cakir43A, A. Calcaterra20A, G. F. Cao1, S. A. Cetin43B, J. Chai53C,
J. F. Chang1,a, G. Chelkov24,c,d, G. Chen1, H. S. Chen1, J. C. Chen1, M. L. Chen1,a, S. J. Chen30,
X. R. Chen27, Y. B. Chen1,a, X. K. Chu32, G. Cibinetto21A, H. L. Dai1,a, J. P. Dai35,j, A. Dbeyssi14,
D. Dedovich24, Z. Y. Deng1, A. Denig23, I. Denysenko24, M. Destefanis53A,53C, F. De Mori53A,53C,
Y. Ding28, C. Dong31, J. Dong1,a, L. Y. Dong1, M. Y. Dong1,a, O. Dorjkhaidav22, Z. L. Dou30,
S. X. Du57, P. F. Duan1, J. Fang1,a, S. S. Fang1, X. Fang50,a, Y. Fang1, R. Farinelli21A,21B,
L. Fava53B,53C, S. Fegan23, F. Feldbauer23, G. Felici20A, C. Q. Feng50,a, E. Fioravanti21A, M. Fritsch14,23,
7 C. D. Fu1, Q. Gao1, X. L. Gao50,a, Y. Gao42, Y. G. Gao6, Z. Gao50,a, I. Garzia21A, K. Goetzen10,
1 L. Gong31, W. X. Gong1,a, W. Gradl23, M. Greco53A,53C, M. H. Gu1,a, S. Gu15, Y. T. Gu12, A. Q. Guo1,
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A T. Hussain52, W. Ikegami Andersson54, Q. Ji1, Q. P. Ji15, X. B. Ji1, X. L. Ji1,a, X. S. Jiang1,a,
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I. Tapan43C, M. Tiemens26, B. T. Tsednee22, I. Uman43D, G. S. Varner45, B. Wang1, B. L. Wang44,
D. Wang32, D. Y. Wang32, Dan Wang44, K. Wang1,a, L. L. Wang1, L. S. Wang1, M. Wang34, P. Wang1,
P. L. Wang1, W. P. Wang50,a, X. F. Wang42, Y. D. Wang14, Y. F. Wang1,a, Y. Q. Wang23, Z. Wang1,a,
Z. G. Wang1,a, Z. H. Wang50,a, Z. Y. Wang1, Z. Y. Wang1, T. Weber23, D. H. Wei11, P. Weidenkaff23,
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J. J. Xu1, L. Xu1, Q. J. Xu13, Q. N. Xu44, X. P. Xu38, L. Yan53A,53C, W. B. Yan50,a, W. C. Yan50,a,
Y. H. Yan18, H. J. Yang35,j, H. X. Yang1, L. Yang55, Y. H. Yang30, Y. X. Yang11, M. Ye1,a,
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D. H. Zhang1, H. H. Zhang41, H. Y. Zhang1,a, J. Zhang1, J. L. Zhang1, J. Q. Zhang1, J. W. Zhang1,a,
J. Y. Zhang1, J. Z. Zhang1, K. Zhang1, L. Zhang42, S. Q. Zhang31, X. Y. Zhang34, Y. Zhang1,
Y. Zhang1, Y. H. Zhang1,a, Y. T. Zhang50,a, Yu Zhang44, Z. H. Zhang6, Z. P. Zhang50, Z. Y. Zhang55,
G. Zhao1, J. W. Zhao1,a, J. Y. Zhao1, J. Z. Zhao1,a, Lei Zhao50,a, Ling Zhao1, M. G. Zhao31, Q. Zhao1,
S. J. Zhao57, T. C. Zhao1, Y. B. Zhao1,a, Z. G. Zhao50,a, A. Zhemchugov24,c, B. Zheng14,51,
J. P. Zheng1,a, W. J. Zheng34, Y. H. Zheng44, B. Zhong29, L. Zhou1,a, X. Zhou55, X. K. Zhou50,a,
X. R. Zhou50,a, X. Y. Zhou1, Y. X. Zhou12,a, J. Zhu41, K. Zhu1, K. J. Zhu1,a, S. Zhu1, S. H. Zhu49,
X. L. Zhu42, Y. C. Zhu50,a, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1,a, L. Zotti53A,53C, B. S. Zou1, J. H. Zou1
(BESIII Collaboration)
1 Institute of High Energy Physics, Beijing 100049, People’s Republic of China
2 Beihang University, Beijing 100191, People’s Republic of China
3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China
4 Bochum Ruhr-University, D-44780 Bochum, Germany
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6 Central China Normal University, Wuhan 430079, People’s Republic of China
7 China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
8 COMSATS Institute of Information Technology, Lahore,
Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
9 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
10 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
11 Guangxi Normal University, Guilin 541004, People’s Republic of China
12 Guangxi University, Nanning 530004, People’s Republic of China
13 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
14 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
15 Henan Normal University, Xinxiang 453007, People’s Republic of China
16 Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
17 Huangshan College, Huangshan 245000, People’s Republic of China
18 Hunan University, Changsha 410082, People’s Republic of China
19 Indiana University, Bloomington, Indiana 47405, USA
20 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati,
Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy
21 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
22 Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia
23 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
24 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
25 Justus-Liebig-Universitaet Giessen, II. Physikalisches
Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
26 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
27 Lanzhou University, Lanzhou 730000, People’s Republic of China
28 Liaoning University, Shenyang 110036, People’s Republic of China
29 Nanjing Normal University, Nanjing 210023, People’s Republic of China
30 Nanjing University, Nanjing 210093, People’s Republic of China
31 Nankai University, Tianjin 300071, People’s Republic of China
32 Peking University, Beijing 100871, People’s Republic of China
33 Seoul National University, Seoul, 151-747 Korea
34 Shandong University, Jinan 250100, People’s Republic of China
35 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
36 Shanxi University, Taiyuan 030006, People’s Republic of China
37 Sichuan University, Chengdu 610064, People’s Republic of China
38 Soochow University, Suzhou 215006, People’s Republic of China
3
39 Southeast University, Nanjing 211100, People’s Republic of China
40 State Key Laboratory of Particle Detection and Electronics,
Beijing 100049, Hefei 230026, People’s Republic of China
41 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
42 Tsinghua University, Beijing 100084, People’s Republic of China
43 (A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi
University, 34060 Eyup, Istanbul, Turkey; (C)Uludag University, 16059 Bursa,
Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey
44 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
45 University of Hawaii, Honolulu, Hawaii 96822, USA
46 University of Jinan, Jinan 250022, People’s Republic of China
47 University of Minnesota, Minneapolis, Minnesota 55455, USA
48 University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany
49 University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China
50 University of Science and Technology of China, Hefei 230026, People’s Republic of China
51 University of South China, Hengyang 421001, People’s Republic of China
52 University of the Punjab, Lahore-54590, Pakistan
53 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern
Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
54 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
55 Wuhan University, Wuhan 430072, People’s Republic of China
56 Zhejiang University, Hangzhou 310027, People’s Republic of China
57 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at State Key Laboratory of Particle Detection and
Electronics, Beijing 100049, Hefei 230026, People’s Republic of China
b Also at Bogazici University, 34342 Istanbul, Turkey
c Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
d Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia
e Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
f Also at the NRC ”Kurchatov Institute, PNPI, 188300, Gatchina, Russia
g Also at University of Texas at Dallas, Richardson, Texas 75083, USA
h Also at Istanbul Arel University, 34295 Istanbul, Turkey
i Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany
j 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
k Government College Women University, Sialkot - 51310. Punjab, Pakistan.
(Dated: April 5, 2017)
Using1310.6×106 J/ψ and447.9×106 ψ(3686) eventscollected withtheBESIIIdetectoratthe
BEPCII e+e− collider, the branching fractions and the angular distributions of J/ψ and ψ(3686)
decays to ΛΛ¯ and Σ0Σ¯0 final states are measured. The branching fractions are determined, with
much improved precision, to be 19.43±0.03±0.33, 11.64±0.04±0.23, 3.97±0.02±0.12 and
2.44±0.03±0.11 for J/ψ→ΛΛ¯, J/ψ→Σ0Σ¯0, ψ(3686)→ΛΛ¯ and ψ(3686)→Σ0Σ¯0, respectively.
Thepolarangulardistributionsofψ(3686)decaysaremeasuredforthefirsttime,whilethoseofJ/ψ
decays are measured with much improved precision. In addition, the ratios of branching fractions
B(ψ(3686)→ΛΛ¯) and B(ψ(3686)→Σ0Σ¯0) are determined totest the “12% rule”.
B(J/ψ→ΛΛ¯) B(J/ψ→Σ0Σ¯0)
PACSnumbers: 12.38.Qk,13.25.Gv,23.20.En
I. INTRODUCTION throughout the text), take place through annihila-
tionoftheconstituentcc¯quarkpairintoeitheravir-
Two-body baryonic decays of ψ mesons (ψ de- tualphotonorthreegluons,andtheyprovideagood
notesboththeJ/ψ andψ(3686)charmoniumstates laboratory for testing Quantum Chromodynamics
4
(QCD)intheperturbativeenergyregimeandstudy- ψ(3686)[19]eventscollectedwiththeBESIIIdetec-
ingthepropertiesofbaryons[1]. PerturbativeQCD tor at the BEPCII collider.
(pQCD) predicts that the ratio of branching frac-
tions between the J/ψ and ψ(3686)decaying into a
givenhadronicfinalstatesfollowsthe“12%rule”[2] II. BESIII DETECTOR AND DATA SET
Bψ(3686)→h Bψ(3686)→l+l−
Q= = ≈(12.4±0.4)%. The BESIII detector [20] at the double-ring
BJ/ψ→h BJ/ψ→l+l− Beijing Electron-PositronCollider (BEPCII) [21] is
(1)
designed for studies of physics in the τ-charm en-
The violation of this rule was first observed in the
ergy region [22]. The peak luminosity of BEPCII
decay of ψ into the final state ρπ, which is well is 1033 cm−2 s−1 at a beam current of 0.93 A.
knownasthe “ρπ puzzle”[3],andthe rulehasbeen
The BESIII detector has a geometrical acceptance
subsequently further tested in a wide variety of ex-
of 93% of 4π solid angle and consists of the fol-
perimental measurements. Reviews of the theoret-
lowing main components: (1) A small-celled, he-
ical and experimental results [5] conclude that the
lium based (40% CO and 60% C H ) main drift
2 3 8
currenttheoreticalunderstanding,especiallyforthe
chamber (MDC) with 43 layers,which has an aver-
ψ decaysintobaryon-antibaryonpairfinalstates,is
age single-wire resolution of 135 µm, a momentum
notmature. Thebranchingfractionsofψ decaysin-
resolution for 1 GeV/c charged particles in a 1 T
toBB¯ (BB¯ referstobothΛΛ¯ andΣ0Σ¯0 throughout magnetic field of 0.5% †, and a specific energy
the text) final states from different experiments [6–
loss (dE/dx) resolution of better than 6%. (2) An
15]andtheParticleDataGroup(PDG)[4]averages
electromagnetic calorimeter (EMC), which consists
are summarized in Table I. Obvious differences be-
of 6240 CsI (Tl) crystals arranged in a cylindrical
tween the different experiments are observed, and
shape (barrel)plus two end-caps. For1.0GeV pho-
the uncertainties are relatively large. Hence, high-
tons, the energy resolutionis 2.5% (5%) in the bar-
er precision measurements of the ψ decays into BB¯
rel (end-caps), and the position resolution is 6 mm
pairs are desirable to help in understanding the dy-
(9 mm) for the barrel (end-caps). (3) A time-of-
namics of ψ decay.
flight(TOF)system,whichisusedforparticleiden-
The angular distribution of the decays e+e− →
tification (PID). It is composed of a barrel made of
ψ →BB¯ can be expressed in form [1]
twolayers,eachconsistingof88piecesof5cmthick
and 2.4 m long plastic scintillators, as well as two
dN
∝1+αcos2θ, (2) end-capseachwith96fan-shaped5cmthickplastic
dcosθ
scintillators. The time resolution is 80 ps (110 ps)
where θ is the angle between the outgoing baryon in the barrel (end-caps), providing a K/π separa-
and the beam direction in the e+e− center-of-mass tionofmorethan2σ formomentaupto1.0GeV/c.
(c.m.) system, and α is a constant, which is re- (4) A muon chamber system, which is made of re-
lated to the decay properties. The equation is de- sistive plate chambers (RPCs) arranged in 9 layers
rived from the general helicity formalism [1], tak- (8 layers) in the barrel (end-caps) with ∼ 2 cm po-
ing into account the gluon spin, the quark distribu- sition resolution. It is incorporated into the return
tion amplitudes in e+e− → ψ → BB¯, and hadron iron yoke of the superconducting magnet.
helicity conservation. The α values in the decays Theoptimizationoftheeventselectionandthees-
J/ψ → BB¯ have been calculated with pQCD to timationsofthesignaldetectionefficiencyandback-
first-order[16]. It is believed that the masses ofthe ground are determined using Monte Carlo (MC)
baryon and quark must be taken into consideration simulations. The GEANT4-based [23] simulation
in the α calculation since a large violation of he- softwareBOOST[24], whichincludes the geometric
licity conservation is observed in ψ decays [16, 17]. andmaterialdescriptionoftheBESIIIdetector,the
Table II summarizesthe theoreticalpredictionsand detectorresponseanddigitizationmodels,aswellas
experimental α values for the decays J/ψ → BB¯. the tracking of the detector running conditions and
To date, the experimental α values for the decays performance, is used to generate MC samples. The
J/ψ → BB¯ have poor precision [6, 7, 11], and analysisisperformedintheframeworkoftheBESIII
the alpha values in the decay ψ(3686) → BB¯ have offlinesoftwaresystem(BOSS)[25]whichtakescare
not yet been measured. It is worth noting that ofthedetectorcalibration,eventreconstructionand
there is an indication that the α value in the de- data storage.
cay J/ψ →Σ0Σ¯0 is negative in Ref. [11].
In this paper, we report precise measurements
of the branching fractions and α values for the
decays ψ → BB¯, based on the data samples of † For the J/ψ data sample collected in 2012, the magnetic
(1310.6±7.0)×106J/ψ [18]and(447.9±2.9)×106 fieldwas0.9T.
5
TABLEI:ExperimentalmeasurementsandPDGaveragesforthebranchingfractionsofthedecayψ→BB¯(×10−4).
J/ψ→ΛΛ¯ ψ(3686)→ΛΛ¯ J/ψ→Σ0Σ¯0 ψ(3686)→Σ0Σ¯0
MARKIICollab. [6] 15.8±0.8±1.9 ... 15.8±1.6±2.5 ...
DM2 Collab. [7] 13.8±0.5±2.0 ... 10.6±0.4±2.3 ...
BES Collab. [8, 9] 10.8±0.6±2.4 1.8±0.2±0.3 ... 1.2±0.4±0.4
CLEO Collab. [10] ... 3.3±0.3±0.3 ... 2.6±0.4±0.4
BESII Collab. [11,12] 20.3±0.3±1.5 3.4±0.2±0.4 13.3±0.4±1.1 2.4±0.4±0.4
BaBar Collab. [13] 19.3±2.1±0.5 6.4±1.8±0.1 11.5±2.4±0.3 ...
S.Dobbs et al. [14] ... 3.8±0.1±0.3 ... 2.3±0.2±0.2
PDG[4] 16.1±1.5 3.6±0.2 12.9±0.9 2.3±0.2
polar angle of the track. Photons are reconstruct-
TABLE II: Theoretical predictions and experimental
ed from isolated showers in the EMC which are at
measurements of α for J/ψ→BB¯.
least 30 degrees away from the anti-proton and 10
degrees from other charged tracks. The energy de-
αJ/ψ→ΛΛ¯ αJ/ψ→Σ0Σ¯0 posited in the nearby TOF counters is included to
0.32 0.31 [16]
Theory improvethephotonreconstructionefficiencyanden-
0.51 0.43 [17]
0.72±0.36 0.70±1.10 [6] ergy resolution. Photon candidates are required to
Experiment 0.62±0.22 0.22±0.31 [7] be within the barrel region (|cosθ| < 0.8) of the
0.65±0.14 −0.22±0.19 [11] EMC with deposited energy of at least 25 MeV, or
within the end cap regions (0.86 < |cosθ| < 0.92)
with at least 50 MeV, where θ is the polar angle of
thephoton. Inordertosuppresselectronicnoiseand
energy deposits unrelated to the event, the timing
Generic inclusive MC samples, which include
1,225×106 J/ψ and 460×106 ψ(3686) events, are information t from the EMC for the photon candi-
date must be in coincidence with the collisionevent
usedtostudythepotentialbackgrounds. Theψ are
produced via e+e− →ψ processes by the generator (0≤t≤700 ns). At least two photons are required
in the analysis of ψ →Σ0Σ¯0 decays.
KKMC[26],whichincludesthebeamenergyspread
according to the measurement of BEPCII and the MC studies indicate that the proton and pion
effect of initial state radiation (ISR). The known fromΛdecayarewellseparatedkinematically since
decay modes are generated with BesEvtGen [27] the proton carries most of the energy. A charged
according to world average branching fraction val- track with momentum p > 0.5 GeV/c is assumed
ues [4]; the remaining unknown decay modes are to be a proton, while that with p < 0.5 GeV/c is
simulated using the LundCharm model [28]. To de- assumed to be a pion. The Λ (Λ¯) candidate is re-
termine the detection efficiencies, large ψ → BB¯ constructed with any pπ− (p¯π+) combination sat-
signal MC samples are generated for each process, isfying a secondary vertex fit [29] and having a de-
wheretheangulardistributionsofthebaryonsuseα caylengthlargerthan0.2cmtosuppressthenon-Λ
values obtainedin this analysis. The Λ andΣ0 par- (non-Λ¯) decays. The decay length is the distance
ticles are simulated in the Λ → pπ− and Σ0 → γΛ between its primary vertex and decay point to pπ−
decay modes. (p¯π+), where the primary vertex is approximated
bytheinteractionpointaveragedovermanyevents.
If more than one Λ (Λ¯) candidate is found, the one
with the largestdecay length is retained for further
III. EVENT SELECTION
analysis.
In the study of ψ → Σ0Σ¯0 decay, a variable
In this analysis, the four decay modes ψ → BB¯
are studied by fully reconstructing both B and ∆m = q(MΛγ1 −MΣ0)2+(MΛ¯γ2 −MΣ¯0)2 is de-
B¯, where the Λ(Λ¯) and Σ0(Σ¯0) candidates are re- fined. All possible photon pairs are combined with
constructed with the pπ−(p¯π+) and γΛ(γΛ¯) decay the selected Λ and Λ¯ candidates, and the γ and γ
1 2
modes, respectively. Therefore, the decays ψ →ΛΛ¯ candidates, which yield the smallest ∆ , are taken
m
and ψ → Σ0Σ¯0 have the final states pp¯π+π− and as the photons from the Σ0 and Σ¯0 decays, respec-
pp¯π+π−γγ, respectively. tively.
Events with at least four charged tracks with to- To suppress backgrounds, the ΛΛ¯ invariant
tal charge zero are selected. Each charged track mass, MΛΛ¯, is required to be within [3.05,3.15],
is required to have |cosθ| < 0.93, where θ is the [2.82,3.02], [3.63,3.75] and [3.34,3.61] GeV/c2 for
6
the J/ψ → ΛΛ¯, J/ψ → Σ0Σ¯0, ψ(3686) → ΛΛ¯ datasamplestakenatthec.m.energiesof3.08GeV
andψ(3686)→Σ0Σ¯0 decays,respectively. Herethe and3.65GeV,whichhaveintegratedluminositiesof
mass window requirements for the individual decay 30 pb−1 and 44 pb−1 [18, 19], respectively. By ap-
modesaredeterminedbyMCstudies. Inthedecays plying the same selectioncriteria, no event survives
ψ → ΛΛ¯, the Λ¯ candidate is required to have mass intheselectionofJ/ψ →BB¯,whileintheselection
satisfying|Mp¯π+−MΛ¯|<3σMΛ¯,whereMΛ¯ isthe Λ¯ of ψ(3686) → BB¯, only a few events survive, and
nominal mass, and σ is the corresponding mass no obvious peak is observed in the Λ/Σ0 mass re-
MΛ¯
resolution, which is 2.3 MeV/c2 (4.0 MeV/c2) for gion. The contaminationfrom the QCD continuum
the J/ψ (ψ(3686)) decay. In the decays ψ →Σ0Σ¯0, processescanbetreatedasnon-peakingbackground
the Σ¯0 candidate is required to have mass satisfy- when determining the signal yields.
ing |Mp¯π+γ −MΣ¯0| < 3σMΣ¯0, where MΣ¯0 is the Σ¯0
nominal mass, σ is the corresponding mass res-
MΣ¯0
olution, which is 4.3 MeV/c2 (6.0 MeV/c2) for the
J/ψ (ψ(3686)). Thecandidatesarefurtherrequired V. RESULTS
to satisfy θΣ0Σ¯0 >178◦ and θΣ0Σ¯0 >178.5◦ for the
J/ψ and ψ(3686) decays, respectively, where θΣ0Σ¯0 A. Branching fractions
is the opening angle between the reconstructed Σ0
and Σ¯0 candidates in the c.m. system.
With the above selection criteria, the distribu-
tions of Mpπ−/Mpπ−γ in a range of ±8 times
the mass resolution around the Λ/Σ0 nominal
IV. BACKGROUND ESTIMATION
mass in the J/ψ and ψ(3686) decays are shown
in Fig. 1. Clear Λ/Σ0 peaks are observed with
Tostudythebackgrounds,thesameselectioncri-
low background. To determine the signal yields,
teriaareappliedtothegenericinclusiveψ MCsam-
unbinned maximum likelihood fits are applied to
bpalecsk.groFuonrdtshaeredefcoauyndJ/toψ b→e JΛ/ψΛ¯,→theΛΣ¯do0m+inca.cn.t, eMdptπo−±/M3ptπim−γeswoifthretshoelumtiaosnsooffΛ¯p¯/πΣ¯+0/p¯nπo+mγin′ arelsmtraicsts-.
J/ψ → γKsKs, and J/ψ → γηc with the sub- In the fit, the Λ/Σ0 signal shape is described by
sequent decay η → ΛΛ¯. For the decay J/ψ →
c the simulatedMC shapeconvolvedwithaGaussian
Σ0Σ¯0, the main backgrounds are from J/ψ →
function to account for the difference in mass reso-
ΛΣ¯0 + c.c., J/ψ → γη with the subsequent de-
c lutionbetweendataandMC simulation. The peak-
cay η → ΛΛ¯, Σ0Σ¯0, ΛΣ¯0 + c.c., and J/ψ →
c ingbackgroundsaredescribedwiththeshapesfrom
Σ0Σ¯∗0 + c.c.. For ψ(3686) → ΛΛ¯, the potential
exclusiveMCsimulationswithfixedmagnitudesac-
backgrounds are ψ(3686) → π+π−J/ψ,J/ψ → pp¯,
cording to the branching fractions of background
ψ(3686) → Σ0Σ¯0, and ψ(3686) → ΛΣ¯0 +c.c.. For
listed in the PDG [4], and the non-peaking back-
ψ(3686) → Σ0Σ¯0, the dominant backgrounds are
groundsaredescribedwithsecond-orderpolynomial
from ψ(3686) → γχ ,χ → ΛΛ¯ (J = 0,1,2) and
cJ cJ functions withfreeparametersinthefit. Thefitre-
ψ(3686) → Ξ0Ξ¯0,Ξ0 → Λπ0,Ξ¯0 → Λ¯π0. All above
sultsareillustratedinFig.1,andthecorresponding
backgrounds can be classified into two categories,
signal yields are summarized in Table III.
i.e., backgrounds with or without ΛΛ¯ in the final
The branching fractions are calculated using
state. Theformercategorybackgroundsareexpect-
ed to produce a peak around the Λ/Σ0 signal re-
gion in the pπ−/pπ−γ invariant mass distributions B(ψ→BB¯)= Nobs , (3)
and can be estimated, with the exclusive MC simu- Nψ·ǫ·Bi
lation samples using the decay branching fractions
set according to the PDG [4]. The additional un- where N is the number of signal events minus
obs
determined decays of η → Σ0Σ¯0, ΛΣ¯0 +c.c. and peaking background; ǫ is the detection efficiency,
c
ψ(3686)→ΛΣ¯0+c.c.areestimatedusingtheresults which is estimated with MC simulation incorporat-
from previous experiments for charmonium decay- ing the cosθ distributions obtained in this analysis
ing to BB¯ states (reference decays) [11, 12, 30], to andthe scalefactorstoaccountforthe differencein
be 1 and 0.1 times that for the decay η →ΛΛ¯ and efficiency between data and MC simulation as de-
c
0.1 times that for ψ(3686)→ΛΛ¯, respectively. The scribed below; B is the product of branching frac-
i
contributions of other decays to the peaking back- tionsfortheintermediatestatesinthecascadedecay
ground are negligible. The latter category of back- from the PDG [4]; and N is the total number of ψ
ψ
grounds are expected to be distributed smoothly in eventsestimatedby countingthe inclusivehadronic
the corresponding mass distributions. events [18, 19]. The corresponding detection effi-
The backgrounds from continuum QED process- ciencies and the resultant branching fractions are
es, i.e. e+e− →BB¯ decays, are estimated with the also summarized in Table III.
7
TABLEIII:ThenumbersofobservedsignaleventsN ,thecorrecteddetectionefficiencyǫ,thenumbersofpeaking
obs
backgroundsN ,thenumbersofsmoothbackgroundsN ,theresultantαvaluesfortheangulardistributionsand
pk sm
the branchingfractions B, where theerrors are statistical only.
Channel N ǫ(%) N N α B (×10−4)
obs pk sm
J/ψ→ΛΛ¯ 440,675±670 42.37±0.14 1,819 154±166 0.469±0.026 19.43±0.03
J/ψ→Σ0Σ¯0 111,026±335 17.83±0.06 820 131±12 −0.449±0.020 11.64±0.04
ψ(3686)→ΛΛ¯ 31,119±187 42.83±0.34 252 352±65 0.824±0.074 3.97±0.02
ψ(3686)→Σ0Σ¯0 6,612±82 14.79±0.12 89 17±5 0.71±0.11 2.44±0.03
2 Events / 0.1 MeV/c11111000010-23411.1 M1.1p1π- (Ge1V.1/2c2) 1(.a1)3 2 Events / 0.25 MeV/c111100010-231 1M.1pπ- (G1e.1V2/c2) 1(.b14) Number of Events00..0001..55201-1×106 -0.5 co0sθΛ 0.5 (a) 1 Number of Events 1500-1×103 -0.5 co0sθΛ 0.5(b) 1
2ents / 0.5 MeV/c111100010234 (c) 2vents / 1 MeV/c111001023 (d) mber of Events 246000×103 (c) mber of Events 24×103 (d)
Ev10-1 1.16 Mp1π.1-γ8 (Ge1V./2c2) 1.22 E101-1.14 1.16Mp1π-.γ1 8(Ge1V.2/c21).22 1.24 Nu 0-1 -0.5 cos0θΣ0 0.5 1 Nu 0-1 -0.5 cos0θΣ0 0.5 1
FIG. 1: (color online) The Mpπ− distributions for the FIG. 2: (color online) The distributions of efficiency
decays (a) J/ψ → ΛΛ¯ and (b) ψ(3686) → ΛΛ¯, and the corrected polar angle of the baryon for the decays (a)
(Md)pπψ−(γ36d8is6t)ri→buΣtio0Σn¯s0,fowrhtehreedtehceaydsot(sc)wJit/hψe→rroΣr0bΣ¯ar0saanrde (Jd/)ψψ→(36Λ8Λ6¯),→(b)Σψ0Σ¯(306,8w6h)e→retΛhΛ¯e,d(oct)sJw/itψh→errΣor0Σb¯a0r,saanrde
data, the red solid curves are the overall fit results, the data, and thered solid curvesare the fit results.
greendashedhistogramsarethebackgroundsestimated
with theexclusive MC simulated samples, and the blue
dotted line describes theremaining backgrounds.
various control samples, where θ is the polar an-
gle of the hyperon. The efficiency differences are
due to differences in the efficiencies of charged par-
ticle tracking, photon detection, and hyperon re-
B. Angular distributions
construction. For example, the efficiencies related
with charged particle tracking and Λ reconstruc-
The baryon cosθ distributions in the c.m. sys- tion are studied with a special control sample of
tem corrected by detection efficiency are shown in ψ → ΛΛ¯ events, where a Λ¯ tag has been recon-
Fig. 2, and the signal yields in each of the 20 bins structed. Events with two or more charged tracks,
are determined with the same method as that in inwhichap¯andπ+havebeenidentifiedusingparti-
the branching fraction measurements. The detec- cle identification,are selected. The Λ¯ tag candidate
tion efficiencies in each bin are estimated with the must satisfy a secondary vertex fit, have a decay
signal MC samples and scaled with correction fac- length greater than 0.2 cm, and satisfy mass and
tors to compensate for the efficiency difference be- momentumrequirements. ThenumbersoftaggedΛ
tween data and MC simulation. The efficiency cor- events, N , are obtained by fitting the Λ peak in
tag
rected cosθ distributions are fitted with Eq. 2 with the distribution of invariant mass recoiling against
aleastsquaresmethod,thecorrespondingfitresults theΛ¯ tag. ThenumbersofΛsignalevents,N ,are
sig
are shown in Fig. 2, and the resultant α values are obtained by fitting the recoil mass distribution for
summarized in Table III. events where, in addition, a Λ signalis reconstruct-
The correctionfactorsusedto correctfor the effi- ed on the recoil side, which requires two oppositely
ciency differences between data and MC simulation charged tracks that satisfy a vertex fit and have a
as a function of cosθ are determined by studying decay length greater than 0.2 cm. The combined
8
efficiencyofchargedtracking(protonandpion)and correction factors, which are determined with
Λ reconstruction is then N /N . The ratios of control samples are 0.9974±0.0041, 0.9936±
sig tag
the data and MC simulation efficiencies as a func- 0.0064,0.980±0.011,and0.954±0.022forthe
tionofcosθ aretakenasthecorrectionfactors. The decays J/ψ → ΛΛ¯, J/ψ → Σ0Σ¯0, ψ(3686) →
Λ¯ correctionfactorsaredeterminedinananalogous ΛΛ¯ and ψ(3686) → Σ0Σ¯0, respectively. To
way using ψ → ΛΛ¯ events with a Λ tag. The over- estimate the corresponding uncertainties, the
all correctionfactor in the different cosθ bins is the correctionfactorsarechangedby±1standard
product of the Λ and Λ¯ correction factors. deviations, and the resultant changes in the
In an analogous way, the combined efficiency of branching fractions are taken as the system-
photon detection and Σ0 reconstruction is studied atic uncertainties.
with a control sample of ψ → Σ0Σ¯0 events, which
have a Σ¯0 tag and an additional Λ. Events are se- 2. The uncertainties related with the MΛΛ¯ re-
lected that have a Λ and Λ¯ using the same criteria quirement are estimated by varying the mass
as above and at least one additional photon. The requirement edges by ±10 MeV/c2. The un-
Λ¯ and photon must have an invariant mass consis- certainties related with the Λ¯/Σ¯0 mass re-
tent with that of a Σ¯0. The numbers of tagged Σ0 quirement are estimated by changing the re-
events are obtained by fitting the Σ0 peak in the quirement by ±1 times the mass resolution.
distribution of mass recoiling against the Σ¯0 tag. The uncertainties due to the requirement on
We then search for another photon and reconstruct the opening angle θΣ0Σ¯0 in the decays ψ →
the Σ0 by requiring the invariant mass of the pho- Σ0Σ¯0 are estimated by changing the require-
ton and tagged Λ be consistent with the Σ0 mass. ment to be 175◦. The relative changes in the
The number of events with a Σ0 signal divided by branching fractions are individually taken as
the number of taggedΣ0 events is the combined ef- the systematic uncertainties.
ficiency of photon detection and Σ0 reconstruction.
3. MCsimulationsindicatethatthedetectionef-
The ratios of detection efficiencies in the different
ficiencies depend on the distributions of bary-
cosθ bins between data and MC simulation, deter-
on polar angular cosθ. In the analysis, the
mine the correction factors. The overall correction
measured α values are used for the cosθ dis-
factorinthedifferentcosθbinsistheproductofthe
tributions in the MC simulation. Alternative
Σ0, Σ¯0, Λ, and Λ¯ correction factors.
MC samples are generated by changing the α
valuesby±1standarddeviationsandareused
to estimate the detection efficiencies. The re-
VI. SYSTEMATIC UNCERTAINTY
sultant changes in the detection efficiencies
withrespecttotheir nominalvaluesaretaken
A. Branching Fraction
as the systematic uncertainties.
Systematic uncertainties in the branching frac- 4. The sources of systematic uncertainty asso-
tionmeasurementsaremainlyduetothedifferences ciated with the fit procedure include the fit
of detection efficiency and resolution between data range, the signal shape and the modeling of
and MC simulation. The sources of uncertainty re- backgrounds. The uncertainties related with
lated with the detection efficiency include charged the fit range are estimated by changing the
tracking, photon detection, and Λ/Σ0 reconstruc- rangeby ±1 times the mass resolutionfor the
tion. The sources of uncertainty due to the resolu- fits. The signal shapes are modeled with the
tion difference include the MΛΛ¯ and MΛ¯/MΣ¯0 mass signal MC simulated shapes convolvedwith a
requirements, and the opening angle θΣ0Σ¯0 require- Gaussianfunctioninthenominalfit. Thecor-
ment in the decays ψ → Σ0Σ¯0. Additional uncer- responding uncertainties are estimated with
tainty sources including the model of the baryon alternative fits with different signal shapes,
polar angular distribution, the fit procedure, the i.e., a Breit-Wigner function convolved with
decay branching fractions of Λ/Σ0 states and the a Gaussian function for Λ and with a Crystal
total number of ψ events are also considered. All Ball function [31] for Σ0, where the Gaussian
of systematic uncertainties are studied in detail as function and Crystal Ball function represent
discussed in the following: the corresponding mass resolutions. The un-
certainties related with the peaking back-
1. As described above, the detection efficiencies grounds, which are estimated with the ex-
related with the tracking, photon detection, clusive MC samples in the nominal fits, are
and Λ/Σ0 reconstruction are corrected bin- studied by changing the branching fractions
by-bin in cosθ to decrease the difference be- of the individual background, or by changing
tween data and MC simulation. The overall the branching fractions for the reference de-
9
cays which the estimated branching fractions with the same fit method as that used in the
for the undetermined backgrounds are based branching fraction measurements. The un-
on, by ±1 times their uncertainties from the certainties of the signal yield in each cosθ
PDG [4]. The uncertainties associated with bin are mainly from the fit range, the signal
the non-peaking backgrounds are estimated shape and the background modeling. We in-
with alternative fits by replacing the second dividually estimate the uncertainty ofthe sig-
order polynomial function with a first order nal yield in each cosθ interval with the same
polynomial function. The resultant changes methods as those used in the branching frac-
from the above changes in the signal yields tionmeasurementsforthedifferentuncertain-
are taken individually as the systematic un- ty sources, and then repeat the cosθ fit pro-
certainties. cedure with the changed signal yields. The
resultantchangesin the α values with respect
5. The uncertainties related with the branching
to the nominal values are taken as systematic
fractionsofbaryonandanti-baryondecaysare
uncertainties.
takenfromthePDG[4]. Thetotalnumbersof
ψ events are obtained by studying the inclu- 2. The sources of systematic uncertainty related
sive hadronic events, and their uncertainties to the cosθ fit procedure include the fit range
are 0.6% and 0.7% for the J/ψ and ψ(3686) and the number of bins in the cosθ distribu-
data samples [18, 19], respectively. tion. We repeat the fit procedures with the
alternativefitrange[−0.9,0.9]andalternative
The various systematic uncertainties in the
numberofbins (40). Theresultantchangesof
branchingfractionmeasurementsaresummarizedin
α values are taken as the systematic uncer-
TableIV.Thetotalsystematicuncertaintiesareob-
tainties.
tainedby summing the individualvalues inquadra-
ture. The individual absolute uncertainties in the po-
lar angular distribution measurements are summa-
rizedinTableV.The totalsystematicuncertainties
TABLE IV: Systematic uncertainties in the measure-
are obtained by summing the individual values in
ment of branchingfractions (%).
quadrature.
J/ψ ψ(3686)
ΛΛ¯ Σ0Σ¯0 ΛΛ¯ Σ0Σ¯0 TABLE V: Absolute systematic uncertainties in the
measurement of α.
Efficiency correction 0.5 0.7 1.2 2.3
MΛΛ¯ requirement 0.1 0.1 0.1 0.2 J/ψ ψ(3686)
Λ¯/Σ¯0 mass requirement 0.1 0.3 0.3 0.2 ΛΛ¯ Σ0Σ¯0 ΛΛ¯ Σ0Σ¯0
θΣ0Σ¯0 requirement − 0.3 − 0.2 Mass fit range 0.001 0.001 0.003 0.005
Baryon polar angle 0.8 0.9 2.0 3.1
Signal shape 0.001 0.002 0.001 0.003
Fit range 0.1 0.1 0.2 0.2
Peaking bkg. 0.006 0.005 0.006 0.015
Signal shape 0.1 0.3 0.1 0.2
Non-peakingbkg. 0.002 0.001 0.004 0.002
Peaking bkg. 0.3 0.4 0.3 1.2
α fit range 0.001 0.003 0.007 0.019
Non-peakingbkg. 0.1 0.1 0.3 0.2
Numberof bins 0.004 0.005 0.001 0.024
Branching fractions 1.2 1.2 1.2 1.2
Total 0.008 0.008 0.011 0.035
N /N 0.6 0.6 0.7 0.7
J/ψ ψ(3686)
Total 1.7 1.9 2.8 4.3
VII. SUMMARY
B. Angular Distribution
In summary, using the data samples of 1310.6×
106 J/ψ events and 447.9×106 ψ(3686)events col-
The sources of systematic uncertainties in the
lected with the BESIII detector at the BEPCII col-
baryonpolarangularmeasurementsincludethe sig-
lider, the J/ψ and ψ(3686) decaying into ΛΛ¯ and
nal yields in different cosθ intervals and the cosθ
Σ0Σ¯0 pairs are studied. The decay branching frac-
fit procedure. The MC statistics and correction er-
tions and α values are measured, and the results
rors are already included in the error referred to as
are summarized in Table VI. The branching frac-
“statistical”.
tionsforJ/ψdecaysareingoodagreementwiththe
1. In the polar angular measurements, the sig- results of BESII [11] and BaBar [13] experiments,
nal yield in a given cosθ interval is obtained andthose for ψ(3686)decaysarein agreementwith
10
the results of CLEO [10], BESII [12] and S. Dobbs strong support. This work is supported in part by
et al. [14] with a maximum of 2 times of standard NationalKeyBasicResearchProgramofChinaun-
deviations. The earlier experimental results [6–9] der Contract Nos. 2009CB825200, 2015CB856700;
have significantdifferences with those ofthis analy- National Natural Science Foundation of China
sis. The precisions of our branching fraction results (NSFC) under Contracts Nos. 10905034,10935007,
are much improved than those of previous experi- 11125525,11235011,11322544,11335008,11425524;
ments listed in Table I. The α values in the decays the Chinese Academy of Sciences (CAS) Large-
ψ(3686)→ ΛΛ¯ and ψ(3686)→ Σ0Σ¯0 are measured Scale Scientific Facility Program; the CAS Center
for the first time, while those of J/ψ → ΛΛ¯ and for Excellence in Particle Physics (CCEPP); the
J/ψ →Σ0Σ¯0 decaysareofmuchimprovedprecision Collaborative Innovation Center for Particles and
compared to previous measurements. It is worth Interactions (CICPI); Joint Large-Scale Scientific
noting that the α value in the decay J/ψ → Σ0Σ¯0 Facility Funds of the NSFC and CAS under
is negative,which confirms the results in Ref. [11]. Contracts Nos. 11179007, U1232106, U1232201,
U1332201;NaturalScienceFoundationofShandong
Province under Contract No. ZR2009AQ002; CAS
TABLE VI: Results for measured α values and branch- under Contracts Nos. KJCX2-YW-N29, KJCX2-
ing fractions B in this analysis. The first uncertainties
YW-N45; 100 Talents Program of CAS; National
are statistical, and thesecond are systematic.
1000 Talents Program of China; INPAC and
Shanghai Key Laboratory for Particle Physics and
Channel α B (×10−4)
J/ψ→ΛΛ¯ 0.469±0.026±0.008 19.43±0.03±0.33 Cosmology;GermanResearchFoundationDFGun-
J/ψ→Σ0Σ¯0 −0.449±0.020±0.008 11.64±0.04±0.23 der Contract No. Collaborative Research Center
ψ(3686)→ΛΛ¯ 0.82±0.08±0.02 3.97±0.02±0.12 CRC-1044, FOR-2359; Istituto Nazionale di Fisica
ψ(3686)→Σ0Σ¯0 0.71±0.11±0.04 2.44±0.03±0.11 Nucleare, Italy; Joint Funds of the National
Science Foundation of China under Contract No.
U1232107; Ministry of Development of Turkey un-
To test the “12%rule”, we also obtain the Q val- der Contract No. DPT2006K-120470; Russian
ues to be B(ψ(3686)→ΛΛ¯) = (20.43±0.11±0.58)% Foundation for Basic Research under Contract
B(J/ψ→ΛΛ¯)
No. 14-07-91152; The Swedish Resarch Council;
and B(ψ(3686)→Σ0Σ¯0) = (20.96±0.27±0.92)%,where
B(J/ψ→Σ0Σ¯0) U. S. Department of Energy under Contracts
the common systematic uncertainties between J/ψ Nos. DE-FG02-04ER41291, DE-FG02-05ER41374,
andψ(3686)decaysarecancelled. TheQvaluesare de-sc0012069,DESC0010118;U.S. NationalScience
of high precision, and differ from the expectation Foundation; University of Groningen (RuG) and
from pQCD by more than 3 standard deviations. the Helmholtzzentrum fuer Schwerionenforschung
GmbH (GSI), Darmstadt; WCU Program of
National Research Foundation of Korea under
VIII. ACKNOWLEDGMENTS Contract No. R32-2008-000-10155-0.
The BESIII collaboration thanks the staff of
BEPCII and the IHEP computing center for their
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