This is the accepted manuscript made available via CHORUS. The article has been
published as:
Observation of the doubly radiative decay η^{′}→γγπ^{0}
M. Ablikim et al. (BESIII Collaboration)
Phys. Rev. D 96, 012005 — Published 26 July 2017
DOI: 10.1103/PhysRevD.96.012005
Observation of the doubly radiative decay ′ 0η → γγπ
M. Ablikim1, M. N. Achasov9,d, S. Ahmed14, X. C. Ai1, O. Albayrak5, M. Albrecht4, D. J. Ambrose45, A. Amoroso50A,50C ,
F. F. An1, Q. An47,38, J. Z. Bai1, O. Bakina23, R. Baldini Ferroli20A, Y. Ban31, D. W. Bennett19, J. V. Bennett5,
N. Berger22, M. Bertani20A, D. Bettoni21A, J. M. Bian44, F. Bianchi50A,50C , E. Boger23,b, I. Boyko23, R. A. Briere5, H. Cai52,
X. Cai1,38, O. Cakir41A, A. Calcaterra20A , G. F. Cao1,42 , S. A. Cetin41B , J. F. Chang1,38, G. Chelkov23,b,c, G. Chen1,
H. S. Chen1,42, J. C. Chen1, M. L. Chen1,38, S. Chen42, S. J. Chen29, X. Chen1,38, X. R. Chen26, Y. B. Chen1,38, X. K. Chu31,
G. Cibinetto21A, H. L. Dai1,38, J. P. Dai34,h, A. Dbeyssi14, D. Dedovich23, Z. Y. Deng1, A. Denig22, I. Denysenko23,
M. Destefanis50A,50C , F. De Mori50A,50C , Y. Ding27, C. Dong30, J. Dong1,38, L. Y. Dong1,42, M. Y. Dong1,38,42, Z. L. Dou29,
S. X. Du54, P. F. Duan1, J. Z. Fan40, J. Fang1,38, S. S. Fang1,42, X. Fang47,38, Y. Fang1, R. Farinelli21A,21B , L. Fava50B,50C ,
F. Feldbauer22, G. Felici20A, C. Q. Feng47,38, E. Fioravanti21A, M. Fritsch22,14, C. D. Fu1, Q. Gao1, X. L. Gao47,38 , Y. Gao40,
Z. Gao47,38 , I. Garzia21A , K. Goetzen10, L. Gong30, W. X. Gong1,38, W. Gradl22, M. Greco50A,50C , M. H. Gu1,38, Y. T. Gu12,
Y. H. Guan1, A. Q. Guo1, L. B. Guo28, R. P. Guo1, Y. Guo1, Y. P. Guo22, Z. Haddadi25, A. Hafner22, S. Han52, X. Q. Hao15,
F. A. Harris43, K. L. He1,42, F. H. Heinsius4, T. Held4, Y. K. Heng1,38,42, T. Holtmann4, Z. L. Hou1, C. Hu28, H. M. Hu1,42,
J. F. Hu50A,50C , T. Hu1,38,42, Y. Hu1, G. S. Huang47,38, J. S. Huang15, X. T. Huang33, X. Z. Huang29, Z. L. Huang27,
T. Hussain49, W. Ikegami Andersson51, Q. Ji1, Q. P. Ji15, X. B. Ji1,42, X. L. Ji1,38, L. W. Jiang52, X. S. Jiang1,38,42 ,
X. Y. Jiang30 , J. B. Jiao33 , Z. Jiao17 , D. P. Jin1,38,42 , S. Jin1,42, T. Johansson51, A. Julin44, N. Kalantar-Nayestanaki25,
X. L. Kang1, X. S. Kang30, M. Kavatsyuk25, B. C. Ke5, P. Kiese22, R. Kliemt10, B. Kloss22, O. B. Kolcu41B,f , B. Kopf4,
M. Kornicer43, A. Kupsc51, W. Kühn24, J. S. Lange24, M. Lara19, P. Larin14, H. Leithoff22, C. Leng50C , C. Li51,
Cheng Li47,38, D. M. Li54, F. Li1,38, F. Y. Li31, G. Li1, H. B. Li1,42, H. J. Li1, J. C. Li1, Jin Li32, K. Li33, K. Li13, Lei Li3,
P. R. Li42,7, Q. Y. Li33, T. Li33, W. D. Li1,42, W. G. Li1, X. L. Li33, X. N. Li1,38, X. Q. Li30, Y. B. Li2, Z. B. Li39,
H. Liang47,38, Y. F. Liang36, Y. T. Liang24, G. R. Liao11, D. X. Lin14, B. Liu34,h, B. J. Liu1, C. X. Liu1, D. Liu47,38,
F. H. Liu35, Fang Liu1, Feng Liu6, H. B. Liu12, H. H. Liu16, H. H. Liu1, H. M. Liu1,42, J. Liu1, J. B. Liu47,38, J. P. Liu52,
J. Y. Liu1, K. Liu40, K. Y. Liu27, L. D. Liu31, P. L. Liu1,38, Q. Liu42, S. B. Liu47,38, X. Liu26, Y. B. Liu30, Y. Y. Liu30,
Z. A. Liu1,38,42, Zhiqing Liu22, H. Loehner25, X. C. Lou1,38,42, H. J. Lu17, J. G. Lu1,38, Y. Lu1, Y. P. Lu1,38, C. L. Luo28,
M. X. Luo53, T. Luo43, X. L. Luo1,38, X. R. Lyu42, F. C. Ma27, H. L. Ma1, L. L. Ma33, M. M. Ma1, Q. M. Ma1, T. Ma1,
X. N. Ma30, X. Y. Ma1,38, Y. M. Ma33, F. E. Maas14 , M. Maggiora50A,50C , Q. A. Malik49, Y. J. Mao31, Z. P. Mao1,
S. Marcello50A,50C , J. G. Messchendorp25, G. Mezzadri21B , J. Min1,38, T. J. Min1, R. E. Mitchell19, X. H. Mo1,38,42 ,
Y. J. Mo6, C. Morales Morales14 , N. Yu. Muchnoi9,d, H. Muramatsu44, P. Musiol4, Y. Nefedov23, F. Nerling10,
I. B. Nikolaev9,d, Z. Ning1,38, S. Nisar8, S. L. Niu1,38, X. Y. Niu1, S. L. Olsen32, Q. Ouyang1,38,42, S. Pacetti20B , Y. Pan47,38,
M. Papenbrock51, P. Patteri20A, M. Pelizaeus4, H. P. Peng47,38, K. Peters10,g , J. Pettersson51, J. L. Ping28, R. G. Ping1,42,
R. Poling44 , V. Prasad1, H. R. Qi2, M. Qi29, S. Qian1,38, C. F. Qiao42, L. Q. Qin33, N. Qin52, X. S. Qin1, Z. H. Qin1,38,
J. F. Qiu1, K. H. Rashid49,i, C. F. Redmer22, M. Ripka22, G. Rong1,42, Ch. Rosner14, X. D. Ruan12, A. Sarantsev23,e,
M. Savrié21B , C. Schnier4, K. Schoenning51, W. Shan31, M. Shao47,38, C. P. Shen2, P. X. Shen30, X. Y. Shen1,42,
H. Y. Sheng1, W. M. Song1, X. Y. Song1, S. Sosio50A,50C , S. Spataro50A,50C , G. X. Sun1, J. F. Sun15, S. S. Sun1,42,
X. H. Sun1, Y. J. Sun47,38, Y. Z. Sun1, Z. J. Sun1,38, Z. T. Sun19, C. J. Tang36, X. Tang1, I. Tapan41C , E. H. Thorndike45,
M. Tiemens25 , I. Uman41D, G. S. Varner43, B. Wang30, B. L. Wang42, D. Wang31, D. Y. Wang31, K. Wang1,38, L. L. Wang1,
L. S. Wang1, M. Wang33, P. Wang1, P. L. Wang1, W. Wang1,38, W. P. Wang47,38, X. F. Wang40, Y. Wang37, Y. D. Wang14,
Y. F. Wang1,38,42 , Y. Q. Wang22, Z. Wang1,38, Z. G. Wang1,38, Z. H. Wang47,38, Z. Y. Wang1, Z. Y. Wang1, T. Weber22,
D. H. Wei11, P. Weidenkaff22, S. P. Wen1, U. Wiedner4, M. Wolke51, L. H. Wu1, L. J. Wu1, Z. Wu1,38, L. Xia47,38, L. G. Xia40,
Y. Xia18, D. Xiao1, H. Xiao48, Z. J. Xiao28, Y. G. Xie1,38, Y. H. Xie6, Q. L. Xiu1,38, G. F. Xu1, J. J. Xu1, L. Xu1, Q. J. Xu13,
Q. N. Xu42, X. P. Xu37, L. Yan50A,50C , W. B. Yan47,38, W. C. Yan47,38, Y. H. Yan18, H. J. Yang34,h, H. X. Yang1, L. Yang52,
Y. X. Yang11, M. Ye1,38, M. H. Ye7, J. H. Yin1, Z. Y. You39, B. X. Yu1,38,42, C. X. Yu30, J. S. Yu26, C. Z. Yuan1,42,
Y. Yuan1, A. Yuncu41B,a, A. A. Zafar49, Y. Zeng18, Z. Zeng47,38, B. X. Zhang1, B. Y. Zhang1,38, C. C. Zhang1,
D. H. Zhang1, H. H. Zhang39, H. Y. Zhang1,38, J. Zhang1, J. J. Zhang1, J. L. Zhang1, J. Q. Zhang1, J. W. Zhang1,38,42,
J. Y. Zhang1, J. Z. Zhang1,42, K. Zhang1, L. Zhang1, S. Q. Zhang30, X. Y. Zhang33, Y. Zhang1, Y. H. Zhang1,38,
Y. N. Zhang42, Y. T. Zhang47,38, Yu Zhang42, Z. H. Zhang6, Z. P. Zhang47, Z. Y. Zhang52, G. Zhao1, J. W. Zhao1,38,
J. Y. Zhao1, J. Z. Zhao1,38, Lei Zhao47,38, Ling Zhao1, M. G. Zhao30, Q. Zhao1, Q. W. Zhao1, S. J. Zhao54, T. C. Zhao1,
Y. B. Zhao1,38, Z. G. Zhao47,38, A. Zhemchugov23,b, B. Zheng48,14, J. P. Zheng1,38, W. J. Zheng33, Y. H. Zheng42,
B. Zhong28, L. Zhou1,38, X. Zhou52, X. K. Zhou47,38, X. R. Zhou47,38, X. Y. Zhou1, K. Zhu1, K. J. Zhu1,38,42, S. Zhu1,
S. H. Zhu46, X. L. Zhu40, Y. C. Zhu47,38, Y. S. Zhu1,42, Z. A. Zhu1,42, J. Zhuang1,38, L. Zotti50A,50C , 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
2
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 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
23 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
24 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
25 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
26 Lanzhou University, Lanzhou 730000, People’s Republic of China
27 Liaoning University, Shenyang 110036, People’s Republic of China
28 Nanjing Normal University, Nanjing 210023, People’s Republic of China
29 Nanjing University, Nanjing 210093, People’s Republic of China
30 Nankai University, Tianjin 300071, People’s Republic of China
31 Peking University, Beijing 100871, People’s Republic of China
32 Seoul National University, Seoul, 151-747 Korea
33 Shandong University, Jinan 250100, People’s Republic of China
34 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
35 Shanxi University, Taiyuan 030006, People’s Republic of China
36 Sichuan University, Chengdu 610064, People’s Republic of China
37 Soochow University, Suzhou 215006, People’s Republic of China
38 State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of China
39 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
40 Tsinghua University, Beijing 100084, People’s Republic of China
41 (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
42 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
43 University of Hawaii, Honolulu, Hawaii 96822, USA
44 University of Minnesota, Minneapolis, Minnesota 55455, USA
45 University of Rochester, Rochester, New York 14627, USA
46 University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China
47 University of Science and Technology of China, Hefei 230026, People’s Republic of China
48 University of South China, Hengyang 421001, People’s Republic of China
49 University of the Punjab, Lahore-54590, Pakistan
50 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern
Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
51 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
52 Wuhan University, Wuhan 430072, People’s Republic of China
53 Zhejiang University, Hangzhou 310027, People’s Republic of China
54 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at Bogazici University, 34342 Istanbul, Turkey
b Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
c Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia
d Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
e Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
f Also at Istanbul Arel University, 34295 Istanbul, Turkey
g Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany
h 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
i Government College Women University, Sialkot - 51310. Punjab, Pakistan.
Based on a sample of 1.31 billion J/ψ events collected with the BESIII detector, we report the
study of the doubly radiative decay η′ → γγπ0 for the first time, where the η′ meson is produced via
the J/ψ → γη′ decay. The branching fraction of η′ → γγπ0 inclusive decay is measured to be B(η′ →
γγπ0)Incl. = (3.20 ± 0.07(stat) ± 0.23(sys)) 10
−3
× , while the branching fractions of the dominant
process η′ → γω and the non-resonant component are determined to be B(η′ → γω)×B(ω → γπ0) =
3
(23.7 ± 1.4(stat) ± 1.8(sys)) 10−4× and B(η′ → γγπ0)NR = (6.16 ± 0.64(stat) ± 0.67(sys)) × 10
−4,
respectively. In addition, the M2γγ -dependent partial widths of the inclusive decay are also presented.
PACS numbers: 13.40.Gp, 13.40.Hq, 13.20.Jf, 14.40.Be
I. INTRODUCTION helicity amplitude formalism. For the non-resonant η′ →
γγπ0 decay, the VMD model [7, 8] is used to generate the
MC sample with ρ(1450)- or ω(1650)-exchange. Inclusive
The η′ meson provides a unique stage for understand- J/ψ decays are generated with kkmc [15] generator; the
ing the distinct symmetry-breaking mechanisms present known J/ψ decay modes are generated by evtgen [14]
in low-energy Quantum Chromodynamics (QCD) [1–5] with branching fractions setting at Particle Data Group
and its decays play an important role in exploring the (PDG) world average values [16]; the remaining unknown
effective theory of QCD at low energy [6]. Recently, the decays are generated with lundcharm [17].
doubly radiative decay η′ → γγπ0 was studied in the
frameworks of the Linear σ Model (LσM) and the Vec-
tor Meson Dominance (VMD) model [7, 8]. It has been
demonstrated that the contributions from the VMD are III. EVENT SELECTION AND BACKGROUND
dominant. Experimentally, only an upper limit of the ESTIMATION
non-resonant branching fraction of B(η′ → γγπ0)NR <
8×10−4 at the 90% confidence level has been determined
by the GAMS-2000 experiment [9]. Electromagnetic showers are reconstructed from clus-
ters of energy deposits in the electromagnetic calorime-
In this article, we report the first measurement of the ter (EMC). The energy deposited in nearby time-of-light
branching fraction of the inclusive η′ → γγπ0 decay and (TOF) counters is included to improve the reconstruction
the determination of the M2γγ dependent partial widths, efficiency and energy resolution. The photon candidate
whereMγγ is the invariant mass of the two radiative pho- showers must have a minimum energy of 25 MeV in the
tons. The inclusive decay is defined as the η′ decay into barrel region (| cos θ| < 0.80) or 50 MeV in the end cap
the final state γγπ0 including all possible intermediate region (0.86 < | cos θ| < 0.92). Showers in the region
contributions from the ρ− and ω−mesons below the η′ between the barrel and the end caps are poorly mea-
mass threshold and the non-resonant contribution from sured and excluded from the analysis. In this analysis,
the excited vector meson above the η′ mass threshold. only the events without charged particles are subjected
Since the contribution from mesons above the η′ thresh- to further analysis. The average event vertex of each run
old actually derives from the low-mass tail and looks like is assumed as the origin for the selected candidates. To
a contact term, we call this contribution ’non-resonant’. select J/ψ → γη′, η′ → γγπ0 (π0 → γγ) signal events,
The branching fraction for the non-resonant η′ → γγπ0 only the events with exactly five photon candidates are
decay is obtained from a fit to the γπ0 invariant mass dis- selected.
tribution by excluding the coherent contributions from
the ρ and ω intermediate states. The measurement of To improve resolution and reduce background, a
the M2γγ dependent partial widths will provide direct in-
five-constraint kinematic (5C) fit imposing energy-
puts to the theoretical calculations on the transition form momentum conservation and a π
0 mass constraint is per-
0 0
factors of η′ → γγπ0 and improve the theoretical under- formed to the γγγπ hypothesis, where the π candidate
standing of the η′ decay mechanisms. is reconstructed with a pair of photons. For events with
more than one π0 candidate, the combination with the
smallest χ25c is selected. Only events with χ
2
5c < 30 are
retained. The χ25C distribution is shown in Fig. 1 withII. EXPERIMENTAL DETAILS
events in the η′ signal region of |Mγγπ0 −Mη′| < 25 MeV
(Mη′ is the η
′ nominal mass from PDG [16]). In order to
The source of η′ mesons is the radiative J/ψ → γη′ suppress the multi-π0 backgrounds and remove the mis-
decay in a sample of 1.31× 109 J/ψ events [10, 11] col- combined π0 candidates, an event is vetoed if any two of
lected by the BESIII detector. Details on the features five selected photons (except for the combination for the
and capabilities of the BESIII detector can be found in π0 candidate) satisfies |M 2γγ−Mπ0 | < 18 MeV/c , where
Ref. [12]. M 0π0 is the π nominal mass. After the application of the
above requirements, the most energetic photon is taken
The response of the BESIII detector is modeled with
as the primary photon from the J/ψ decay, and the re-
a Monte Carlo (MC) simulation based on geant4 [13].
maining two photons and the π0 are used to reconstruct
The program evtgen [14] is used to generate a J/ψ →
′ the η
′ candidates. Figure 2 shows the γγπ0 invariant
γη MC sample with an angular distribution of 1+cos2 θγ , mass spectrum.
where θγ is the angle of the radiative photon relative to
the positron beam direction in the J/ψ rest frame. The Detailed MC studies indicate that no peaking back-
decays η′ → γω(ρ), ω(ρ) → γπ0 are generated using the ground remains after all the selection criteria. The
4
IV. SIGNAL YIELDS AND BRANCHING
FRACTIONS
Signal + BG
600 η’→γγπ0
Class I background A fit to the γγπ0 invariant mass distribution is per-
Class II background formed to determine the inclusive η′ → γγπ0 signal yield.
400 The probability density function (PDF) for the signal
component is represented by the signal MC shape, which
is obtained from the signal MC sample generated with an
200 incoherent mixture of ρ, ω and the non-resonant compo-
nents according to the fractions obtained in this analysis.
Both the shape and the yield for the Class I background
are fixed to the MC simulations and their expected inten-
0
0 20 40 60 80 100 sities. The shape for the Class II background is described
χ
5C by a third-order Chebychev Polynomial, and the corre-
sponding yield and PDF parameters are left free in the
2
FIG. 1: Distribution of the χ2 of the 5C kinematic fit for fit to data. The fit range is 0.70− 1.10 GeV/c . Figure 25C
the inclusive η′ decay. Dots with error bars are data; the shows the results of the fit. The fit quality assessed with
heavy (black) solid-curve is the sum of signal and expected the binned distribution is χ
2/n.d.f = 108/95 = 1.14. The
backgrounds from MC simulations; the light (red) solid-curves signal yield and the MC-determined signal efficiency for
is signal components which are normalized to the fitted yields; the inclusive η′ decay are summarized in Table I.
the (green) dotted-curve is the Class I background; and the
(pink) dot-dashed-curve is the Class II background. In this analysis, the partial widths can be obtained
by studying the efficiency-corrected signal yields for each
given M2 bin i for the inclusive η′ → γγπ0γγ decay. The
resolution inM2γγ is found to be about 5×10
2 (MeV/c2)2
800
from the MC simulation, which is much smaller than
Global fit 1.0×104 (MeV/c2)2, a statistically reasonable bin width,
η’→γγπ0 and hence no unfolding is necessary. The η′ signal yield in
600 Class I background
eachM2γγ bin is obtained by performing bin-by-bin fits toClass II background
the γγπ0 invariant mass distributions using the fit proce-
dure described above. Thus the background-subtracted,
400
efficiency-corrected signal yield can be used to obtain the
partial width for each givenM2γγ interval, where the PDG
value is used for the total width of the η′ meson [16]. The
200
results for dΓ(η′ → γγπ0)/dM2γγ in eachM
2
γγ interval are
listed in Table II and depicted in Fig. 3, where the con-
tributions from each component obtained from the MC
0
0.7 0.8 0.9 1 1.1 simulations are normalized with the yields by fitting to
M  (GeV/c2γγπ0 ) Mγπ0 as displayed in Fig. 4.
Assuming that the inclusive decay η′ → γγπ0 can
FIG. 2: Results of the fit to Mγγπ0 for the selected inclusive be attributed to the vector mesons ρ and ω and the
η′ 0→ γγπ signal events. The (black) dots with error bars are non-resonant contribution, we apply a fit to the γπ0
the data. invariant mass to determine the branching fraction for
the non-resonant η′ → γγπ0 decay using the η′ signal
events with |Mγγπ0 − mη′ | < 25 MeV/c
2. In the fit,
sources of backgrounds are divided into two classes. the ρ-ω interference is considered, but possible interfer-
Background events of Class I are from J/ψ → γη′ with ence between the ω (ρ) and the non-resonant process is
η′ decaying into final states other than the signal final neglected. To validate our fit, we also determine the
′
states. These background events accumulate near the product branching fraction for the decay chain η → γω,
0
lower side of the η′ signal region and are mainly from ω → γπ . Figure 4 shows the Mγπ0 distribution. Since
η′ → π0π0η (η → γγ), η′ → 3π0 and η′ → γγ, as the doubly radiative photons are indistinguishable, two
shown as the (green) dotted curve in Fig. 2. Background entries are filled into the histogram for each event. For
′
events in Class II are mainly from J/ψ decays to final the PDF of the coherent ω and ρ produced in η →
0 3 3
states without η′, such as J/ψ → γπ0π0 and J/ψ → ωη γγπ , we use [ε(Mγπ0)×E η′ ×E ω(ρ) × |BWω(Mγπ0) +γ γ
(ω → γπ0, η → γγ) decays, which contribute a smooth αeiθBWρ(Mγπ0)|
2×B2η′×B
2
ω(ρ)]⊗G(0, σ), where ε(Mγπ0)
distribution under the η′ signal region as displayed as the is the detection efficiency determined by the MC simula-
(pink) dot-dashed curve in Fig. 2. tions; Eγη′(ω/ρ) is the energy of the transition photon in
EEvveennttss//((44..00MMeeVV//cc22)) Events/ 2.5
5
TABLE I: Observed η′ signal yields (Nη
′
) and detection efficiencies (ǫ) for inclusive η′ 0 ′ 0→ γγπ , η → γω(ω → γπ ), and the
non-resonant η′ → γγπ0 decays. The measured branching fractionsc in this work, comparison of values from the PDG [16] and
theoretical predictions are listed. The first errors are statistical and the second ones are systematic.
η′ γγπ0→ (Inclusive) η′ → γω, ω → γπ0 η′ 0→ γγπ (Non-resonant)
η′N 3435± 76± 244 2340 ± 141 ± 180 655± 68± 71
ǫ 16.1% 14.8% 15.9%
(10−4B ) 32.0 ± 0.7± 2.3 23.7± 1.4± 1.8a 6.16± 0.64 ± 0.67
(10−4BPDG ) – 21.7 1.3
b
± < 8
Predictions (10−4) 57 [7],65 [8] – –
a The product branching fraction B(η′ → γω) · B(ω → γπ0). b The product branching fraction B(η′ → γω) · B(ω → γπ0) from PDG [16].
c The product branching fraction B(η′ → γρ0) · B(ρ0 → γπ0) is determined to be (1.92± 0.16(stat))× 10−4 using the fitted yield in
Fig. 4, which is in agreement with the PDG value of (1.75± 0.23)× 10−4 [16].
TABLE II: Results for dΓ(η′ γγπ0)/dM2→ γγ (in units of keV/(GeV/c
2)2) for thirteen intervals of M2γγ . The first uncertainties
are statistical and the second systematic.
M2γγ ((GeV/c
2)2) [0.0, 0.01] [0.01, 0.04] [0.04, 0.06] [0.06, 0.09] [0.09, 0.12]
dΓ(η′ → γγπ0)/M2γγ 3.17± 0.44± 0.24 2.57± 0.18 ± 0.19 2.60± 0.15± 0.18 1.87± 0.12± 0.14 1.76± 0.11± 0.13
M2 ((GeV/c2)2γγ ) [0.12, 0.16] [0.16, 0.20] [0.20, 0.25] [0.25, 0.28] [0.28, 0.31]
dΓ(η′ → γγπ0)/M2γγ 1.63± 0.10± 0.12 1.76± 0.09 ± 0.13 1.97± 0.10± 0.14 2.00± 0.17± 0.15 1.07± 0.20± 0.08
M2 2 2γγ ((GeV/c ) ) [0.31, 0.36] [0.36, 0.42] [0.42, 0.64]
dΓ(η′ → γγπ0)/M2γγ 0.34± 0.06± 0.03 0.12± 0.03 ± 0.01 0.06± 0.01± 0.01
the rest frame of η′ (ω/ρ); BWω(Mγπ0) is a relativistic from the PDG [16]. Figure 4 shows the results. The
Breit-Wigner (BW) function, and BWρ(Mγπ0) is a rel- yields for the vector mesons ρ, ω and their interfer-
ativistic BW function with mass-dependent width [18]. ence are determined to be (183± 15), (2340± 141), and
The masses and widths of the ρ and ω meson are fixed to (174±92), respectively. The signal yields and efficiencies
their PDG values [16]. B2η′(ω/ρ) is the Blatt-Weisskopf as well as the corresponding branching fractions for the
centrifugal barrier factor for the η′(ω/ρ) decay vertex η′ → γω(ω → γπ0) and non-resonant decays are summa-
with radius R = 0.75 fm [19, 20], and B2 rized in Table I.η′(ω/ρ) is used
to damp the divergent tail due to the factor E3
γη′(ω/ρ)
.
The Gaussian function G(0, σ) is used to parameterize
the detector resolution. The combinatorial background V. SYSTEMATIC UNCERTAINTIES
is produced by the combination of the π0 and the pho-
ton from the η′ meson, and its PDF is described with
a fixed shape from the MC simulation. The ratio of The systematic uncertainties on the branching fraction
yields between the combinatorial backgrounds and the measurements are summarized in Table III. The uncer-
coherent sum of ρ-ω signals is fixed from the MC simu- tainty due to the photon reconstruction is determined to
lations. The shape of the non-resonant signal η′ → γγπ0 be 1% per photon as described in Ref. [21]. The uncer-
is determined from the MC simulation, and its yield is tainties associated with the other selection criteria, kine-
determined in the fit. The background from the Class matic fit with χ25C < 30, the number of photons equal to
I as discussed above is fixed to the shape and yield of 5 and π0 veto (|Mγγ −Mπ0 | > 18 MeV/c
2) are studied
the MC simulation. Finally, the shape from the Class with the control sample J/ψ → γη′, η′ → γω, ω → γπ0
II background is obtained from the η′ mass sidebands decay, respectively. The systematic error in each of the
(738− 788 and 1008− 1058 MeV/c2), and its normaliza- applied selection criteria is numerically estimated from
tion is fixed in the fit. The Mγπ0 mass range used in the the ratio of the number of events with and without the
fit is 0.20−0.92 GeV/c2. In the fit, the interference phase corresponding requirement. The corresponding resulting
θ between the ρ- and ω-components is allowed. Due to efficiency differences between data and MC (2.7%, 0.5%,
the low statistics of the ρ meson contribution, we fix the and 1.9% , respectively) are taken to be representative of
ratio α of ρ and ω intensities to the value for the ratio of the corresponding systematic uncertainties.
B(η′ → γρ) · B(ρ → γπ0) and B(η′ → γω) · B(ω → γπ0)
In the fit for the inclusive η′ decay, the signal shape
6
4 changed from 0.75 fm to 0.35 fm are performed, and the
Total changes of the signal yields are taken as the uncertainty
η’→γω due to the signal shape.
3 η’→γρ In the fit to the Mγγπ0 distribution, the signal shape is
Non-resonant η’→γγπ0 described with an incoherent sum of contributions from
processes involving ρ and ω and non-resonant processes
2 obtained from MC simulation, where the non-resonant
process is modeled with the VMD model. A fit with an
alternative signal model for the different components, i.e.
1 a coherent sum for the ρ-, ω-components and a uniform
angular distribution in phase space (PHSP) for the non-
resonant process, is performed. The resultant changes in
0 the branching fractions are taken as the uncertainty re-
0 0.2 0.4 0.6
M2  (GeV/c2)2 lated to the signal model. An alternate fit to the Mγπ
0
γγ distribution is performed, where the PDF of the non-
resonant decay is extracted from the PHSP MC sam-
FIG. 3: Partial width (in keV) versus M2γγ for the inclusive ple. The changes in the measured branching fractions
η′ → γγπ0 decay. The error includes the statistic and sys- are considered to be the uncertainty arising from the sig-
tematic uncertainties. The (blue) histogram is the sum of
nal model.
an incoherent mixture of ρ-ω and the non-resonant compo-
nents from MC simulations; the (back) dotted-curves is ω- In the fit to theMγπ0 distribution, the uncertainty due
contribution; the (red) dot-dashed-curve is the ρ-contribution; to the fixed relative ρ intensity is evaluated by changing
and the (green) dashed-curve is the non-resonant contribu- its expectation by one standard deviation. An alterna-
tion. All the components are normalized using the yields ob- tive fit in which the ratio of yields between combinato-
tained in Fig. 4. rial backgrounds and the coherent sum of ρ−ω signals is
changed by one standard deviation from the MC simula-
1500 tion is performed, and the change observed in the signal
Global fit yield is assigned as the uncertainty. A series of fits us-
η’→ γω ing different fit ranges is performed and the maximum
η’→ γρ change of the branching fraction is taken as a systematic
ρ-ω interference
1000 uncertainty.
Non-resonant η’→ γγπ0
Combinatorial BG The uncertainty due to the Class I background is es-
Class II background timated by varying the numbers of expected background
events by one standard deviation according to the errors
500
on the branching fraction values in PDG [16]. The un-
certainty due to the Class II background is evaluated by
changing the order of the Chebychev polynomial from 3
′
0 to 4 for the fit to the η inclusive decay, and varying the
ranges of η′ sidebands for the fit to the γπ0 invariant
0.2 0.4 0.6 0.8 mass distribution, respectively.
Mγπ0 (GeV/c
2)
The number of J/ψ events is NJ/ψ = (1310.6±10.5)×
6
FIG. 4: Distribution of the invariant mass M and fit re- 10 [10, 11], corresponding to an uncertainty of 0.8%.γπ0
′ 0
sults in the η′ mass region. The points with error bars are The branching fractions for the J/ψ → γη and π → γγ
data; the (black) dotted-curve is from the ω-contribution; the decays are taken from the PDG [16], and the correspond-
(red) long dashed-curve is from the ρ-contribution; the (blue) ing uncertainties are taken as a systematic uncertainty.
short dashed-curve is the contribution of ρ-ω interference; the The total systematic errors are 7.1%, 7.7%, 10.8% for the
(green) long dashed curve is the non-resonance; the (pink) his- inclusive decay, ω-contribution and non-resonant decay,
togram is from the Class II background; the (black) short dot- respectively, as summarized in Table III.
dashed curve is the combinatorial backgrounds of η′ → γω,
γρ. The (blue) solid line shows the total fit function.
VI. SUMMARY
is fixed to the MC simulation. The uncertainty due to
the signal shape is considered by convolving a Gaussian In summary, with a sample of 1.31×109 J/ψ events col-
function to account for the difference in the mass resolu- lected with the BESIII detector, the doubly radiative de-
tion between data and MC simulation. In the fit to the cay η′ → γγπ0 has been studied. The branching fraction
γπ0 distribution, alternative fits with the mass resolution of the inclusive decay is measured for the first time to be
left free in the fit and the radius R in the barrier factor B(η′ → γγπ0)Incl. = (3.20±0.07(stat)±0.23(sys))×10
−3.
0
EEvveennttss//((1155MMeeVV//cc22)) dΓ(η’→π γγ)/dM2  (keV/(GeV/c2)2)γγ
7
the light meson decay mechanisms.
TABLE III: Summary of relative systematic uncertainties (%)
for the branching fraction measurements. Here η′ ′Incl., ηω and
η′NR represent the inclusive η
′
→ γγπ0, η′ → γω(ω γπ0→ )
and non-resonant decays, respectively. Acknowledgments
η′ η′ η′Incl. ω NR
Photon detection 5.0 5.0 5.0 The BESIII collaboration thanks the staff of BEPCII
5C kinematic fit 2.7 2.7 2.7 and the IHEP computing center for their strong sup-
Number of Photons 0.5 0.5 0.5 port. This work is supported in part by National
π0 veto 1.9 1.9 1.9 Key Basic Research Program of China under Contract
Signal shape 0.5 1.5 2.3 No. 2015CB856700; Joint Funds of the National Nat-
Signal Model 1.7 1.0 4.3 ural Science Foundation of China under Contracts Nos.
ρ relative intensity – 1.3 4.9 11079008, 11179007, U1232201, U1332201; National Nat-
Combinatorial backgrounds – 1.3 0.8 ural Science Foundation of China (NSFC) under Con-
Fit range 0.8 1.6 2.1 tracts Nos. 10935007, 11121092, 11125525, 11235011,
Class I background 0.1 0.2 0.6 11322544, 11335008, 11335009, 11505111, 11675184; the
Class II background 0.3 1.8 4.2 Chinese Academy of Sciences (CAS) Large-Scale Sci-
Cited branching fractions 3.1 3.1 3.1 entific Facility Program; CAS under Contracts Nos.
Number of J/ψ events 0.8 0.8 0.8 KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents Pro-
Total systematic error 7.1 7.7 10.8 gram of CAS; INPAC and Shanghai Key Laboratory
for Particle Physics and Cosmology; German Research
Foundation DFG under Contract No. Collaborative Re-
The M2γγ dependent partial decay widths are also de- search Center CRC-1044; Istituto Nazionale di Fisica
termined. In addition, the branching fraction for the Nucleare, Italy; Ministry of Development of Turkey un-
non-resonant decay is determined to be B(η′ → γγπ0)NR der Contract No. DPT2006K-120470; Russian Foun-
= (6.16 ± 0.64(stat) ± 0.67(sys)) × 10−4, which agrees dation for Basic Research under Contract No. 14-07-
with the upper limit measured by the GAMS-2000 ex- 91152; U. S. Department of Energy under Contracts
periment [9]. As a validation of the fit, the product Nos. DE-FG02-04ER41291, DE-FG02-05ER41374, DE-
branching fraction with the omega intermediate state in- FG02-94ER40823, DE-SC-0010118; U.S. National Sci-
volved is obtained to be B(η′ → γω) · B(ω → γπ0) = ence Foundation; University of Groningen (RuG) and
(2.37± 0.14(stat)± 0.18(sys))× 10−3, which is consistent the Helmholtzzentrum fuer Schwerionenforschung GmbH
with the PDG value [16]. These results are useful to test (GSI), Darmstadt; WCU Program of National Research
QCD calculations on the transition form factor, and pro- Foundation of Korea under Contract No. R32-2008-000-
vide valuable inputs to the theoretical understanding of 10155-0.
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