arXiv:1409.6577v1 [hep-ex] 23 Sep 2014
M. Ablikim1, M. N. Achasov8,a, X. C. Ai1, O. Albayrak4, M. Albrecht3, D. J. Ambrose42, A. Amoroso46A,46C, F. F. An1, Q. An43, J. Z. Bai1, R. Baldini Ferroli19A, Y. Ban30, D. W. Bennett18, J. V. Bennett4, M. Bertani19A, D. Bettoni20A, J. M. Bian41, F. Bianchi46A,46C, E. Boger22,g, O. Bondarenko24, I. Boyko22, R. A. Briere4, H. Cai48, X. Cai1, O. Cakir38A, A. Calcaterra19A, G. F. Cao1, S. A. Cetin38B, J. F. Chang1, G. Chelkov22,b, G. Chen1, H. S. Chen1, H. Y. Chen2, J. C. Chen1,
M. L. Chen1, S. J. Chen28, X. Chen1, X. R. Chen25, Y. B. Chen1, H. P. Cheng16, X. K. Chu30, Y. P. Chu1, G. Cibinetto20A, D. Cronin-Hennessy41, H. L. Dai1, J. P. Dai1, D. Dedovich22, Z. Y. Deng1, A. Denig21, I. Denysenko22, M. Destefanis46A,46C,
F. De Mori46A,46C, Y. Ding26, C. Dong29, J. Dong1, L. Y. Dong1, M. Y. Dong1, S. X. Du50, P. F. Duan1, J. Z. Fan37, J. Fang1, S. S. Fang1, X. Fang43, Y. Fang1, L. Fava46B,46C, F. Feldbauer21, G. Felici19A, C. Q. Feng43, E. Fioravanti20A,
C. D. Fu1, Q. Gao1, Y. Gao37, I. Garzia20A, K. Goetzen9, W. X. Gong1, W. Gradl21, M. Greco46A,46C, M. H. Gu1, Y. T. Gu11, Y. H. Guan1, A. Q. Guo1, L. B. Guo27, T. Guo27, Y. Guo1, Y. P. Guo21, Z. Haddadi24, A. Hafner21, S. Han48,
Y. L. Han1, F. A. Harris40, K. L. He1, Z. Y. He29, T. Held3, Y. K. Heng1, Z. L. Hou1, C. Hu27, H. M. Hu1, J. F. Hu46A, T. Hu1, Y. Hu1, G. M. Huang5, G. S. Huang43, H. P. Huang48, J. S. Huang14, X. T. Huang32, Y. Huang28, T. Hussain45, Q. Ji1, Q. P. Ji29, X. B. Ji1, X. L. Ji1, L. L. Jiang1, L. W. Jiang48, X. S. Jiang1, J. B. Jiao32, Z. Jiao16, D. P. Jin1, S. Jin1, T. Johansson47, A. Julin41, N. Kalantar-Nayestanaki24, X. L. Kang1, X. S. Kang29, M. Kavatsyuk24, B. C. Ke4, R. Kliemt13,
B. Kloss21, O. B. Kolcu38B,c, B. Kopf3, M. Kornicer40, W. Kuehn23, A. Kupsc47, W. Lai1, J. S. Lange23, M. Lara18, P. Larin13, M. Leyhe3, Cheng Li43, D. M. Li50, F. Li1, G. Li1, H. B. Li1, J. C. Li1, Jin Li31, K. Li12, K. Li32, Q. J. Li1, T. Li32,
W. D. Li1, W. G. Li1, X. L. Li32, X. M. Li11, X. N. Li1, X. Q. Li29, Z. B. Li36, H. Liang43, Y. F. Liang34, Y. T. Liang23, G. R. Liao10, D. X. Lin13, B. J. Liu1, C. L. Liu4, C. X. Liu1, F. H. Liu33, Fang Liu1, Feng Liu5, H. B. Liu11, H. H. Liu1, H. H. Liu15, H. M. Liu1, J. Liu1, J. P. Liu48, J. Y. Liu1, K. Liu37, K. Y. Liu26, L. D. Liu30, Q. Liu39, S. B. Liu43, X. Liu25,
X. X. Liu39, Y. B. Liu29, Z. A. Liu1, Zhiqiang Liu1, Zhiqing Liu21, H. Loehner24, X. C. Lou1,d, H. J. Lu16, J. G. Lu1, R. Q. Lu17, Y. Lu1, Y. P. Lu1, C. L. Luo27, M. X. Luo49, T. Luo40, X. L. Luo1, M. Lv1, X. R. Lyu39, F. C. Ma26, H. L. Ma1,
Q. M. Ma1, S. Ma1, T. Ma1, X. N. Ma29, X. Y. Ma1, F. E. Maas13, M. Maggiora46A,46C, Q. A. Malik45, Y. J. Mao30, Z. P. Mao1, S. Marcello46A,46C, J. G. Messchendorp24, J. Min1, T. J. Min1, R. E. Mitchell18, X. H. Mo1, Y. J. Mo5,
H. Moeini24, C. Morales Morales13, K. Moriya18, N. Yu. Muchnoi8,a, H. Muramatsu41, Y. Nefedov22, F. Nerling13, I. B. Nikolaev8,a, Z. Ning1, S. Nisar7, S. L. Niu1, X. Y. Niu1, S. L. Olsen31, Q. Ouyang1, S. Pacetti19B, P. Patteri19A, M. Pelizaeus3, H. P. Peng43, K. Peters9, J. L. Ping27, R. G. Ping1, R. Poling41, Y. N. Pu17, M. Qi28, S. Qian1, C. F. Qiao39,
L. Q. Qin32, N. Qin48, X. S. Qin1, Y. Qin30, Z. H. Qin1, J. F. Qiu1, K. H. Rashid45, C. F. Redmer21, H. L. Ren17, M. Ripka21, G. Rong1, X. D. Ruan11, V. Santoro20A, A. Sarantsev22,e, M. Savri´e20B, K. Schoenning47, S. Schumann21, W. Shan30, M. Shao43, C. P. Shen2, P. X. Shen29, X. Y. Shen1, H. Y. Sheng1, M. R. Shepherd18, W. M. Song1, X. Y. Song1,
S. Sosio46A,46C, S. Spataro46A,46C, B. Spruck23, G. X. Sun1, J. F. Sun14, S. S. Sun1, Y. J. Sun43, Y. Z. Sun1, Z. J. Sun1, C. J. Tang34, X. Tang1, I. Tapan38C, E. H. Thorndike42, M. Tiemens24, D. Toth41, M. Ullrich23, I. Uman38B, G. S. Varner40,
B. Wang29, B. L. Wang39, D. Wang30, D. Y. Wang30, K. Wang1, L. L. Wang1, L. S. Wang1, M. Wang32, P. Wang1, P. L. Wang1, Q. J. Wang1, S. G. Wang30, W. Wang1, X. F. Wang37, Y. F. Wang1, Y. Q. Wang21, Z. Wang1, Z. G. Wang1,
Z. H. Wang43, Z. Y. Wang1, D. H. Wei10, J. B. Wei30, P. Weidenkaff21, S. P. Wen1, U. Wiedner3, M. Wolke47, L. H. Wu1, Z. Wu1, L. G. Xia37, Y. Xia17, D. Xiao1, Z. J. Xiao27, Y. G. Xie1, Q. L. Xiu1, G. F. Xu1, L. Xu1, Q. J. Xu12, Q. N. Xu39, X. P. Xu35, Z. Xue1, L. Yan43, W. B. Yan43, W. C. Yan43, Y. H. Yan17, H. X. Yang1, L. Yang48, Y. Yang5, Y. X. Yang10, H. Ye1, M. Ye1, M. H. Ye6, J. H. Yin1, B. X. Yu1, C. X. Yu29, H. W. Yu30, J. S. Yu25, C. Z. Yuan1, W. L. Yuan28, Y. Yuan1, A. Yuncu38B,f, A. A. Zafar45, A. Zallo19A, Y. Zeng17, B. X. Zhang1, B. Y. Zhang1, C. Zhang28, C. C. Zhang1, D. H. Zhang1,
H. H. Zhang36, H. T. Zhang1, H. Y. Zhang1, J. J. Zhang1, J. L. Zhang1, J. Q. Zhang1, J. W. Zhang1, J. Y. Zhang1, J. Z. Zhang1, K. Zhang1, L. Zhang1, S. H. Zhang1, X. J. Zhang1, X. Y. Zhang32, Y. Zhang1, Y. H. Zhang1, Z. H. Zhang5,
Z. P. Zhang43, Z. Y. Zhang48, G. Zhao1, J. W. Zhao1, J. Y. Zhao1, J. Z. Zhao1, Lei Zhao43, Ling Zhao1, M. G. Zhao29, Q. Zhao1, Q. W. Zhao1, S. J. Zhao50, T. C. Zhao1, Y. B. Zhao1, Z. G. Zhao43, A. Zhemchugov22,g, B. Zheng44, J. P. Zheng1,
Y. H. Zheng39, B. Zhong27, L. Zhou1, Li Zhou29, X. Zhou48, X. K. Zhou43, X. R. Zhou43, X. Y. Zhou1, K. Zhu1, K. J. Zhu1, S. Zhu1, X. L. Zhu37, Y. C. Zhu43, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1, 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 Bochum Ruhr-University, D-44780 Bochum, Germany 4 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 5 Central China Normal University, Wuhan 430079, People’s Republic of China
6 China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
7 COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan 8 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
9 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany 10 Guangxi Normal University, Guilin 541004, People’s Republic of China
11 GuangXi University, Nanning 530004, People’s Republic of China 12 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China 13 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
14 Henan Normal University, Xinxiang 453007, People’s Republic of China
16Huangshan College, Huangshan 245000, People’s Republic of China 17Hunan University, Changsha 410082, People’s Republic of China
18 Indiana University, Bloomington, Indiana 47405, USA
19(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy
20 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy 21Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
22 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
23 Justus Liebig University Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany 24 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
25Lanzhou University, Lanzhou 730000, People’s Republic of China 26Liaoning University, Shenyang 110036, People’s Republic of China 27 Nanjing Normal University, Nanjing 210023, People’s Republic of China
28 Nanjing University, Nanjing 210093, People’s Republic of China 29Nankai University, Tianjin 300071, People’s Republic of China
30 Peking University, Beijing 100871, People’s Republic of China 31Seoul National University, Seoul, 151-747 Korea 32Shandong University, Jinan 250100, People’s Republic of China 33 Shanxi University, Taiyuan 030006, People’s Republic of China 34 Sichuan University, Chengdu 610064, People’s Republic of China
35 Soochow University, Suzhou 215006, People’s Republic of China 36Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
37Tsinghua University, Beijing 100084, People’s Republic of China
38 (A)Ankara University, Dogol Caddesi, 06100 Tandogan, Ankara, Turkey; (B)Dogus University, 34722 Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey
39 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 40 University of Hawaii, Honolulu, Hawaii 96822, USA
41 University of Minnesota, Minneapolis, Minnesota 55455, USA 42University of Rochester, Rochester, New York 14627, USA
43 University of Science and Technology of China, Hefei 230026, People’s Republic of China 44 University of South China, Hengyang 421001, People’s Republic of China
45 University of the Punjab, Lahore-54590, Pakistan
46 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
47 Uppsala University, Box 516, SE-75120 Uppsala, Sweden 48Wuhan University, Wuhan 430072, People’s Republic of China 49Zhejiang University, Hangzhou 310027, People’s Republic of China 50Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
bAlso at the Moscow Institute of Physics and Technology, Moscow 141700, Russia and at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia
c Currently at Istanbul Arel University, Kucukcekmece, Istanbul, Turkey d Also at University of Texas at Dallas, Richardson, Texas 75083, USA
e Also at the PNPI, Gatchina 188300, Russia f Also at Bogazici University, 34342 Istanbul, Turkey g
Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
Using data collected with the BESIII detector operating at the Beijing Electron Positron Collider at center-of-mass energies of√s = 4.23, 4.26, and 4.36 GeV, we observe e+e−
→ π0π0h
cfor the first time. The Born cross sections are measured and found to be about half of those of e+e−
→ π+π− hc within less than 2σ. In the π0h
c mass spectrum, a structure at 4.02 GeV/c2 that is most likely the neutral isospin partner of the Zc(4020)± observed in the process of e+e−→ π+π−hc is found. A fit to the π0h
cinvariant mass spectrum with the width of the Zc(4020)0 fixed to that of its charged isospin partner and possible interferences with non-Zc(4020)0 amplitudes neglected, gives a mass of (4023.9 ± 2.2 ± 3.8) MeV/c2 for the Z
c(4020)0, where the first error is statistical and the second systematic.
PACS numbers: 14.40.Rt, 13.66.Bc, 14.40.Pq
In the study of e+e− → π+π−J/ψ, a distinct charged structure, Z
spec-trum by the BESIII [1] and Belle [2] experiments, and confirmed shortly thereafter with CLEO-c data [3]. A similar charged structure but with a slightly higher mass, Zc(4020)±, was soon reported in e+e−→ π+π−hc[4] by
BESIII. As there are at least four quarks within these two charmoniumlike structures, they are interpreted as either tetraquark states, D ¯D∗ molecules, hadrocharmonia, or
other configurations [8]. More recently, charged struc-tures in the same mass region were observed via their decays into charmed meson pairs, including the charged Zc(4025)± in e+e− → π±(D∗D¯∗)∓ [9] and the charged
Zc(3885)± in e+e−→ π±(D ¯D∗)∓ [10]. These structures
together with the recently confirmed Z(4430)− [11–13]
and similar structures observed in the bottomonium sys-tem [14] indicate that a new class of hadrons has been observed. An important question is whether all these charged structures are part of isospin I = 1 triplets, in which case neutral partners with Iz = 0 should also be
found. Evidence for a neutral Zc(3900) was observed in
e+e−→ π0π0J/ψ process with CLEO-C data at
center-of-mass energy (CME) √s=4.17 GeV [3]. A neutral structure, the Zc(4020)0, is expected to couple to the
π0h
c final state and be produced for in e+e− → π0π0hc
processes.
In this Letter, we present the first observation of e+e− → π0π0h
c at √s = 4.23 GeV, 4.26 GeV, and
4.36 GeV, and the observation of a neutral charmoni-umlike structure Zc(4020)0 in the π0hc spectrum. We
follow closely the analysis of e+e− → π+π−h
c [4] with
the selection of π+π−replaced with the selection of a pair
of π0s. The data samples were collected with the BESIII detector [5]. The CMEs and corresponding integrated luminosities are listed in Table I.
We use a GEANT4 [6] based Monte Carlo (MC) sim-ulation to optimize the event selection criteria, deter-mine the detection efficiency, and estimate backgrounds. In the studies presented here, the hc is reconstructed
via its electric-dipole (E1) transition hc → γηc with
ηc → Xi, where Xi denotes 16 hadronic final states: p¯p,
π+π−K+K−, π+π−p¯p, 2(K+K−), 2(π+π−), 3(π+π−),
2(π+π−)K+K−, K
SK±π∓, KSK±π∓π+π−, K+K−π0,
K+K−η, p¯pπ0, π+π−η, π+π−π0π0, 2(π+π−)η, and
2(π+π−π0). The initial state radiation (ISR) is simulated
with KKMC [7], where the Born cross section of e+e−→
π0π0h
c is assumed to follow the e+e− → π+π−hc
line-shape [4].
The selection of charged tracks, photons, and K0 S →
π+π− candidates are described in Refs. [4, 15]. A
candi-date π0 (η) is reconstructed from a pair of photons with
an invariant mass in the range |Mγγ− mπ0| <15 MeV/c2
(|Mγγ − mη| <15 MeV/c2), where mπ0 (mη) is the
nominal π0 (η) mass [16]. The event candidates of
e+e− → π0π0h
c, hc → γηc are required to have at
least one γπ0π0 combination with the mass recoiling
against π0π0, Mrecoil
π0π0, in the hc mass region (Mπrecoil0π0 ∈
[3.3, 3.7] GeV/c2) and with the mass recoiling against γπ0π0, Mrecoil
γπ0π0, in the ηc mass region ( Mγπrecoil0π0 ∈
[2.8, 3.2] GeV/c2).
To determine the species of final state particles and to select the best photon candidates when additional pho-tons (and π0or η candidates) are found in an event, the
combination with the minimum value of χ2 = χ2 4C +
ΣN
i=1χ2PID(i) + χ21C is selected for further analysis. Here
χ2
4C is the χ2 of the initial-final four-momentum
conser-vation (4C) kinematic fit, χ2
PID(i) is the χ2 of particle
identification (PID) of each charged track using the en-ergy loss in the main drift chamber and the time mea-sured with the time-of-flight system, N is the number of the charged tracks, and χ2
1C is the sum of the 1C
χ2s of the π0s and η in each final state with the mass
of the daughter photons constrained to that of the par-ent. There is also a χ2
4Crequirement, which is optimized
by maximizing the figure of merit S/√S + B, where S and B are the numbers of Monte Carlo (MC) simulated signal and background events, respectively. The require-ment χ2
4C< 30 has an efficiency of 61% for ηcdecays with
only charged or K0
S particles in the final states, while the
requirement χ2
4C < 25 has an efficiency of 36% for the
other decays [17]. A similar optimization is performed to determine the ηc candidate mass window around its
nominal value, which is found to be ±35 MeV/c2with an efficiency of 59% for ηc decays with only charged or KS0
particles in final states and 22% for the other decays. The inset of Fig. 1 shows the scatter plot of Mrecoil
γπ0π0,
which corresponds to the invariant mass of the recon-structed ηc candidate, versus Mπrecoil0π0, which corresponds
to the invariant mass of the reconstructed hc
candi-date, summed over the events at √s = 4.23, 4.26, and 4.36 GeV, where a clear cluster of events correspond-ing to the hc → γηc signal is observed. Figure 1 shows
the projection of the invariant mass distribution of γηc
candidates for events in the ηc signal region (Mγπrecoil0π0 ∈
[2.945, 3.015] GeV/c2 ), where a clear peak at the h c
mass is observed. The events in the sideband regions, 2.865 GeV/c2 < Mrecoil
γπ0π0 < 2.900 GeV/c2 and 3.050
GeV/c2< Mrecoil
γπ0π0< 3.085 GeV/c2 are used to study the
background. To extract the number of π0π0h
c signal
events, the Mrecoil
π0π0 mass spectrum is fitted with a MC
simulated signal shape convolved with a Gaussian func-tion to represent the data-MC mass resolufunc-tion difference, together with a linear background term. A simultaneous fit to the Mrecoil
π0π0 mass spectrum summed over the 16 ηc
decay modes at the three CME points yields the numbers of π0π0h
c signal events (nobshc ) listed in Table I. Figure 1
also shows the fit results summed over the three CME points.
The Born cross section σB(e+e− → π0π0h
c) is
calcu-lated with the formula
σB(e+e−→ π0π0hc) = nobs hc L(1+δr )(1+δv ) 16 P i=1 ǫiB(ηc→Xi)B(hc→γηc) , (1) where nobs
hc is the number of observed hc signal events;
L is the integrated luminosity; (1 + δr) is the initial
TABLE I. Energies (√s), luminosities (L), numbers of events (nobs hc), average efficiencies ( 16 P i=1 ǫiB(ηc → Xi)), initial state radiative correction factor (1 + δr) [4], vacuum polarization factor (1 + δv), Born cross sections σB(e+e−
→ π0π0h c) and ratios Rππhc= σ(e+ e−→π0 π0hc)
σ(e+e−→π+π−hc), where the third errors are from the uncertainty in B(hc→ γηc) [20].
√ s (GeV) L (pb−1) nobs hc 16 P i=1 ǫiB(ηc→ Xi) 1 + δr 1 + δv σB(e+e − → π0π0h c) (pb) Rππhc 4.230 1090.0 82.5 ± 15.6 6.82 × 10−3 0.756 1.056 25.6 ± 4.8 ± 2.6 ± 4.0 0.54 ± 0.11 ± 0.06 4.260 826.8 62.8 ± 13.3 6.54 × 10−3 0.831 1.054 24.4 ± 5.2 ± 3.2 ± 3.8 0.63 ± 0.14 ± 0.10 4.360 544.5 64.3 ± 11.5 6.68 × 10−3 0.856 1.051 36.2 ± 6.5 ± 4.1 ± 5.7 0.73 ± 0.14 ± 0.10 3.350 3.4 3.45 3.5 3.55 3.6 3.65 50 100 150 200 250 300 350 400
)
2(GeV/c
recoil 0 π 0 πM
3.35 3.4 3.45 3.5 3.55 3.6 3.65)
2Events/0.0125(GeV/c
0 50 100 150 200 250 300 350 400 ) 2 (GeV/c recoil 0 π 0 π M 3.3 3.4 3.5 3.6 3.7 ) 2 (GeV/c recoil γ 0π 0 π M 2.8 2.9 3 3.1 3.2FIG. 1. The Mπrecoil0π0 distribution for the events with an ηc candidate. The plot shows the sum over three CME points. Dots with error bars are data; the solid curve is the best fit; the dashed black line is the background; the green shaded histogram shows the normalized ηcsideband events. The inset shows the scatter plot of Mrecoil
γπ0π0 versus Mπrecoil0π0. The two red
dashed lines represent the signal region of ηc.
as that for the analysis of e+e− → π+π−h
c [4]; (1 + δv)
is the vacuum polarization factor [18]; ǫi is the
detec-tion efficiency for the ith η
c decay mode in the decay
e+e−→ π0π0h
cwithout consideration of any possible
in-termediate structures and with ISR and vacuum polariza-tion effects considered in the MC simulapolariza-tion; B(ηc→ Xi)
is the corresponding ηc branching fraction; B(hc→ γηc)
is the branching fraction of hc→ γηc.
The measured Born cross sections are listed in Table I. The ratios of the Born cross sections for the neutral and charged e+e− → ππh
c modes are also listed in Table I;
the cross sections for the charged channel are taken from Ref. [4], where vacuum polarization effects were not taken into account. A corresponding correction factor (1+δv) is
applied to the previous Born cross section. The common systematic uncertainties in the two measurements cancel in the ratio calculation. The combined ratio Rππhc is
obtained with a weighted least squares method [19] and determined to be (0.63 ± 0.09), which is within 2σ of the
expectation of isospin symmetry, 0.5.
Systematic uncertainties in the cross section measure-ment mainly come from the luminosity measuremeasure-ment (δL), branching fraction of hc → γηc, branching
frac-tions of ηc → Xi, detection efficiencies (δǫi·B(ηc→Xi)),
radiative correction factors (δISR), vacuum polarization
factors (δVac) [18], and fits to the mass spectrum. The
integrated luminosity at each CME points is measured using large-angle Bhabha events and has an estimated uncertainty of 1.0%. The hc→ γηcand ηc→ Xi
branch-ing fractions are taken from Refs. [15, 20], and the uncer-tainties in the radiative correction are the same as those used in the analysis of e+e− → π+π−h
c [4]. The
uncer-tainties in the vacuum polarization factor are 0.5% [18]. The detection efficiency uncertainty estimates are done with the same way as described in Refs. [15, 21]. The un-certainty due to the ηc mass (δηc−mass) is estimated by
changing its mass by ±1σ of its world average value [16]; the uncertainties due to the background shapes (δbkg) are
estimated by changing the background function from a first-order to a second-order polynomial; the uncertainty from the mass resolution (δres) is estimated by varying
the mass resolution difference between data and MC sim-ulation by one standard deviation; the uncertainty from fit range (δfit) is estimated by extending the fit range;
the uncertainty from the π0π0h
c substructure (δsub) is
estimated by considering the efficiency with and without the inclusion of a Zc(4020)0. The contribution from each
source of systematic error are listed in Table II.
Assuming all of the above uncertainties are indepen-dent, the total systematic uncertainties in the e+e− →
π0π0hccross section measurements are determined to be
between 10% and 13%. The uncertainty in B(hc→ γηc),
not listed in Table II but common to all CME points, is 15.7% [16] and is quoted separately in the cross section measurement.
Intermediate states are studied by examining the Mrecoil
π0 distribution (which corresponds to the
recon-structed π0h
c invariant mass) for the selected π0π0hc
candidate events. The hc signal events are selected
by requiring 3.51 GeV/c2 < Mrecoil
π0π0 <3.55 GeV/c2,
and events in the sideband regions 3.45 GeV/c2 <
Mrecoil
π0π0 <3.49 GeV/c2 and 3.57 GeV/c2 <
Mrecoil
TABLE II. The systematic uncertainties (%) in σB(e+e−
→ π0π0hc). √
s (GeV) δL δfit δres δbkg δηc−mass δsub δISR δVac δǫiB(ηc→Xi)
4.230 1.0 1.3 0.9 5.9 1.6 2.1 2.2 0.5 7.2 4.260 1.0 0.9 0.4 9.5 4.8 1.6 2.3 0.5 7.3 4.360 1.0 1.0 0.1 7.1 4.6 0.6 0.4 0.5 7.2
From the two combinations of the π0 recoil mass in each
event, we retain the one with the larger π0 recoil mass
value, and denote this as Mrecoil
π0 |max. Fig. 2 shows a
Dalitz plot of all the π0π0h
c candidate events summed
over the three center-of-mass energies, where there is an evident horizontal band of Mrecoil
π0 |max values. Figure 3
shows the Mrecoil
π0 |max distribution for the signal events
where there is an obvious peak near 4.02 GeV/c2, which
corresponds to the expected position of a Zc(4020)0
sig-nal. 2
)
2(GeV/c
2)
0 π 0 π(M
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2)
2(GeV/c
2)
max|
0 π recoil(M
15 15.5 16 16.5 17 17.5 18FIG. 2. Dalitz plot of (Mrecoil
π0 |max)2 versus (Mπ0π0)2 for
selected e+e− → π0π0hc events summed over three CME points. The two red dashed lines represent the potential region of the structure candidates.
An unbinned maximum likelihood fit is applied to the Mrecoil
π0 |max distribution summed over all 16 ηc decay
modes. The data at √s = 4.23, 4.26, and 4.36 GeV are fitted simultaneously with the same signal function with common mass and width. The signal shape is parametrized with a constant-width relativistic Breit-Wigner function convolved with a Gaussian-distributed mass resolution, where the mass resolution is determined from a fit to a MC sample with the width set to zero. Because of the limited statistics of the Zc(4020)0 signal,
its width is fixed to that of its charged partner, (7.9±2.6) MeV [4]. Assuming the spin and parity of the Zc(4020)0
are 1+, a phase space factor pq3is included in the partial width, where p is the Zc(4020)0momentum in the e+e−
rest frame and q is the hc momentum in the Zc(4020)0
rest frame.
)
2(GeV/c
max|
0 π recoilM
3.85 3.9 3.95 4 4.05 4.1 4.15 4.2 4.25)
2Events/(0.01GeV/c
0 5 10 15 20 25 30 35 40 45 3.85 3.9 3.95 4 4.05 4.1 4.15 4.2 4.25 0 5 10 15 20 25 30 35 40 45FIG. 3. Sum of the simultaneous fit to the Mrecoil
π0 |max distri-bution at√s = 4.23, 4.26 and 4.36 GeV as described in the text. Dots with errors bars are data; the green shaded his-togram shows the normalized hc sideband events; the black dashed curve is the background from the fit; the red histogram shows the result from a phase space MC simulation. The solid blue line shows the total fit.
There are two types of backgrounds in the Mrecoil π0 |max
distribution. One is the non-hc background in the hc
signal region, which can be represented by the hc
side-band events, and the other is the non-Zc(4020)0 π0π0hc
events that may come from three-body π0π0h
c decays or
from production of intermediate scalar states, such as the f0(980), that decay into π0π0. Since the widths of the
low-mass scalar particles are large, these non-Zc(4020)0
π0π0h
c events can be reasonably well described with a
phase space distribution. For the non-hc background, a
comparison of the hc sideband events with the simulated
phase space events indicates that it can also be described with a three-body phase space distribution. Thus, in the fit all of the background sources are described with a single MC-simulated phase space shape with a total nor-malization that is left as a free parameter. In the fit, the signal shape mentioned above is multiplied by the effi-ciency which depends on Mπrecoil0 |max, but possible
inter-ference between the signal and background is neglected. The solid curve in Fig. 3 shows the fit results, which yields a Zc(4020)0 mass of 4023.9 ± 2.2 MeV/c2. By
projecting the events into a histogram with 50 bins, the goodness of the fit is calculated from the combined χ2
values, the number of bins and the number of free param-eters at three CME points, and found to be χ2/n.d.f. =
28.6/33. Here the event number in each bin used in the χ2 evaluation is required to be larger than 7. The
sta-tistical significance of the Zc(4020)0signal is determined
from a comparison of the fit likelihoods with and without the signal. Additional fit are also performed with differ-ent signal shapes, and background shapes. In all cases, the minimum significance is found to be above 5σ. The numbers of Zc(4020)0signal events are listed in Table III.
The Born cross section σB(e+e− → π0Z
c(4020)0 →
π0π0h
c) is calculated with eq. 1, with the measured
num-bers of observed signal and MC-determined detection ef-ficiencies for the π0Z
c(4020)0channel.
The systematic uncertainties on the Zc(4020)0 mass
come from uncertainties in the mass calibration and en-ergy scale, parametrizations of the signal and background shapes, mass dependence of the efficiency, width assump-tion, MC modeling with a different JP value, and mass
resolution. The uncertainty from the mass calibration is estimated by using the difference, (2.3±1.5) MeV/c2,
be-tween the measured and known hcmass. The uncertainty
from the photon energy scale is estimated with ψ′ →
γχc1,2, χc1,2→ γJ/ψ, J/ψ → µ+µ−for photons with low
energy, and with radiative Bhabha processes for photons with high energy [20]. After adjusting the MC energy scale accordingly, the resulting changes in the mass of Zc(4020)0 are negligible. The JP value of Zc(4020)0 is
uncertain; two possible alternatives, JP = 1−and 2+, are
used to estimate the corresponding systematic errors. A difference of 0.4 MeV/c2 in the Z
c(4020)0 mass is found
under different JP assumptions. The uncertainty due
to the background shape is determined by changing the phase space shape to a parametrized background func-tion, f (M ) = [(M − Ma)1/2+ c1(M − Ma)3/2] × [(Mb−
M )1/2+ c
2(Mb− M)3/2]. Here M is mass of the
back-ground, Ma and Mb are the two extreme points
deter-mined by the minimal and maximal mass. f (M ) = 0 for (M − Ma) < 0 or (Mb− M) < 0. The coefficients
c1 and c2 are determined by the fit [10]. A difference of
0.1 MeV/c2 is found and taken as the systematic
uncer-tainty. The uncertainty due to the mass dependence of the efficiency is determined by assuming a uniform effi-ciency in the whole Mrecoil
π0 |max recoil mass region, and
the difference is found to be negligible. The uncertainty due to the mass resolution is estimated by varying the data-MC difference in resolution by one standard devia-tion of the measured uncertainty in the mass resoludevia-tion of the hc signal; the difference in the Zc(4020)0 mass
is negligible. Similarly, the uncertainty due to the fixed Zc(4020)0width is estimated by varying the width
deter-mined for its charged partner by one standard deviation. The difference is 0.1 MeV/c2 and is taken as the
system-atic error. Assuming all the sources of the systemsystem-atic uncertainty are independent, the total systematic error is estimated to be 3.8 MeV/c2.
The systematic uncertainties in the measured Born cross section, σ(e+e−→ π0Z
c(4020)0→ π0π0hc), are
es-timated in the same way as for e+e−→ π0π0h
c. In
addi-tion to those common parts in the e+e−→ π0π0h c
mea-surement, the uncertainties due to signal parametriza-tion (δsignal), background shape (δbkg), hc signal window
selection (δhc−signal), mass resolution (δres), efficiency
(δǫcurve), and MC model (δMC−model) are considered; their
values are summarized in Table IV.
The ratios of Born cross section for e+e− →
πZc(4020) → ππhc between neutral and charged modes
at three center-of-mass energies are listed in Table III. Similar to the calculation of the σ(e+e− → π0π0h
c)
ra-tio, the same correction factor (1 + δv) is also applied
to the previously measured e+e− → π±Z
c(4020)∓ Born
cross section. The common systematic uncertainty be-tween neutral and charged mode cancel. The combined ratio RπZc(4020) is determined to be (0.99 ± 0.31) with
the same method as for the combined Rππhc, which is
within 1σ of the expectation of isospin symmetry, 1.0. In summary, we observe e+e− → π0π0h
cat√s = 4.23,
4.26, and 4.36 GeV for the first time. The measured Born cross sections are about half of those for e+e− →
π+π−h
c, and agree with expectations based on isospin
symmetry within systematic uncertainties. A narrow structure with a mass of (4023.9±2.2±3.8) MeV/c2is ob-served in the Mrecoil
π0 |max mass spectrum. This structure
is most likely the neutral isospin partner of the charged Zc(4020) observed in the e+e− → π+π−hc process [4].
This observations indicate that there is no anomalously large isospin violations in ππhc and πZc(4020) system.
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong sup-port. This work is supported in part by the Min-istry of Science and Technology of China under Contract No. 2009CB825200; Joint Funds of the National Nat-ural Science Foundation of China under Contracts Nos. 11079008, 11179007, U123210, and U1332201; National Natural Science Foundation of China (NSFC) under Con-tracts Nos. 10625524, 10821063, 10825524, 10835001, 10935007, 11079023, 11125525, 11235011; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Fa-cility Program; CAS under Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents Program of CAS; German Research Foundation DFG under Con-tract No. Collaborative Research Center CRC-1044; Is-tituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470; U. S. Department of Energy under Contracts Nos. FG02-04ER41291, FG02-05ER41374, DE-FG02-94ER40823, DESC0010118; U.S. National Sci-ence Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
TABLE III. Energies (√s), numbers of events (nobs
Zc(4020)0), average efficiencies (
16 P i=1
ǫiB(ηc → Xi)), initial state radiative correction factor (1 + δr) [4],vacuum polarization factor (1 + δv), Born cross sections σ(e+e−
→ π0Z
c(4020)0 → π0π0hc), and ratios RπZc(4020)=
σ(e+e−→π0Z
c(4020)0→π0π0hc)
σ(e+e−→π±Zc(4020)∓→π±π∓hc), where the third errors are from the uncertainty in B(hc→ γηc) [15].
√ s (GeV) nobs Zc(4020)0 (1 + δ r) 1 + δv P16 i=1 ǫiB(ηc→ Xi) σB(e+e−→ π0Zc(4020)0→ π0π0hc) (pb) RπZc(4020) 4.230 21.7 ± 7.4 0.756 1.056 7.08 × 10−3 6.5 ± 2.2 ± 0.7 ± 1.0 0.77 ± 0.31 ± 0.25 4.260 22.5 ± 7.7 0.831 1.054 6.72 × 10−3 8.5 ± 2.9 ± 1.1 ± 1.3 1.21 ± 0.50 ± 0.38 4.360 17.2 ± 7.2 0.856 1.051 6.56 × 10−3 9.9 ± 4.1 ± 1.3 ± 1.5 1.00 ± 0.48 ± 0.32
TABLE IV. Systematic uncertainties (%) in the σ(e+e−→ π0Zc(4020)0→ π0π0hc) measurement, in addition to part of those in σ(e+e−
→ π0π0h c).
√s (GeV) δ
signal δbkg δres δhc−signal δǫcurve δMC−model
4.230 0.3 5.8 0.5 5.1 0.3 0.6
4.260 1.1 3.5 0.2 8.6 0.3 0.6
4.360 0.8 4.8 0.2 3.5 0.0 0.6
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![TABLE I. Energies ( √ s), luminosities (L), numbers of events (n obshc ), average efficiencies ( 16 P i=1 ǫ i B(η c → X i )), initial state radiative correction factor (1 + δ r ) [4], vacuum polarization factor (1 + δ v ), Born cross sections σ B (e + e −](https://thumb-eu.123doks.com/thumbv2/9libnet/4233256.66687/4.918.128.795.186.273/energies-luminosities-average-efficiencies-radiative-correction-polarization-sections.webp)
