This is the accepted manuscript made available via CHORUS. The article has been
published as:
Determination of the Spin and Parity of the Z_{c}(3900)
M. Ablikim et al. (BESIII Collaboration)
Phys. Rev. Lett. 119, 072001 — Published 16 August 2017
DOI: 10.1103/PhysRevLett.119.072001
1 Determination of spin and parity of the Zc(3900)
2 M. Ablikim1, M. N. Achasov9,f , X. C. Ai1, O. Albayrak5, M. Albrecht4, D. J. Ambrose44, A. Amoroso49A,49C ,
3 F. F. An1, Q. An46,a, J. Z. Bai1, R. Baldini Ferroli20A, Y. Ban31, D. W. Bennett19, J. V. Bennett5, M. Bertani20A,
4 D. Bettoni21A, J. M. Bian43, F. Bianchi49A,49C , E. Boger23,d, I. Boyko23, R. A. Briere5, H. Cai51, X. Cai1,a, O.
Cakir40A,b, A. Calcaterra20A, G. F. Cao15 , S. A. Cetin40B , J. F. Chang1,a, G. Chelkov23,d,e, G. Chen1, H. S. Chen1,
H. Y. Chen2, J. C. Chen16 , M. L. Chen1,a, S. Chen41, S. J. Chen29, X. Chen1,a, X. R. Chen26, Y. B. Chen1,a,
7 H. P. Cheng17, X. K. Chu31, G. Cibinetto21A, H. L. Dai1,a, J. P. Dai34, A. Dbeyssi14, D. Dedovich23, Z. Y. Deng1,
A. Denig22, I. Denysenko23, M. Destefanis49A,49C , F. De Mori49A,49C8 , Y. Ding27, C. Dong30, J. Dong1,a,
L. Y. Dong19 , M. Y. Dong1,a, Z. L. Dou29, S. X. Du53, P. F. Duan1, J. Z. Fan39, J. Fang1,a, S. S. Fang1, X. Fang46,a,
10 Y. Fang1, R. Farinelli21A,21B, L. Fava49B,49C , O. Fedorov23, F. Feldbauer22, G. Felici20A, C. Q. Feng46,a,
11 E. Fioravanti21A, M. Fritsch14,22, C. D. Fu1, Q. Gao1, X. L. Gao46,a, X. Y. Gao2, Y. Gao39, Z. Gao46,a,
12 I. Garzia21A, K. Goetzen10, L. Gong30, W. X. Gong1,a, W. Gradl22, M. Greco49A,49C, M. H. Gu1,a, Y. T. Gu12,
13 Y. H. Guan1, A. Q. Guo1, L. B. Guo28, R. P. Guo1, Y. Guo1, Y. P. Guo22, Z. Haddadi25, A. Hafner22, S. Han51,
14 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 ,
1,a 1
15 T. Hu , Y. Hu , G. S. Huang46,a, J. S. Huang15, X. T. Huang33, X. Z. Huang29, Y. Huang29, Z. L. Huang27,
T. Hussain48, Q. Ji1, Q. P. Ji3016 , X. B. Ji1, X. L. Ji1,a, L. W. Jiang51, X. S. Jiang1,a, X. Y. Jiang30, J. B. Jiao33,
17 Z. Jiao17, D. P. Jin1,a, S. Jin1, T. Johansson50, A. Julin43, N. Kalantar-Nayestanaki25, X. L. Kang1, X. S. Kang30,
18 M. Kavatsyuk25, B. C. Ke5, P. Kiese22, R. Kliemt14, B. Kloss22, O. B. Kolcu40B,i, B. Kopf4, M. Kornicer42,
W. Kuehn2419 , A. Kupsc50, J. S. Lange24,a, M. Lara19, P. Larin14, C. Leng49C , C. Li50, Cheng Li46,a, D. M. Li53,
F. Li1,a, F. Y. Li31, G. Li120 , H. B. Li1, H. J. Li1, J. C. Li1, Jin Li32, K. Li13, K. Li33, Lei Li3, P. R. Li41,
21 Q. Y. Li33, T. Li33, W. D. Li1, W. G. Li1, X. L. Li33, X. M. Li12, X. N. Li1,a, X. Q. Li30, Y. B. Li2, Z. B. Li38,
H. Liang46,a22 , J. J. Liang12, Y. F. Liang36, Y. T. Liang24, G. R. Liao11, D. X. Lin14, B. Liu34, B. J. Liu1,
23 C. X. Liu1, D. Liu46,a, F. H. Liu35, Fang Liu1, Feng Liu6, H. B. Liu12, H. H. Liu16, H. H. Liu1, H. M. Liu1,
24 J. Liu1, J. B. Liu46,a, J. P. Liu51, J. Y. Liu1, K. Liu39, K. Y. Liu27, 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, X. C. Lou1,a,h25 , H. J. Lu17,
26 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, F. C. Ma27,
H. L. Ma1, L. L. Ma3327 , M. M. Ma1, Q. M. Ma1, T. Ma1, X. N. Ma30, X. Y. Ma1,a, Y. M. Ma33, F. E. Maas14,
28 M. Maggiora49A,49C, Y. J. Mao31, Z. P. Mao1, S. Marcello49A,49C , J. G. Messchendorp25, J. Min1,a, R. E. Mitchell19,
X. H. Mo1,a29 , Y. J. Mo6, C. Morales Morales14, N. Yu. Muchnoi9,f , H. Muramatsu43, Y. Nefedov23, F. Nerling14,
I. B. Nikolaev9,f , Z. Ning1,a, S. Nisar8, S. L. Niu1,a, X. Y. Niu130 , S. L. Olsen32, Q. Ouyang1,a, S. Pacetti20B,
Y. Pan46,a, P. Patteri20A31 , M. Pelizaeus4, H. P. Peng46,a, K. Peters10, J. Pettersson50, J. L. Ping28, R. G. Ping1,
32 R. Poling43, V. Prasad1, H. R. Qi2, M. Qi29, S. Qian1,a, C. F. Qiao41, L. Q. Qin33, N. Qin51, X. S. Qin1,
Z. H. Qin1,a33 , J. F. Qiu1, K. H. Rashid48, C. F. Redmer22, M. Ripka22, G. Rong1, Ch. Rosner14, X. D. Ruan12,
34 A. Sarantsev23,g, M. Savrié21B, K. Schoenning50, S. Schumann22, W. Shan31, M. Shao46,a, C. P. Shen2,
30
35 P. X. Shen , X. Y. Shen1, H. Y. Sheng1, M. Shi1, W. M. Song1, X. Y. Song1, S. Sosio49A,49C , S. Spataro49A,49C,
36 G. X. Sun1, J. F. Sun15, S. S. Sun1, X. H. Sun1, Y. J. Sun46,a, Y. Z. Sun1, Z. J. Sun1,a, Z. T. Sun19, C. J. Tang36,
37 X. Tang1, I. Tapan40C , E. H. Thorndike44, M. Tiemens25, M. Ullrich24, I. Uman40D, G. S. Varner42, B. Wang30,
B. L. Wang41, D. Wang31, D. Y. Wang3138 , K. Wang1,a, L. L. Wang1, L. S. Wang1, M. Wang33, P. Wang1,
39 P. L. Wang1, S. G. Wang31, W. Wang1,a, W. P. Wang46,a, X. F. Wang39, Y. Wang37, Y. D. Wang14, Y. F. Wang1,a,
40 Y. Q. Wang22, Z. Wang1,a, Z. G. Wang1,a, Z. H. Wang46,a, Z. Y. Wang1, Z. Y. Wang1, T. Weber22, D. H. Wei11,
41 J. B. Wei31, P. Weidenkaff22, S. P. Wen1, U. Wiedner4, M. Wolke50, L. H. Wu1, L. J. Wu1, Z. Wu1,a, L. Xia46,a,
L. G. Xia39, Y. Xia1842 , D. Xiao1, H. Xiao47, Z. J. Xiao28, Y. G. Xie1,a, Q. L. Xiu1,a, G. F. Xu1, J. J. Xu1, L. Xu1,
Q. J. Xu13, Q. N. Xu41, X. P. Xu37, L. Yan49A,49C , W. B. Yan46,a, W. C. Yan46,a, Y. H. Yan18, H. J. Yang3443 ,
44 H. X. Yang1, L. Yang51, Y. X. Yang11, M. Ye1,a, M. H. Ye7, J. H. Yin1, B. X. Yu1,a, C. X. Yu30, J. S. Yu26,
C. Z. Yuan1, W. L. Yuan29, Y. Yuan1, A. Yuncu40B,c, A. A. Zafar4845 , A. Zallo20A, Y. Zeng18, Z. Zeng46,a,
46 B. X. Zhang1, B. Y. Zhang1,a, C. Zhang29, C. C. Zhang1, D. H. Zhang1, H. H. Zhang38, H. Y. Zhang1,a, J. Zhang1,
47 J. J. Zhang1, J. L. Zhang1, J. Q. Zhang1, J. W. Zhang1,a, J. Y. Zhang1, J. Z. Zhang1, K. Zhang1, L. Zhang1,
S. Q. Zhang30, X. Y. Zhang33, Y. Zhang1, Y. H. Zhang1,a, Y. N. Zhang41, Y. T. Zhang46,a48 , Yu Zhang41,
Z. H. Zhang6, Z. P. Zhang4649 , Z. Y. Zhang51, G. Zhao1, J. W. Zhao1,a, J. Y. Zhao1, J. Z. Zhao1,a,
50 Lei Zhao46,a, Ling Zhao1, M. G. Zhao30, Q. Zhao1, Q. W. Zhao1, S. J. Zhao53, T. C. Zhao1, Y. B. Zhao1,a,
51 Z. G. Zhao46,a, A. Zhemchugov23,d, B. Zheng47, J. P. Zheng1,a, W. J. Zheng33, Y. H. Zheng41, B. Zhong28,
2
L. Zhou1,a, X. Zhou51, X. K. Zhou46,a, X. R. Zhou46,a, X. Y. Zhou152 , K. Zhu1, K. J. Zhu1,a, S. Zhu1, S. H. Zhu45,
53 X. L. Zhu39, Y. C. Zhu46,a, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1,a, L. Zotti49A,49C , B. S. Zou1, J. H. Zou1
54 (BESIII Collaboration)
1
55 Institute of High Energy Physics, Beijing 100049, People’s Republic of China
2
56 Beihang University, Beijing 100191, People’s Republic of China
3
57 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China
4
58 Bochum Ruhr-University, D-44780 Bochum, Germany
5
59 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6
60 Central China Normal University, Wuhan 430079, People’s Republic of China
7
61 China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
8
62 COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
9
63 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
10
64 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
11
65 Guangxi Normal University, Guilin 541004, People’s Republic of China
12
66 GuangXi University, Nanning 530004, People’s Republic of China
13
67 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
14
68 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
15
69 Henan Normal University, Xinxiang 453007, People’s Republic of China
16
70 Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
17
71 Huangshan College, Huangshan 245000, People’s Republic of China
18
72 Hunan University, Changsha 410082, People’s Republic of China
19
73 Indiana University, Bloomington, Indiana 47405, USA
20
74 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati,
75 Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy
21
76 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
22
77 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
23
78 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
24
79 Justus Liebig University Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
25
80 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
26
81 Lanzhou University, Lanzhou 730000, People’s Republic of China
27
82 Liaoning University, Shenyang 110036, People’s Republic of China
28
83 Nanjing Normal University, Nanjing 210023, People’s Republic of China
29
84 Nanjing University, Nanjing 210093, People’s Republic of China
30
85 Nankai University, Tianjin 300071, People’s Republic of China
31
86 Peking University, Beijing 100871, People’s Republic of China
32
87 Seoul National University, Seoul, 151-747 Korea
33
88 Shandong University, Jinan 250100, People’s Republic of China
34
89 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
35
90 Shanxi University, Taiyuan 030006, People’s Republic of China
36
91 Sichuan University, Chengdu 610064, People’s Republic of China
37
92 Soochow University, Suzhou 215006, People’s Republic of China
38
93 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
39
94 Tsinghua University, Beijing 100084, People’s Republic of China
40
95 (A)Istanbul Aydin University, 34295 Sefakoy, Istanbul, Turkey; (B)Istanbul Bilgi
96 University, 34060 Eyup, Istanbul, Turkey; (C)Uludag University, 16059 Bursa,
97 Turkey; (D)Near East University, Nicosia, North Cyprus, 10, Mersin, Turkey
41
98 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
42
99 University of Hawaii, Honolulu, Hawaii 96822, USA
43
100 University of Minnesota, Minneapolis, Minnesota 55455, USA
44
101 University of Rochester, Rochester, New York 14627, USA
45
102 University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China
3
46
103 University of Science and Technology of China, Hefei 230026, People’s Republic of China
47
104 University of South China, Hengyang 421001, People’s Republic of China
48
105 University of the Punjab, Lahore-54590, Pakistan
49
106 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern
107 Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
50
108 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
51
109 Wuhan University, Wuhan 430072, People’s Republic of China
52
110 Zhejiang University, Hangzhou 310027, People’s Republic of China
53
111 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a
112 Also at State Key Laboratory of Particle Detection and
113 Electronics, Beijing 100049, Hefei 230026, People’s Republic of China
b
114 Also at Ankara University,06100 Tandogan, Ankara, Turkey
c
115 Also at Bogazici University, 34342 Istanbul, Turkey
d
116 Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
e
117 Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia
f
118 Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
g
119 Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
h
120 Also at University of Texas at Dallas, Richardson, Texas 75083, USA
i
121 Also at Istanbul Arel University, 34295 Istanbul, Turkey
The spin and parity of the Z ±c(3900) state are determined to be J
P = 1+ with a statistical
significance larger than 7σ over other quantum numbers in a partial wav√e analysis of the process
e+e− → π+π−J/ψ. We use a data sample of 1.92 fb−1 accumulated at s = 4.23 and 4.26 GeV
with the BESIII experiment. When parameterizing the Zc(3900)
± with a Flatté-like formula, we
determine its pole mass Mpole = (3881.2±4.2stat ±52.7 2syst) MeV/c and pole width Γpole = (51.8±
4.6stat ± 36.0syst) MeV. We also measure cross sections for the process e+e− → Z + −c(3900) π +
c.c.→ J/ψπ+π− and determine an upper limit at the 90% confidence level for the process e+e− →
Zc(4020)
+π− + c.c.→ J/ψπ+π−.
122 PACS numbers: 14.40.Rt, 13.66.Bc, 14.40.Pq
123 A charged charmoniumlike state, Z±c (Zc denotes in the process e
+e−146 → π+π−J/ψ. The results are
124 Zc(3900) throughout this Letter except when its mass is147 based on a partial wave analysis (PWA) of the e
+e− →
125 explicitly mentioned), was observed by the BESIII [1] and + −148 π π J/ψ events accumulated with the BESIII detec-
126 Belle [2] collaborations in the process e+e− → π+π−J/ψ149 tor [14]. The BESIII detector consists of a helium-gas-
127 and confirmed using CLEO-c’s data [3]. As there are at150 based drift chamber (MDC), a plastic scintillator time-
128 least four quarks in the structure, many theoretical inter-151 of-flight system, and a CsI(Tl) electromagnetic calorime-
129 pretations of the nature and the decay dynamics of the152 ter (EMC), all enclosed in a superconducting solenoidal
130 Zc have been put forward [4–9]. 153 magnet providing a 1.0-T magnetic field. The solenoid is
± 154 supported by an octagonal flux-return yoke with resistive
131 A similar charged structure, the Zc(3885) , was ob-
155 plate counter muon identifier modules interleaved with
132 served in the process e+e− → (DD̄∗)±π∓ [10], with spin
P − 156 steel. The data sample includes 1092 pb
−1 e+e− collision
133 parity (J ) assignment of 1+ favored over the 1 and √
157 data at a center-of-mass (c.m.) energy s = 4.23 GeV,
134 0− hypotheses. However, its mass and width are 2σ −1 √
± 158 and 827 pb data at s = 4.26 GeV [15]. The precise
135 and 1σ, respectively, below those of the Zc observed in
− → − 159 c.m. energies are measured with the di-muon process [16].e+e π+136 π J/ψ. Are the Z ± ±c(3885) and the Zc the
137 same state and do they have the same spin and parity? + − + −
160 The e e → π π J/ψ candidate events are se-
138 This is one of the most important pieces of information
161 lected with the same selection criteria as described in
139 desired in many theoretical analyses [6, 11]. Finally, the
162 Refs. [1, 17] with J/ψ reconstructed from lepton pairs
140 Zc(4020) was observed for the first time in the processes
(ℓ+ℓ− = µ+µ−, e+e−+ − → + − + − → ∗ ∗ ± ∓ 163 ). T√he numbers of selected can-141 e e π π hc [12] and e e (D D̄ ) π [13], but
+ − 164 d√idate events are 4154 at s = 4.23 GeV and 2447 at142 it has not been searched for in the π π J/ψ final state
165 s = 4.26 GeV; the event samples are estimated to
143 yet.
166 contain 365 and 272 background events, respectively, at
144 In this Letter, we report on the determination of spin167 these two points, using the J/ψ mass sidebands as has
145 and parity of the Zc and a search for the Zc(4020)
±
168 been done in Ref. [1].
4
Amplitudes of the PWA are constructed with the201 resonance in the fits, and the probability is calculated
helicity-covariant method [18]; the process e+e− →202 under the χ2 distribution hypothesis taking the change
π+π−J/ψ is assumed to proceed via the Zc resonance,203 of the number of degrees of freedom ∆(ndf) into account.
i.e., e+e− → Z±π∓, Z± → J/ψπ±c c , and via the non-204 With this procedure, the statistical significance of each
Zc decay e
+e− → RJ/ψ, R → π+π−. All processes205 of these states and the nonresonant process is estimated
are added coherently to obtain the total amplitude [19].206 to be larger than 5σ. All of them are therefore includ-
For a particle decaying to the two-body final state, i.e.,207 ed in the nominal fit, which includes the e+e− → σJ/ψ,
A(J,m) → B(s, λ)C(σ, ν), where spin and helicity are208 f0J/ψ, f0(1370)J/ψ, f2(1270)J/ψ, Z± ∓c π and nonreso-
indicated in the parentheses, its helicity amplitude Fλ,ν 209 nant processes.
is related to the covariant amplitude via [18, 20]
210 A simultaneous fit is performed to the two data sets.
√
211 The coupling constants are set as free parameters and are
∑ 2l+ 1 Bl(r)
Fλ,ν = glS 〈l0Sδ|Jδ〉〈sλσ − ν|Sδ〉rl , 212 allowed to be different at the two energy points except
2J + 1 Bl(r0)
lS 213 for the common ones describing Zc decays. The oppo-
(1)214 sitely charged Zc states are regarded as isospin partners;
169 where δ = λ−ν, and glS is the coupling constant in the l-215 they share a common mass and coupling parameters g′1
170 S coupling scheme, the angular brackets denote Clebsch- ′216 √and g2. Figure 1 shows projections of the fit results at
171 Gordan coefficients, r is the magnitude of the momen-217 s = 4.23 and 4.26 GeV, with fit goodness of the Dalitz
172 tum difference between the two final state particles, r 2 ±0218 plot χ /ndf =1.3 and 1.2, respectively. The mass of Zc
173 corresponds to the momentum difference at the nominal219 is measured to be MZ = (3901.5± 2.7 2c stat) MeV/c and
174 mass of the resonance, and Bl is a barrier factor [21].220 the coupling parameters g′ 21 = (0.075 ± 0.006stat) GeV
The nonresonant process, e+e− → π+π−J/ψ, is param- ′ ′175 221 and g2/g1 = 27.1 ± 2.0stat. This measurement is con-
176 eterized with an amplitude based on the QCD multipole222 sistent with the previous result g′ ′2/g1 = 27.1± 13.1 esti-
177 expansion [22]. 223 mated based on the measured decay width ratio Γ(Z±c →
∗
The relative magnitudes and phases of the complex224 (DD̄ )
±)/Γ(Z±c → J/ψπ±) = 6.2± 2.9 [10]. If the Z± is178 c
coupling constants g are determined by an unbinned225 parameterized as a constant width BW function, the si-179 lS
2
180 maximum likelihood fit to data. The minimization is226 multaneous fit gives a mass of (3897.6± 1.2stat) MeV/c
181 performed using the package minuit [23], and the back-227 and a width of (43.5 ± 1.5stat) MeV, but the value of
182 grounds are subtracted from the likelihood as in Ref. [24].228 − lnL increases by 22 with ∆(ndf) = 1. The BW
P + 229 parametrization is thus disfavored with a significance ofIn the nominal fit, we assume the Zc to have J = 1 ,
230 6.6σ.
and its lineshape is described with a Flatté-like formula
taking into account the fact that the Z±c decays are dom-231 Figure 2 shows the polar angle (θZ±) distribution ofc
inated by the final states (DD̄∗)± [10] and J/ψπ± [1],232 Z±c in the process e
+e− → Z+ −c π + c.c. and the helicity
i.e., 233 angle (θJ/ψ) distribution in the decay Z
± ±
c → π J/ψ for
234 the combined data within the Zc mass region mJ/ψπ± ∈
BW (s,M, g′
1 2
, g′ ) = , (2)235 (3.86, 3.92) GeV/c , where θJ/ψ is the angle between the1 2 s−M2 + i[g′1ρ (s) + g′1 2ρ2(s)] 236 momentum of J/ψ in the Zc rest frame and the Zc mo-
mentum in the e+e−→237 rest frame. The fit results, using dif-where the subscripts in g′ (i = 1, 2) represent the Z±183 i c √
± ∗ ± 238 ferent assumptions for the Zc spin and parity, are drawn
184 π J/ψ and (DD̄ ) decays, respectively; ρi(s) = 2ki/ s
239 with a global normalization factor. The distribution indi-
185 is a kinematic factor with ki being the magnitude of the
240 cates that data favors a spin and parity assignment of 1+
186 three-vector momentum of the final state particle (J/ψ ±
′ 241 for the Z . The significance of the Z
±(1+) hypothesis is
187 or D) in the Zc rest frame; and g1 and g
′
2 are the cou-
c c
→ 242 further examined using the hypothesis test [29], in which188 pling strengths of Z±c π±J/ψ and Z±c → (DD̄∗)±,
243 the alternative hypothesis is our nominal fit with an ad-
189 respectively, which will be determined by the fit to data. ± P +
244 ditional Zc (J =6 1 ) state. Possible JP assignments,
190 To describe the π+π− mass spectrum, four reso-
245 other than 1+, are 0−, 1−, 2−, and 2+. The changes
191 nances, σ, f0(980), f2(1270) and f0(1370), are intro-246 −2∆ lnL when the Zc(1+)π∓ amplitude is removed from
192 duced. f0(980) is described with a Flatté formula [25],247 the alternative hypothesis are listed in Table I. Using the
193 and the others are described with relativistic Breit-
248 associated change in the ndf when the Z±c (1
+) is exclud-
194 Wigner (BW) functions. The width of the wide resonance
249 ed, we determine the significance of the 1+ hypothesis
√
4m2
σ is parameterized with Γ (s) = 1− πΓ [26, 27],250 over the alternative JP possibilities to be larger than 7σ.195 σ s
196 and the masses and widths for the f2(1270) and f0(1370)251 The fit results shown in Fig. 1 indicate that process
197 are taken from the Particle Data Group (PDG) [28]. The252 is dominated by the ππ S−wave resonances, i.e. the σ,
198 statistical significance for each resonance is determined253 f0(980) and f0(1370). The fraction of all π
+π− S-wave
199 by examining the probability of the change in log likeli-254 components including the interference between them is
200 hood (logL) values between including and excluding this255 measured to be (61.7 ± 2.1stat)% of the total π+π−J/ψ
5
400
ππ S-Wave J/ψ
300 ππ S-Wave J/ψ (a) 350 f2(1270) J/ψ (b)
f2(1270) J/ψ Z
+
cπ-+c.c.
250 300
+ - totalZcπ +c.c.
200 250total
200
150
150
100
100
50 50
0 0
0.2 0.4 0.6 0.8 1.0 1.2 3.2 3.4 3.6 3.8 4.0 4.2
mπ+π- (GeV/c
2) mJ/ψπ± (GeV/c
2)
180 200
ππ S-Wave J/ψ
160 ππ S-Wave J/ψ 180
(c) f2(1270) J/ψ (d)
140 f (1270) J/ψ 160 Z+ -2 cπ +c.c.
+ - total120 Zcπ +c.c. 140
120
100 total
100
80
80
60 60
40 40
20 20
0 0
0.2 0.4 0.6 0.8 1.0 1.2 3.2 3.4 3.6 3.8 4.0 4.2
mπ+π- (GeV/c
2) m 2J/ψπ± (GeV/c )
√
FIG. 1: (co√lor online) Projections tomπ+π− (a, c) andmJ/ψπ± (b, d) of the fit results with J
P = 1+ for the Zc, at s = 4.23 GeV
(a, b) and s = 4.26 GeV (c, d). The points with error bars are data, and the black histograms are the total fit results including
backgrounds. The shaded histogram denotes backgrounds. The contributions from the π+π− S-wave J/ψ, f2(1270)J/ψ, and
Z±π∓, are shown in the plots. The π+π−c S-wave resonances include the σ, f0(980) and f0(1370). Plots (b) and (d) are filled
with two entries (mJ/ψπ+ and mJ/ψπ−) per event.
259 signal events. They are measured to be N ± = 952.3 ±
TABLE I: Significance of the spin parity 1+ over other quan- √ Zc √
260 39.3 at s = 4.23 GeV and 343.3± 23.3 at s =
tum numbers for Z±c . The significance is obtained for given
stat stat
change in ndf, ∆(ndf). In each case, ∆(ndf) = 2×4+5, where261 4.26 GeV. Here, the errors are statistical only, and they
2×4 ndf account for the coupling strength for e+e− → Z±π∓262 are estimated using the covariance matrix from the fits.c
at the two data sets, and the additional five ndf are the contri-
bution of the common degrees of freedom for the Zc resonant
± → ± 263 To measure amplitudes associated with the polariza-parameters and the coupling strength for Zc J/ψπ .
264 tion of Z± in e+e− → Z±c c π∓ and that of J/ψ in
Hypothesis ∆(−2 lnL) ∆(ndf) Significance ± ±
265 Zc → J/ψπ decays in the nominal fit, the ratios of
1+ over 0− 94.0 13 7.6σ
266 helicity amplitudes with different polarizations as de-
1+ over 1− 158.3 13 10.8σ
+ − 267 fined in Eq. (1) are calculated to be |FZc1,0|2/|FZc |2 =1 over 2 151.9 13 10.5σ 0,0
1+ over 2+ 96.0 13 7.7σ 268 0.22±0.05stat at 4.23 GeV, and 0.21±0.11stat at 4.26 GeV
269 for e+e− → Z± ∓c π , and |Fψ |2 ψ 21,0 /|F0,0| = 0.45 ± 0.15stat
for Z±
Z /ψ
270 c → J/ψπ±, at both energy points. Here F c1,0
Z /ψ
√ √ 271 and F
c
0,0 correspond to transverse and longitudinal po-
256 events at s = 4.23 GeV and (71.4± 4.1stat)% at s =272 larization amplitudes in the decay, respectively. The re-
257 4.26 GeV. The signal yields N of Z±Z± c are calculated by273 sults show that the Zc polarization is dominated by the
c
258 scaling its partial signal ratio with the total number of274 longitudinal component.
EVENTS / 0.02 GeV/c2 EVENTS / 0.02 GeV/c2
EVENTS / 0.015 GeV/c2 EVENTS / 0.015 GeV/c2
6
310 estimated by comparing the nominal fit with two oth-
400 500
450 311 er parameterizations, the PKU ansatz [30] and the Zou-
350 400 312 Bugg approach [31]. The differences in the Zc signal
350 313 yields and mass measurement are taken as the errors,
300 300 314 which are 2.5% (31.0%) for the signal yields at 4.23
250
315 (4.26) GeV and 19.5 MeV for the Zc mass.
250 200
- 150 - 316 The uncertainty due to the f0(980) lineshape is esti-0 2- 0 -
1- 1-
2
200 1+ 2
+ 100 + 2+ 317 mated by varying the couplings by 1σ as determined in1
50 318 the decays J/ψ → φπ+π− and φK+K− [25]. Uncer-
(a) (b)
150 0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 319 tainties associated with the f0(1370) are estimated by
|cos(θ )| |cos(θ )| 320 varying the mass and width by one standard deviationZ±c J/ψ
321 around the world average values [28].
± 322 The uncertainty due to the Zc parametrization is es-FIG. 2: (color online) (a) Polar angle distribution of Zc in the
process e+e− → Z+π− + c.c., (b) helicity angle distribution323 timated by using a constant-width relativistic BW func-c
of J/ψ in the Z± → π±J/ψ. The dots with error bars show324 tion. The simultaneous fit gives the Zc mass of (3897.6±c
the combined data with requirement mJ/ψπ± ∈ (3.86, 3.92)325 1.2stat) MeV/c2 and the width of (43.5 ± 1.5stat) MeV.
GeV/c2, and compared to the total fit results with different326 The difference in the Zc signal yields is 15.5% (7.9%) for
JP hypotheses. 327 the data taken at 4.23 (4.26) GeV.
328 The uncertainty due to the background level is esti-
The Born cross section for Z production is measured329 mated by changing the number of background events by275 c
with the relation σ = N /(L(1 + δ)ǫB), where N is330 1σ around the nominal value, that is, ±25 around 637276 Z± Z±c c
+ − → + − →331 events.277 the signal yield for the process e e Zc π + c.c.
+ −
278 π π J/ψ, L is the integrated luminosity, and ǫ is the332 The barrier radius is usually taken in the range r0 ∈
279 detection efficiency obtained from a MC simulation which333 (0.25, 0.76) fm, with 0.6 fm being used in the nominal fit.
is generated using the amplitude parameters determined334 Uncertainties at both ends are checked. For a conserva-280
in the PWA. The radiative correction factor (1 + δ) is335 tive estimation, the radius r0 = 0.76 fm, which results in281
282 determined to be 0.818 [1]. The Bo√rn cross section is336 the larger difference, is used to estimate the uncertainty.
283 measured to be (22.0±√1.0stat) pb at s = 4.23 GeV and337 The uncertainty due to the mass resolution in the J/ψπ
284 (11.0± 1.2stat) pb at s = 4.26 GeV. 338 invariant mass is estimated with an unfolded Zc width.
285 Using these two data sets, we also search for the pro-339 A truth width is unfolded from the observed Zc width
cess e+e− → Z (4020)+π− + c.c. → π+ −286 c π J/ψ, with the340 using a relation determined by the MC simulation, and
287 Zc(4020)
± assumed to be a 1+ state. In the PWA, its341 its difference from the unfolded width, δΓ/Γ = δg
′ /g′1 1, is
288 mass is taken from Ref. [12], and its width is taken as the342 taken as the systematic uncertainty for the coupling con-
′
289 observed value, which includes the detector resolution.343 stant g1. The uncertainties in the signal yields and the Zc
290 The statistical significance for Z (4020)± → J/ψπ±c is344 mass are determined with the truth coupling constant.
291 found to be 3σ in the combined data. The Born cross345 The nonresonant process is described with a formula
292 sections are measured to be (0.2 ± 0.1stat) pb at 4.23346 derived from the QCD multipole expansion [22]. It in-
293 GeV and (0.8± 0.4stat) pb at s = 4.26 GeV, and the cor-347 cludes the S- and D-wave components. The uncertainty
294 responding upper limits at the 90% confidence level are348 associated with this amplitude is estimated by remov-
295 estimated to be 0.9 pb and 1.4 pb, respectively. 349 ing the insignificant D-wave component and using the
296 Systematic errors associated with the event selection,350 S-wave component only.
297 including the luminosity measurement, tracking efficien-
351 Table II summarizes the systematic uncertainties. As-
298 cy of charged tracks, kinematic fit, initial state radia-
352 suming all of these sources are independent, the total sys-
299 tion (ISR) correction factor and the branching fraction
353 tematic uncertainties are 38.0 MeV for the measurement
300 of Br(J/ψ → ℓ+ℓ−), have been estimated to be 4.8% for
354 of the Zc mass, and 20.√3% (49.2%) for the measurement
301 the cross section measurement and 1.8 MeV for the Zc355 of Zc cross sections at s = 4.23 (4.26) GeV.
302 mass in the previous analysis [1]. √
356 In summary, with 1.92 fb−1 data taken at s = 4.23
303 Uncertainties associated with the amplitude analy-
357 and 4.26 GeV, the Z±c state is studied with an am-
304 sis come from the σ and Zc parametrizations, the358 plitude fit to the e+e− → π+π−J/ψ samples, and
305 background estimation, the parameters in the f0(980)359 its spin and parity have been determined to be 1+
306 Flatté formula, the barrier radius in the barrier factor,
360 with a statistical significance larger than 7σ over oth-
307 the mass resolution and the component of non-resonant
361 er quantum numbers. The mass is measured to be
308 amplitude.
362 MZ = (3901.5 ± 2.7 2c stat ± 38.0syst) MeV/c in the
309 The systematic uncertainty due to the σ lineshape is363 parametrization of a Flatté-like formula with parameters
EVENTS / 0.2
EVENTS / 0.2
7
400 [2] Z. Q. Liu et al. (Belle Collaboration), Phys. Rev. Lett.
TABLE II: Summary of systematic uncertainties on the
P + 2 ′ 2 401 110, 252002 (2013).Zc (J = 1 ) mass MZ (MeV/c ), parameters g1 (GeV )c
′ ′ I 402 [3] T. Xiao, S. Dobbs, A. Tomaradze and K. K. Seth, Phys.and g2/g1, and the signal yields at 4.23 GeV (NZ ) and 4.26c 403 Lett. B 727, 366 (2013).
GeV (N IIZ ). The uncertainties shown for the Zc mass, pa-c 404 [4] N. Brambilla et al., Eur. Phys. J. C 74, 2981 (2014).
rameter g′1 and the ratio g
′
2/g
′
1 are absolute values, while the405 [5] G. T. Bodwin et al., arXiv:1307.7425.
uncertainties for N I and N IIZ Z are relative ones.c c 406 [6] M. B. Voloshin, Phys. Rev. D 87, 091501(R) (2013).
407 [7] A. Esposito et al., Int. J. Mod. Phys. A 30, 1530002
Sources M g′ × 103 g′ /g′ I IIZ 1 2 1 NZ (%) NZ (%) 408 (2014).c c c
Event selection 1.8 ... ... 4.8 4.8 409 [8] X. Liu, Chin. Sci. Bull. 59, 3815 (2014).
σ lineshape 19.5 12.0 0.3 2.5 31.0 410 [9] F.-K. Guo, C. Hidalgo-Duque, J. Nieves and M. Pavon
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Backgrounds 13.9 8.0 0.1 1.9 9.3 412 [10] M. Ablikim et al. (BESIII Collaboration), Phys. Rev.
f0(980), g1, g2/g1 17.5 14.0 0.6 2.4 24.6 413 Lett. 112, 022001 (2014).
f0(1370) 16.7 11.0 0.4 11.5 14.0 414 [11] E. Braaten, Phys. Rev. Lett. 111, 162003 (2013).
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Total 38.0 24.8 1.9 20.3 49.2 418 Lett. 112, 132001 (2014).
419 [14] M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum.
420 Meth. A 614, 345 (2010).
421 [15] M. Ablikim et al. (BESIII Collaboration), Chin. Phys. C
′
364 g = 0.075 ± 0.006stat ± 0.025 2 ′ ′syst GeV , and g /g =422 39, 093001 (2015).1 2 1
365 27.1± 2.0stat ± 1.9syst, which corresponds to the Z pole423 [16] M. Ablikim et al. (BESIII Collaboration), Chin. Phys. Cc
366 mass Mpole = (3881.2 ± 4.2stat ± 52.7 2 424 40, 063001 (2016).syst) MeV/c and
± 425 [17] M. Ablikim et al. (BESIII Collaboration), Phys. Rev.367 pole width Γpole = (51.8 4.6stat± 36.0syst) MeV, where
368 Mpole−
426 Lett. 118, 092001 (2017).
iΓpole/2 is the solution for which the denominator
427 [18] S. U. Chung, Phys. Rev. D 57, 431 (1998); S. U.
369 of Flatté-like formula is zero. The pole mass is consistent
428 Chung, Phys. Rev. D 48, 1225 (1993); S. U. Chung and
370 with the previous measurement [10]. The Born cross sec-429 J. M. Friedrich, Phys. Rev. D 78, 074027 (2008).
+ − + −
371 tions for the process e e → π Z √+ c.c. are measured430 [19] H. Chen and R. G. Ping, Phys. Rev. D 95, 076010 (2017).c
372 to be (21.8± 1.0 ± 4.4 ) pb at s = 4.23 GeV and431 [20] V. Filippini, A. Fontana and A. Rotondi, Phys. Rev. Dstat syst
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375 significant signals are observed, and an upper limit for
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The BESIII collaboration thanks the staff of BEPCII438 [23] F. James, CERN Program Library Long Writeup D 506378
379 and the computing center for their strong support. This439 (1998).
440 [24] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D
380 work is supported in part by the Ministry of Science and
441 86, 072011 (2012).
381 Technology of China under Contract No. 2009CB825200;
442 [25] M. Ablikim et al. (BES Collaboration), Phys. Lett. B
382 Joint Funds of the National Natural Science Foundation443 598, 149 (2004).
383 of China under Contracts Nos. U1332201; National Nat-444 [26] S. M. Berman and M. Jacob, Phys. Rev. B 139, 1608
384 ural Science Foundation of China (NSFC) under Con-445 (1965).
tracts Nos. 11175188, 11375205, 11235011, 11375221,446 [27] M. Ablikim et al. (BES Collaboration), Phys. Lett. B385
11565006, 10825524; German Research Foundation DFG447 645, 19 (2007).386
448 [28] K. A. Olive et al. (Particle Data Group), Chin. Phys. C
387 under Contract No. Collaborative Research Center CRC-
449 38, 090001 (2014).
388 1044, 627240; Istituto Nazionale di Fisica Nucleare, Italy;
450 [29] I. Narsky, Nucl. Instrum. Meth. A 450, 444 (2000); Y. S.
389 Ministry of Development of Turkey under Contract No.451 Zhu, High Energy Physics and Nuclear Physics 30, 331
390 DPT2006K-120470; U.S. Department of Energy under452 (2006).
Contracts Nos. DE-SC-0012069, DE-SC-0010504, DE-453 [30] H. Q. Zheng et al., Nucl. Phys. A 733, 235 (2004).391
SC-0010118, DE-FG02-05ER41374; U.S. National Sci-454 [31] B. S. Zou and D. V. Bugg, Phys. Rev. D 48, 3948 (1993).392
ence Foundation; University of Groningen (RuG) un-455 M. Ablikim et al. (BES Collaboration), Phys. Lett. B,393
456 598 149 (2004).
394 der Contracts No. 530-4CDP03, and the Helmholtzzen-
395 trum fuer Schwerionenforschung GmbH (GSI), Darm-
396 stadt; WCU Program of National Research Foundation
397 of Korea under Contract No. R32-2008-000-10155-0.
398 [1] M. Ablikim et al. (BESIII Collaboration), Phys. Rev.
399 Lett. 110, 252001 (2013).