#  Study of the decay $J/\psi\to\phi\pi^{0}\eta$

M. Ablikim1, M. N. Achasov4,b, P. Adlarson75, X. C. Ai80, R. Aliberti35, A.
Amoroso74A,74C, M. R. An39, Q. An71,58, Y. Bai57, O. Bakina36, I.
Balossino29A, Y. Ban46,g, H.-R. Bao63, V. Batozskaya1,44, K. Begzsuren32, N.
Berger35, M. Berlowski44, M. Bertani28A, D. Bettoni29A, F. Bianchi74A,74C, E.
Bianco74A,74C, A. Bortone74A,74C, I. Boyko36, R. A. Briere5, A. Brueggemann68,
H. Cai76, X. Cai1,58, A. Calcaterra28A, G. F. Cao1,63, N. Cao1,63, S. A.
Cetin62A, J. F. Chang1,58, W. L. Chang1,63, G. R. Che43, G. Chelkov36,a, C.
Chen43, Chao Chen55, G. Chen1, H. S. Chen1,63, M. L. Chen1,58,63, S. J.
Chen42, S. L. Chen45, S. M. Chen61, T. Chen1,63, X. R. Chen31,63, X. T.
Chen1,63, Y. B. Chen1,58, Y. Q. Chen34, Z. J. Chen25,h, S. K. Choi10A, X.
Chu43, G. Cibinetto29A, S. C. Coen3, F. Cossio74C, J. J. Cui50, H. L. Dai1,58,
J. P. Dai78, A. Dbeyssi18, R. E. de Boer3, D. Dedovich36, Z. Y. Deng1, A.
Denig35, I. Denysenko36, M. Destefanis74A,74C, F. De Mori74A,74C, B. Ding66,1,
X. X. Ding46,g, Y. Ding34, Y. Ding40, J. Dong1,58, L. Y. Dong1,63, M. Y.
Dong1,58,63, X. Dong76, M. C. Du1, S. X. Du80, Z. H. Duan42, P. Egorov36,a, Y.
H. Fan45, J. Fang1,58, S. S. Fang1,63, W. X. Fang1, Y. Fang1, Y. Q. Fang1,58,
R. Farinelli29A, L. Fava74B,74C, F. Feldbauer3, G. Felici28A, C. Q. Feng71,58,
J. H. Feng59, Y. T. Feng71,58, K Fischer69, M. Fritsch3, C. D. Fu1, J. L.
Fu63, Y. W. Fu1, H. Gao63, Y. N. Gao46,g, Yang Gao71,58, S. Garbolino74C, I.
Garzia29A,29B, P. T. Ge76, Z. W. Ge42, C. Geng59, E. M. Gersabeck67, A
Gilman69, K. Goetzen13, L. Gong40, W. X. Gong1,58, W. Gradl35, S.
Gramigna29A,29B, M. Greco74A,74C, M. H. Gu1,58, Y. T. Gu15, C. Y Guan1,63, Z.
L. Guan22, A. Q. Guo31,63, L. B. Guo41, M. J. Guo50, R. P. Guo49, Y. P.
Guo12,f, A. Guskov36,a, J. Gutierrez27, K. L. Han63, T. T. Han1, W. Y. Han39,
X. Q. Hao19, F. A. Harris65, K. K. He55, K. L. He1,63, F. H H.. Heinsius3, C.
H. Heinz35, Y. K. Heng1,58,63, C. Herold60, T. Holtmann3, P. C. Hong12,f, G.
Y. Hou1,63, X. T. Hou1,63, Y. R. Hou63, Z. L. Hou1, B. Y. Hu59, H. M. Hu1,63,
J. F. Hu56,i, T. Hu1,58,63, Y. Hu1, G. S. Huang71,58, K. X. Huang59, L. Q.
Huang31,63, X. T. Huang50, Y. P. Huang1, T. Hussain73, N Hüsken27,35, N. in
der Wiesche68, M. Irshad71,58, J. Jackson27, S. Jaeger3, S. Janchiv32, J. H.
Jeong10A, Q. Ji1, Q. P. Ji19, X. B. Ji1,63, X. L. Ji1,58, Y. Y. Ji50, X. Q.
Jia50, Z. K. Jia71,58, H. B. Jiang76, P. C. Jiang46,g, S. S. Jiang39, T. J.
Jiang16, X. S. Jiang1,58,63, Y. Jiang63, J. B. Jiao50, Z. Jiao23, S. Jin42, Y.
Jin66, M. Q. Jing1,63, X. M. Jing63, T. Johansson75, X. K.1, S. Kabana33, N.
Kalantar-Nayestanaki64, X. L. Kang9, X. S. Kang40, M. Kavatsyuk64, B. C. Ke80,
V. Khachatryan27, A. Khoukaz68, R. Kiuchi1, O. B. Kolcu62A, B. Kopf3, M.
Kuessner3, A. Kupsc44,75, W. Kühn37, J. J. Lane67, P. Larin18, L.
Lavezzi74A,74C, T. T. Lei71,58, Z. H. Lei71,58, H. Leithoff35, M. Lellmann35,
T. Lenz35, C. Li43, C. Li47, C. H. Li39, Cheng Li71,58, D. M. Li80, F. Li1,58,
G. Li1, H. Li71,58, H. B. Li1,63, H. J. Li19, H. N. Li56,i, Hui Li43, J. R.
Li61, J. S. Li59, J. W. Li50, Ke Li1, L. J Li1,63, L. K. Li1, Lei Li48, M. H.
Li43, P. R. Li38,k, Q. X. Li50, S. X. Li12, T. Li50, W. D. Li1,63, W. G. Li1,
X. H. Li71,58, X. L. Li50, Xiaoyu Li1,63, Y. G. Li46,g, Z. J. Li59, Z. X.
Li15, C. Liang42, H. Liang71,58, H. Liang1,63, Y. F. Liang54, Y. T.
Liang31,63, G. R. Liao14, L. Z. Liao50, Y. P. Liao1,63, J. Libby26, A.
Limphirat60, D. X. Lin31,63, T. Lin1, B. J. Liu1, B. X. Liu76, C. Liu34, C. X.
Liu1, F. H. Liu53, Fang Liu1, Feng Liu6, G. M. Liu56,i, H. Liu38,j,k, H. B.
Liu15, H. M. Liu1,63, Huanhuan Liu1, Huihui Liu21, J. B. Liu71,58, J. Y.
Liu1,63, K. Liu38,j,k, K. Y. Liu40, Ke Liu22, L. Liu71,58, L. C. Liu43, Lu
Liu43, M. H. Liu12,f, P. L. Liu1, Q. Liu63, S. B. Liu71,58, T. Liu12,f, W. K.
Liu43, W. M. Liu71,58, X. Liu38,j,k, Y. Liu38,j,k, Y. Liu80, Y. B. Liu43, Z.
A. Liu1,58,63, Z. Q. Liu50, X. C. Lou1,58,63, F. X. Lu59, H. J. Lu23, J. G.
Lu1,58, X. L. Lu1, Y. Lu7, Y. P. Lu1,58, Z. H. Lu1,63, C. L. Luo41, M. X.
Luo79, T. Luo12,f, X. L. Luo1,58, X. R. Lyu63, Y. F. Lyu43, F. C. Ma40, H.
Ma78, H. L. Ma1, J. L. Ma1,63, L. L. Ma50, M. M. Ma1,63, Q. M. Ma1, R. Q.
Ma1,63, X. Y. Ma1,58, Y. Ma46,g, Y. M. Ma31, F. E. Maas18, M. Maggiora74A,74C,
S. Malde69, A. Mangoni28B, Y. J. Mao46,g, Z. P. Mao1, S. Marcello74A,74C, Z.
X. Meng66, J. G. Messchendorp13,64, G. Mezzadri29A, H. Miao1,63, T. J. Min42,
R. E. Mitchell27, X. H. Mo1,58,63, B. Moses27, N. Yu. Muchnoi4,b, J.
Muskalla35, Y. Nefedov36, F. Nerling18,d, I. B. Nikolaev4,b, Z. Ning1,58, S.
Nisar11,l, Q. L. Niu38,j,k, W. D. Niu55, Y. Niu 50, S. L. Olsen63, Q.
Ouyang1,58,63, S. Pacetti28B,28C, X. Pan55, Y. Pan57, A. Pathak34, P.
Patteri28A, Y. P. Pei71,58, M. Pelizaeus3, H. P. Peng71,58, Y. Y. Peng38,j,k,
K. Peters13,d, J. L. Ping41, R. G. Ping1,63, S. Plura35, V. Prasad33, F. Z.
Qi1, H. Qi71,58, H. R. Qi61, M. Qi42, T. Y. Qi12,f, S. Qian1,58, W. B. Qian63,
C. F. Qiao63, J. J. Qin72, L. Q. Qin14, X. S. Qin50, Z. H. Qin1,58, J. F.
Qiu1, S. Q. Qu61, C. F. Redmer35, K. J. Ren39, A. Rivetti74C, M. Rolo74C, G.
Rong1,63, Ch. Rosner18, S. N. Ruan43, N. Salone44, A. Sarantsev36,c, Y.
Schelhaas35, K. Schoenning75, M. Scodeggio29A,29B, K. Y. Shan12,f, W. Shan24,
X. Y. Shan71,58, J. F. Shangguan55, L. G. Shao1,63, M. Shao71,58, C. P.
Shen12,f, H. F. Shen1,63, W. H. Shen63, X. Y. Shen1,63, B. A. Shi63, H. C.
Shi71,58, J. L. Shi12, J. Y. Shi1, Q. Q. Shi55, R. S. Shi1,63, X. Shi1,58, J.
J. Song19, T. Z. Song59, W. M. Song34,1, Y. J. Song12, S. Sosio74A,74C, S.
Spataro74A,74C, F. Stieler35, Y. J. Su63, G. B. Sun76, G. X. Sun1, H. Sun63,
H. K. Sun1, J. F. Sun19, K. Sun61, L. Sun76, S. S. Sun1,63, T. Sun51,e, W. Y.
Sun34, Y. Sun9, Y. J. Sun71,58, Y. Z. Sun1, Z. T. Sun50, Y. X. Tan71,58, C. J.
Tang54, G. Y. Tang1, J. Tang59, Y. A. Tang76, L. Y Tao72, Q. T. Tao25,h, M.
Tat69, J. X. Teng71,58, V. Thoren75, W. H. Tian52, W. H. Tian59, Y. Tian31,63,
Z. F. Tian76, I. Uman62B, Y. Wan55, S. J. Wang 50, B. Wang1, B. L. Wang63, Bo
Wang71,58, C. W. Wang42, D. Y. Wang46,g, F. Wang72, H. J. Wang38,j,k, J. P.
Wang 50, K. Wang1,58, L. L. Wang1, M. Wang50, Meng Wang1,63, N. Y. Wang63, S.
Wang12,f, S. Wang38,j,k, T. Wang12,f, T. J. Wang43, W. Wang59, W. Wang72, W.
P. Wang71,58, X. Wang46,g, X. F. Wang38,j,k, X. J. Wang39, X. L. Wang12,f, Y.
Wang61, Y. D. Wang45, Y. F. Wang1,58,63, Y. L. Wang19, Y. N. Wang45, Y. Q.
Wang1, Yaqian Wang17,1, Yi Wang61, Z. Wang1,58, Z. L. Wang72, Z. Y. Wang1,63,
Ziyi Wang63, D. Wei70, D. H. Wei14, F. Weidner68, S. P. Wen1, C. W. Wenzel3,
U. Wiedner3, G. Wilkinson69, M. Wolke75, L. Wollenberg3, C. Wu39, J. F. Wu1,8,
L. H. Wu1, L. J. Wu1,63, X. Wu12,f, X. H. Wu34, Y. Wu71, Y. H. Wu55, Y. J.
Wu31, Z. Wu1,58, L. Xia71,58, X. M. Xian39, T. Xiang46,g, D. Xiao38,j,k, G. Y.
Xiao42, S. Y. Xiao1, Y. L. Xiao12,f, Z. J. Xiao41, C. Xie42, X. H. Xie46,g, Y.
Xie50, Y. G. Xie1,58, Y. H. Xie6, Z. P. Xie71,58, T. Y. Xing1,63, C. F.
Xu1,63, C. J. Xu59, G. F. Xu1, H. Y. Xu66, Q. J. Xu16, Q. N. Xu30, W. Xu1, W.
L. Xu66, X. P. Xu55, Y. C. Xu77, Z. P. Xu42, Z. S. Xu63, F. Yan12,f, L.
Yan12,f, W. B. Yan71,58, W. C. Yan80, X. Q. Yan1, H. J. Yang51,e, H. L.
Yang34, H. X. Yang1, Tao Yang1, Y. Yang12,f, Y. F. Yang43, Y. X. Yang1,63,
Yifan Yang1,63, Z. W. Yang38,j,k, Z. P. Yao50, M. Ye1,58, M. H. Ye8, J. H.
Yin1, Z. Y. You59, B. X. Yu1,58,63, C. X. Yu43, G. Yu1,63, J. S. Yu25,h, T.
Yu72, X. D. Yu46,g, C. Z. Yuan1,63, L. Yuan2, S. C. Yuan1, Y. Yuan1,63, Z. Y.
Yuan59, C. X. Yue39, A. A. Zafar73, F. R. Zeng50, S. H. Zeng72, X. Zeng12,f,
Y. Zeng25,h, Y. J. Zeng1,63, X. Y. Zhai34, Y. C. Zhai50, Y. H. Zhan59, A. Q.
Zhang1,63, B. L. Zhang1,63, B. X. Zhang1, D. H. Zhang43, G. Y. Zhang19, H.
Zhang71, H. C. Zhang1,58,63, H. H. Zhang59, H. H. Zhang34, H. Q. Zhang1,58,63,
H. Y. Zhang1,58, J. Zhang80, J. Zhang59, J. J. Zhang52, J. L. Zhang20, J. Q.
Zhang41, J. W. Zhang1,58,63, J. X. Zhang38,j,k, J. Y. Zhang1, J. Z. Zhang1,63,
Jianyu Zhang63, L. M. Zhang61, L. Q. Zhang59, Lei Zhang42, P. Zhang1,63, Q. Y.
Zhang39,80, Shuihan Zhang1,63, Shulei Zhang25,h, X. D. Zhang45, X. M. Zhang1,
X. Y. Zhang50, Y. Zhang69, Y. Zhang72, Y. T. Zhang80, Y. H. Zhang1,58, Yan
Zhang71,58, Yao Zhang1, Z. D. Zhang1, Z. H. Zhang1, Z. L. Zhang34, Z. Y.
Zhang43, Z. Y. Zhang76, G. Zhao1, J. Y. Zhao1,63, J. Z. Zhao1,58, Lei
Zhao71,58, Ling Zhao1, M. G. Zhao43, R. P. Zhao63, S. J. Zhao80, Y. B.
Zhao1,58, Y. X. Zhao31,63, Z. G. Zhao71,58, A. Zhemchugov36,a, B. Zheng72, J.
P. Zheng1,58, W. J. Zheng1,63, Y. H. Zheng63, B. Zhong41, X. Zhong59, H.
Zhou50, L. P. Zhou1,63, X. Zhou76, X. K. Zhou6, X. R. Zhou71,58, X. Y. Zhou39,
Y. Z. Zhou12,f, J. Zhu43, K. Zhu1, K. J. Zhu1,58,63, L. Zhu34, L. X. Zhu63, S.
H. Zhu70, S. Q. Zhu42, T. J. Zhu12,f, W. J. Zhu12,f, Y. C. Zhu71,58, Z. A.
Zhu1,63, J. H. Zou1, J. Zu71,58 (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 Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
6 Central China Normal University, Wuhan 430079, People’s Republic of China
7 Central South University, Changsha 410083, People’s Republic of China
8 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
9 China University of Geosciences, Wuhan 430074, People’s Republic of China
10 Chung-Ang University, Seoul, 06974, Republic of Korea
11 COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind
Road, 54000 Lahore, Pakistan
12 Fudan University, Shanghai 200433, People’s Republic of China
13 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
14 Guangxi Normal University, Guilin 541004, People’s Republic of China
15 Guangxi University, Nanning 530004, People’s Republic of China
16 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
17 Hebei University, Baoding 071002, People’s Republic of China
18 Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
19 Henan Normal University, Xinxiang 453007, People’s Republic of China
20 Henan University, Kaifeng 475004, People’s Republic of China
21 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
22 Henan University of Technology, Zhengzhou 450001, People’s Republic of
China
23 Huangshan College, Huangshan 245000, People’s Republic of China
24 Hunan Normal University, Changsha 410081, People’s Republic of China
25 Hunan University, Changsha 410082, People’s Republic of China
26 Indian Institute of Technology Madras, Chennai 600036, India
27 Indiana University, Bloomington, Indiana 47405, USA
28 INFN Laboratori Nazionali di Frascati , (A)INFN Laboratori Nazionali di
Frascati, I-00044, Frascati, Italy; (B)INFN Sezione di Perugia, I-06100,
Perugia, Italy; (C)University of Perugia, I-06100, Perugia, Italy
29 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara,
Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
30 Inner Mongolia University, Hohhot 010021, People’s Republic of China
31 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
32 Institute of Physics and Technology, Peace Avenue 54B, Ulaanbaatar 13330,
Mongolia
33 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica
1000000, Chile
34 Jilin University, Changchun 130012, People’s Republic of China
35 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
36 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
37 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
38 Lanzhou University, Lanzhou 730000, People’s Republic of China
39 Liaoning Normal University, Dalian 116029, People’s Republic of China
40 Liaoning University, Shenyang 110036, People’s Republic of China
41 Nanjing Normal University, Nanjing 210023, People’s Republic of China
42 Nanjing University, Nanjing 210093, People’s Republic of China
43 Nankai University, Tianjin 300071, People’s Republic of China
44 National Centre for Nuclear Research, Warsaw 02-093, Poland
45 North China Electric Power University, Beijing 102206, People’s Republic of
China
46 Peking University, Beijing 100871, People’s Republic of China
47 Qufu Normal University, Qufu 273165, People’s Republic of China
48 Renmin University of China, Beijing 100872, People’s Republic of China
49 Shandong Normal University, Jinan 250014, People’s Republic of China
50 Shandong University, Jinan 250100, People’s Republic of China
51 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
52 Shanxi Normal University, Linfen 041004, People’s Republic of China
53 Shanxi University, Taiyuan 030006, People’s Republic of China
54 Sichuan University, Chengdu 610064, People’s Republic of China
55 Soochow University, Suzhou 215006, People’s Republic of China
56 South China Normal University, Guangzhou 510006, People’s Republic of China
57 Southeast University, Nanjing 211100, People’s Republic of China
58 State Key Laboratory of Particle Detection and Electronics, Beijing 100049,
Hefei 230026, People’s Republic of China
59 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
60 Suranaree University of Technology, University Avenue 111, Nakhon
Ratchasima 30000, Thailand
61 Tsinghua University, Beijing 100084, People’s Republic of China
62 Turkish Accelerator Center Particle Factory Group, (A)Istinye University,
34010, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus,
99138, Mersin 10, Turkey
63 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
64 University of Groningen, NL-9747 AA Groningen, The Netherlands
65 University of Hawaii, Honolulu, Hawaii 96822, USA
66 University of Jinan, Jinan 250022, People’s Republic of China
67 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
68 University of Muenster, Wilhelm-Klemm-Strasse 9, 48149 Muenster, Germany
69 University of Oxford, Keble Road, Oxford OX13RH, United Kingdom
70 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
71 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
72 University of South China, Hengyang 421001, People’s Republic of China
73 University of the Punjab, Lahore-54590, Pakistan
74 University of Turin and INFN, (A)University of Turin, I-10125, Turin,
Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy;
(C)INFN, I-10125, Turin, Italy
75 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
76 Wuhan University, Wuhan 430072, People’s Republic of China
77 Yantai University, Yantai 264005, People’s Republic of China
78 Yunnan University, Kunming 650500, People’s Republic of China
79 Zhejiang University, Hangzhou 310027, People’s Republic of China
80 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at the Moscow Institute of Physics and Technology, Moscow 141700,
Russia
b Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
c Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
d Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany
e 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
f Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and
Institute of Modern Physics, Fudan University, Shanghai 200443, People’s
Republic of China
g Also at State Key Laboratory of Nuclear Physics and Technology, Peking
University, Beijing 100871, People’s Republic of China
h Also at School of Physics and Electronics, Hunan University, Changsha
410082, China
i Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of
Quantum Matter, South China Normal University, Guangzhou 510006, China
j Also at MOE Frontiers Science Center for Rare Isotopes, Lanzhou University,
Lanzhou 730000, People’s Republic of China
k Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou
730000, People’s Republic of China
l Also at the Department of Mathematical Sciences, IBA, Karachi 75270,
Pakistan

###### Abstract

Based on $(10.09\pm 0.04)\times 10^{9}$ $J/\psi$ events collected with the
BESIII detector operating at the BEPCII collider, a partial wave analysis of
the decay $J/\psi\to\phi\pi^{0}\eta$ is performed. We observe for the first
time two new structures on the $\phi\eta$ invariant mass distribution, with
statistical significances of $24.0\sigma$ and $16.9\sigma$; the first with
$J^{\rm PC}$ = $1^{+-}$, mass M = (1911 $\pm$ 6 (stat.) $\pm$ 14 (sys.))
$\mathrm{MeV}/c^{2}$, and width $\Gamma=$ (149 $\pm$ 12 (stat.) $\pm$ 23
(sys.)) $\mathrm{MeV}$, the second with $J^{\rm PC}$ = $1^{--}$, mass M =
(1996 $\pm$ 11 (stat.) $\pm$ 30 (sys.)) $\mathrm{MeV}/c^{2}$, and width
$\Gamma$ = (148 $\pm$ 16 (stat.) $\pm$ 66 (sys.)) $\mathrm{MeV}$. These
measurements provide important input for the strangeonium spectrum. In
addition, the $f_{0}(980)-a_{0}(980)^{0}$ mixing signal in $J/\psi\to\phi
f_{0}(980)\to\phi a_{0}(980)^{0}$ and the corresponding electromagnetic decay
$J/\psi\to\phi a_{0}(980)^{0}$ are measured with improved precision, providing
crucial information to understand the nature of $a_{0}(980)^{0}$ and
$f_{0}(980)$.

Studies of the strangeonium ($s\bar{s}$) spectrum and of exotic states
containing $s$ and $\bar{s}$ quarks offer a unique platform to deepen our
understanding of Quantum Chromodynamics (QCD) in the nonperturbative regime
Godfrey:1985xj ; ParticleDataGroup:2020ssz . At present, our knowledge of the
$s\bar{s}$ spectrum is incomplete and only a small fraction of the predicted
$s\bar{s}$ states is confirmed in the mass region below 2.2
$\mathrm{GeV}/c^{2}$ ParticleDataGroup:2020ssz ; Barnes:2002mu ; Li:2020xzs .
Although the existence of many of these states has been studied by
experiments, their nature is still controversial. The lightest axial-vector
state $h_{1}(1415)$ was observed by both LASS Aston:1987ak  and Crystal Barrel
CrystalBarrel:1997kda  collaborations about thirty years ago, and its
parameters were recently measured with improved precision by BESIII
BESIII:2015vfb ; BESIII:2018ede . The possible interpretations of its internal
nature include a mixture between $SU(3)$-singlet $1^{1}P_{1}$ and
$SU(3)$-octet $1^{3}P_{1}$ mesons Li:2005eq  or a $q\bar{q}$ state as
predicted by the relativistic quark model Godfrey:1985xj . Its excitations,
e.g., $h_{1}(2P)$ and $h_{1}(3P)$, have been theoretically predicted
Barnes:2002mu . Their measurements, however, are still limited by the current
experimental sensitivity. The search for these $s\bar{s}$ excited states and
their systematical investigation are crucial to improve our understanding of
the $h_{1}$ family Chen:2015iqa . Since gluons and light quarks are produced
abundantly in the decay of charmonium states, they offer an excellent
opportunity for $s\bar{s}$ spectroscopy. Different approaches to search for
new $s\bar{s}$ states in charmonium decays were proposed Barnes:2002mu .

The light scalar mesons $a_{0}(980)^{0}$ and $f_{0}(980)$ are considered as
candidates for exotic states. The mixing mechanism of the
$a_{0}(980)^{0}-f_{0}(980)$ system provides an important access to understand
their nature Achasov:1979xc ; Close:2000ah ; Close:2001ay ; Hanhart:2007bd ;
Wu:2007jh ; Wu:2008hx . By using $1.31\times 10^{9}$ $J/\psi$ and $4.48\times
10^{8}$ $\psi(3686)$ events, BESIII has discovered $a_{0}(980)^{0}-f_{0}(980)$
mixing signals with the statistical significance of 7.4$\sigma$ and
5.5$\sigma$ in the decays $J/\psi\to\phi\pi^{0}\eta$ and
$\chi_{c1}\to\pi^{+}\pi^{-}\pi^{0}$ BESIII:2018ozj , respectively, where the
destructive and constructive solutions of the mixing intensities are
presented, too. A more precise measurement of the mixing intensity will
improve our understanding of the nature of $a_{0}(980)^{0}$ and $f_{0}(980)$.

In this Letter, a partial wave analysis (PWA) on the isospin violating decay
$J/\psi\to\phi\pi^{0}\eta$ is performed based on $(10.09\pm 0.04)\times
10^{9}$ $J/\psi$ events BESIII:2021cxx  accumulated with the BESIII detector
operating at the BEPCII collider. Two new structures are observed on the
$\phi\eta$ invariant mass distribution, and their parameters are hereby
determined. In addition, the mixing of the $f_{0}(980)\to a_{0}(980)^{0}$
signal is confirmed, and the corresponding mixing intensity is measured with
improved precision.

The BESIII detector records symmetric $e^{+}e^{-}$ collisions provided by the
BEPCII storage ring Yu:IPAC2016-TUYA01  in the center-of-mass energy range
from 2.0 to 4.95 GeV, with a peak luminosity of $1\times
10^{33}\;\text{cm}^{-2}\text{s}^{-1}$ achieved at $\sqrt{s}=3.77\;\text{GeV}$.
The detailed description of the BESIII detector can be found in Ref.
Ablikim:2009aa . The simulated Monte Carlo (MC) samples based on the geant4
GEANT4:2002zbu  package, incorporating the geometric description of the BESIII
detector detvis  and the detector response, are used to determine the
detection efficiencies and to estimate the background. In the simulation, the
beam energy spread and the initial state radiation in the $e^{+}e^{-}$
annihilation are incorporated with the generator kkmc Jadach:2000ir ;
Jadach:1999vf . An inclusive MC sample, including both the production of the
$J/\psi$ resonance and the continuum processes, is generated with kkmc
Jadach:2000ir ; Jadach:1999vf  for the same number of events as in real data.
The known decay modes are incorporated with evtgen Lange:2001uf ; Ping:2008zz
taking the branching fractions from the Particle Data Group (PDG)
ParticleDataGroup:2020ssz , while the remaining unknown charmonium decays are
modelled with lundcharm Chen:2000tv ; Yang:2014vra . Final state radiation
from charged particles in the final state is incorporated with photos
Barberio:1993qi . Signal MC samples for the process $J/\psi\to\phi\pi^{0}\eta$
with the subsequent decays $\phi\to K^{+}K^{-}$, $\pi^{0}\to\gamma\gamma$, and
$\eta\to\gamma\gamma$ are generated uniformly in phase space.

Candidate events for the decay $J/\psi\to\phi\pi^{0}\eta$ are selected using
the criteria described in Ref. BESIII:2018ozj , where the $\phi$ signal is
reconstructed by the $K^{+}K^{-}$ decay and the $\pi^{0}$ and $\eta$ mesons
are reconstructed by the $\gamma\gamma$ decay mode. A four-constraint (4C)
kinematic fit enforcing energy-momentum conservation is carried out under the
hypothesis of $J/\psi\to K^{+}K^{-}\gamma\gamma\gamma\gamma$. For the events
with more than four photons, the combination with the smallest $\chi_{4\rm
C}^{2}$ is kept, and $\chi^{2}_{4\rm C}<45$ is additionally required. The
$\pi^{0}$ and $\eta$ candidates are reconstructed by minimizing
$\chi^{2}_{\pi^{0}\eta}=(M_{\gamma_{1}\gamma_{2}}-m_{\pi^{0}})^{2}/\sigma_{\pi^{0}}^{2}+(M_{\gamma_{3}\gamma_{4}}-m_{\eta})^{2}/\sigma_{\eta}^{2}$,
where $m_{\pi^{0}}$ and $m_{\eta}$ are the nominal mass values of $\pi^{0}$
and $\eta$ quoted from the PDG ParticleDataGroup:2020ssz ,
$M_{\gamma_{1}\gamma_{2}}$ and $M_{\gamma_{3}\gamma_{4}}$ are the invariant
masses of the $\gamma_{1}\gamma_{2}$ and $\gamma_{3}\gamma_{4}$ combinations,
and $\sigma_{\pi^{0}}$ and $\sigma_{\eta}$ are their corresponding resolutions
estimated by the MC sample $J/\psi\to\phi\pi^{0}\eta$ to be 4.4
$\mathrm{MeV}/c^{2}$ and 7.3 $\mathrm{MeV}/c^{2}$, respectively. The $\pi^{0}$
and $\eta$ candidates are selected by requiring
$|M_{\gamma_{1}\gamma_{2}}-m_{\pi^{0}}|<15~{}\mathrm{MeV}/c^{2}$ and
$|M_{\gamma_{3}\gamma_{4}}-m_{\eta}|<25~{}\mathrm{MeV}/c^{2}$, respectively.
To reject the background from $J/\psi\to K^{+}K^{-}\pi^{0}\pi^{0}$ and
$J/\psi\to K^{+}K^{-}\eta\eta$, two $\chi^{2}$ functions analogous to
$\chi^{2}_{\pi^{0}\eta}$ are defined for the $\pi^{0}\pi^{0}$ and $\eta\eta$
pairs, requiring that $\chi^{2}_{\pi^{0}\pi^{0}}>90$ and
$\chi^{2}_{\eta\eta}>8$. The $\chi^{2}$ requirements are optimized to maximize
the figure of merit $S/\sqrt{S+B}$, where $S$ is the signal and $B$ is the
background. The $\phi$ candidates are selected by requiring the $K^{+}K^{-}$
invariant mass being in the range
$|M_{K^{+}K^{-}}-m_{\phi}|<10~{}\mathrm{MeV}/c^{2}$, where $m_{\phi}$ is the
$\phi$ nominal mass. To improve the kinematic resolution, a six-constraint
(6C) kinematic fit is performed, using the $\eta$ and $\pi^{0}$ masses taken
from PDG ParticleDataGroup:2020ssz  as well as energy and momentum
conservation as constraints. The resulting kinematic variables are used in the
further analysis.

After applying all the above selection criteria, the distribution of the
$K^{+}K^{-}$ invariant mass ($M_{K^{+}K^{-}}$) of the remaining events is
shown in Fig. 1, where the $\phi$ signal is observed clearly together with a
considerable non-$\phi$ background. Detailed studies of MC simulation indicate
that the background includes also contributions with no $\pi^{0}$ and no
$\eta$ mesons in the final state. Therefore, a sophisticated $Q$-factor method
Williams:2008sh  is applied to subtract the corresponding background. For each
event, a weight factor $Q_{i}$ is assigned, that is determined by analyzing
the signal-to-background ratio by fitting the two-dimensional distribution
$M_{\gamma_{1}\gamma_{2}}$ versus $M_{\gamma_{3}\gamma_{4}}$ in a very small
cell of the available phase space around each event. The corresponding
$Q$-weighted $M_{K^{+}K^{-}}$ distribution is shown as the shaded plot in Fig.
1. From the $M_{K^{+}K^{-}}$ distribution we obtain 14585 events within the
$\phi$ signal region ($1.01<M_{K^{+}K^{-}}<1.03~{}\mathrm{GeV}/c^{2}$) without
weighting, and 12561 events after the $Q$-weighting. The weighted
$M_{\gamma\gamma}$ distributions are shown in the supplementary materials
suppl . To validate the $Q$-factor method, the number of non-$\pi^{0}$ and
non-$\eta$ background events is also estimated by analyzing events in the
$\pi^{0}$ and $\eta$ sideband regions, and an agreement of $\sim 0.6\%$ on the
number of background events in the signal region between the two methods is
achieved.

Figure 1:  Distribution of the $K^{+}K^{-}$ invariant mass. The black dots are
data, the blue-shaded area shows the $Q$-weighted distribution.

Figure 2 shows the distributions of $\phi\eta$, $\phi\pi^{0}$, and
$\eta\pi^{0}$ invariant mass ($M_{\phi\eta}$, $M_{\phi\pi^{0}}$, and
$M_{\eta\pi^{0}}$) and the corresponding angular distributions, after the
$Q$-weighting, for the candidate events within the $\phi$ signal region.
Besides the well established $a_{0}(980)^{0}-f_{0}(980)$ mixing signal in the
$M_{\eta\pi^{0}}$ distribution BESIII:2018ozj , two structures with
$M_{\phi\eta}$ lower than 2 $\mathrm{GeV}/c^{2}$ and a prominent peak at
$M_{\phi\pi^{0}}$ around 1.4 $\mathrm{GeV}/c^{2}$ are observed clearly. A
similar peak around 1.4 $\mathrm{GeV}/c^{2}$ in the $M_{\phi\pi^{0}}$
distribution is observed for the events in the $\phi$ sideband region, defined
as $1.05<M_{K^{+}K^{-}}<1.07~{}\mathrm{GeV}/c^{2}$, shown in the supplementary
materials suppl . This indicates that this structure is not from the
$\phi\pi^{0}$ decay mode, but from the $K^{+}K^{-}\pi^{0}$ channel.

To identify the properties of the new observed structures and precisely
measure the intensity of the $a_{0}(980)^{0}-f_{0}(980)$ mixing signal, a PWA
based on the GPUPWA framework Berger:2010zza  is carried out. Detailed studies
on the candidate events in the $\phi$ sideband region and in the MC simulation
indicate that the components of the non-$\phi$ background are very complicated
due to the $K^{*(\prime)}$ contributions. Therefore, to better model the
non-$\phi$ background, a similar PWA is performed on the candidate events with
$M_{K^{+}K^{-}}$ in the range between 1.07 and 1.5 $\mathrm{GeV}/c^{2}$,
including the different $K^{*(\prime)}$ components. The supplementary
materials suppl  show the invariant mass and angular distributions of data
used in the above PWA and the MC simulation projection based on the PWA
results, as well as the comparison of the invariant mass and angular
distributions for the events in the $\phi$ sideband region between the data
and the MC projections. The MC projections describe the data very well.

\begin{overpic}[width=138.76157pt]{mphieta_fulldraftv7.eps} \put(65.0,55.0){
(a)} \end{overpic}\begin{overpic}[width=138.76157pt]{mphipi0_fulldraftv7.eps}
\put(70.0,55.0){ (b)}
\end{overpic}\begin{overpic}[width=138.76157pt]{metapi0_fulldraftv8.eps}
\put(83.0,55.0){ (c)}
\end{overpic}\begin{overpic}[width=138.76157pt]{cosphiinphieta_fulldraftv7.eps}
\put(65.0,55.0){ (d)}
\end{overpic}\begin{overpic}[width=138.76157pt]{cospi0inpi0eta_fulldraftv7.eps}
\put(70.0,55.0){ (e)}
\end{overpic}\begin{overpic}[width=138.76157pt]{cosphieta_fulldraftv7.eps}
\put(83.0,55.0){ (f)} \end{overpic}

Figure 2:  Invariant mass distributions of (a) $\phi\eta$, (b) $\phi\pi^{0}$,
and (c) $\eta\pi^{0}$, and angular distributions of (d) cos$\theta_{\phi}$ in
the $\phi\eta$ helicity frame, (e) cos$\theta_{\pi^{0}}$ in the $\pi^{0}\eta$
helicity frame, (f) cos$\theta_{\phi\eta}$ in the center-of-mass rest frame.
The black dots are the background-subtracted data, the black continuous lines
are the PWA fit projections, the colored non-continuous lines show the
components of the fit model.

In the PWA, the two-body decay amplitudes in the sequential decays are
constructed using the covariant tensor amplitudes as in Ref. Zou:2002ar .
Except for the $a_{0}(980)^{0}$ state, the $f_{0}(980)\to a_{0}(980)^{0}$
mixing signal and the $\phi(1680)$ state, the intermediate states are
parameterized with relativistic Breit-Wigner (BW) functions using the quoted
masses and widths from the PDG. The $f_{0}(980)$ and $a_{0}(980)^{0}$ states
are described by the Flatté formula with fixed parameters as in Refs.
BES:2004twe ; BESIII:2016tqo . The $f_{0}(980)\to a_{0}(980)^{0}$ mixing
signal is parameterized as in Ref. BESIII:2018ozj . The $\phi(1680)$ state,
whose mass is close to the $\phi\eta$ and $K^{*}K$ mass thresholds, is
parameterized with a three-channel-coupled formula ($\phi\eta$, $K^{*}K$, and
$\phi\pi\pi$), in which the coupled parameters are fixed according to Ref.
BaBar:2011btv , and its mass and width are free parameters in the fit. The
resolution effect on the narrow signals, i.e. the $\phi(1020)$ meson and the
$f_{0}(980)\to a_{0}(980)^{0}$ mixing signal, is taken into account by
convolving the propagator with two independent Gaussian functions determined
by the signal MC sample. The total decay amplitude for the $i$-th candidate
event $M(\xi_{i})$ with kinematic variables $\xi_{i}$ is the sum of the
amplitudes of all possible decay processes $A_{j}(\xi_{i})$ together with the
amplitude for the non-$\phi$ background $B(\xi_{i})$,
$M(\xi_{i})=\sum_{j}A_{j}(\xi_{i})+B(\xi_{i})$, where $A_{j}(\xi_{i})$ and
$B(\xi_{i})$ are the amplitudes for the $J/\psi$ decay process including
intermediate resonances. The complex coefficients of the amplitudes (relative
magnitudes and phases) and the resonance parameters (mass and width) in
$A_{j}(\xi_{i})$ are obtained by minimizing

$S(\xi)=-\ln\mathcal{L}=-\alpha\sum_{i}^{N}Q_{i}\ln\left(\frac{|M(\xi_{i})|^{2}\varepsilon(\xi_{i})}{\sigma^{\prime}}\right)$
(1)

with an unbinned maximum likelihood fit using MINUIT James:1975dr . Here,
$\varepsilon(\xi_{i})$ is the corresponding detection efficiency,
$\sigma^{\prime}=\int|M(\xi)|^{2}\varepsilon(\xi)d\xi$ is the normalization
integral and $Q_{i}$ is the $Q$-factor of each event. The global factor
$\alpha=\sum_{i=1}^{N}Q_{i}/\sum_{i=1}^{N}Q_{i}^{2}$ is introduced to take
into account the correction on the statistical uncertainty for the weighted
likelihood function Qf1 ; Qf2 . The parameters in $B(\xi_{i})$ are fixed to
the results from the PWA fit on the candidate events with $M_{K^{+}K^{-}}$ in
the range between 1.07 and 1.5 $\mathrm{GeV}/c^{2}$.

In the PWA fit we include all the possible intermediate states listed in the
PDG which can decay into $\phi\eta$, $\phi\pi^{0}$, or $\pi^{0}\eta$ final
states, and do not violate conservation of the quantum numbers $J^{PC}$. To
take into account the contribution from the coherent non-resonant component,
the amplitudes modeled with the same sequential process and with a very broad
and given $J^{PC}$ intermediate state are also included. The statistical
significance of each individual process is obtained by examining the changes
of the likelihood value and of the number of degrees of freedom between the
cases with and without the corresponding process included in the fit, and only
those processes with statistical significance larger than 5$\sigma$ are kept
in the baseline solution. Based on this solution, each dropped process is
reintroduced individually and the corresponding statistical significance is
estimated to verify that the process can be safely excluded.

Table 1 summarizes the dominant components in the baseline solution, their
statistical significance, and the product branching fractions. Beside the
$a_{0}(980)^{0}-f_{0}(980)$ mixing signal and the $J/\psi\to\phi
a_{0}(980)^{0}$ electromagnetic decay, the dominant processes are those
including intermediate states with masses at 1.68 and 1.9 $\mathrm{GeV}/c^{2}$
on the $M_{\phi\eta}$ distribution. There are additional contributions of
$\rho(1570)$, $\rho(1900)$, $\rho(2050)$, and $\rho(2150)$ states on the
$M_{\phi\pi^{0}}$ distribution, $\phi(1680)$ and $\phi(2170)$ states on the
$M_{\phi\eta}$ distribution, $a_{0}(1450)$, $a_{0}(1950)$, $a_{2}(1320)$, and
$a_{2}(1700)$ states on the $M_{\pi^{0}\eta}$ distribution suppl . These have
small branching fractions and are strongly affected by the non-$\phi$
background; therefore, they are not reported in detail in this Letter. The
prominent structure at 1.4 $\mathrm{GeV}/c^{2}$ on the $M_{\phi\pi^{0}}$
distribution can be well described by the non-$\phi$ background processes. In
the PWA, different $J^{PC}$ assignments for the intermediate states are
investigated to determine their $J^{PC}$ individually. A detailed comparison
between the data and the MC projection indicates that the structure at 1.9
$\mathrm{GeV}/c^{2}$ on the $M_{\phi\eta}$ distribution can not be described
only by a new axial-vector state (named $h_{1}(1900)$ thereafter), but
requires an additional vector state (named $X(2000)$ thereafter). The values
of mass and width of the intermediate states, summarized in Table 1, are
obtained by performing a scan of the likelihood values under different
hypotheses and finding the minima of the distributions suppl . The comparison
of the invariant mass and angular distributions between data and MC
projections is shown in Fig. 2. The $\chi^{2}/nbin$ values for each
distribution are indicated to estimate the goodness of the fits, where $nbin$
is the number of bins in each histogram and $\chi^{2}$ is defined as

$\chi^{2}=\sum_{i=1}^{nbin}\frac{(n_{i}-\nu_{i})^{2}}{n_{i}},$ (2)

where $n_{i}$ and $\nu_{i}$ are the number of events for the data and the fit
projection in the $i$-th bin, respectively.

Table 1: The values of mass, width, product branching fraction ($\mathcal{B}$) and statistical significance ($\sigma$) from the PWA fit for different subdecays, where the first uncertainties are statistical and the second systematic. Process |  M (MeV/$c^{2}$) |  $\Gamma$ (MeV) |  $\mathcal{B}$ ($10^{-6}$) | $\sigma$
---|---|---|---|---
$\phi(1680)\pi^{0}$ | $1668\pm 7\pm 25$ | $147\pm 14\pm 35$ |  5.34 $\pm$ 0.25 $\pm$ 0.88 | 36
$X(2000)\pi^{0}$ | $1996\pm 11\pm 30$ | $148\pm 16\pm 66$ |  2.76 $\pm$ 0.22 $\pm$ 0.67 | 17
$h_{1}(1900)\pi^{0}$ | $1911\pm 6\pm 14$ | $149\pm 12\pm 23$ |  9.29 $\pm$ 0.33 $\pm$ 0.72 | 24
$\phi a_{0}(980)_{\rm EM}$ | – | – |  2.81 $\pm$ 0.24 $\pm$ 0.55 | 19
$\phi a_{0}(980)_{\rm mix}$ | – | – |  2.73 $\pm$ 0.14 $\pm$ 0.19 | 32

Two categories of systematic uncertainties are considered in this analysis.
The first category affects only the branching fraction measurements and
includes uncertainties associated with the photon detection (1.0% per photon)
BESIII:2010ank , the MDC tracking (1.0% per charged track) BESIII:2011wmh ,
the PID (1.0% per kaon) BESIII:2011ysp , the kinematic fit (1.3%), the $\phi$
mass resolution (0.9%), the branching fractions of intermediate state decays
(1.1%) ParticleDataGroup:2020ssz , and the total number of $J/\psi$ events
(0.4%) BESIII:2021cxx . The uncertainty related to the 4C kinematic fit is
estimated by correcting the helix parameters of the simulated charged tracks
to compensate the resolution difference between data and MC simulation
BESIII:2012mpj . The systematic uncertainties from the branching fractions of
intermediate states in the subsequent decays are taken from the PDG
ParticleDataGroup:2020ssz . The second category of uncertainties, which are
mostly from the PWA fit procedure, affects both the branching fraction and the
resonance parameters measurements. To estimate these uncertainties,
alternative fits with different scenarios are performed, and the resultant
changes on the branching fractions and the resonance parameters are taken as
the systematic uncertainties. Uncertainties from the BW parameterization are
estimated by replacing the constant-width BW with the mass-dependent width.
Uncertainties associated with the resonance parameters, taken from the PDG and
fixed in the fit, are estimated by individually varying the parameters by $\pm
1\sigma$ in the fit. The largest changes with respect to the nominal results
are taken as the systematic uncertainties. To estimate the uncertainty due to
the non-$\phi$ background model, alternative fits for the candidate events
with $M_{K^{+}K^{-}}$ within [1.07, 1.3] $\mathrm{GeV}/c^{2}$ are carried out
to model the background and the PWA fit for the signal candidate events. The
uncertainties associated with the additional resonances are estimated by
alternative fits including the components $X(1750)$ on the $M_{\phi\eta}$
distribution and $\rho(1700)$ on the $M_{\phi\pi^{0}}$ distribution, which
have the highest significances, but less than 5$\sigma$ with respect to the
baseline solution. Assuming that all the sources of uncertainties are
independent, the total uncertainties are estimated as the quadratic sum of the
above individual values, shown in the supplemental material suppl .

In summary, using 10 billion $J/\psi$ events collected with the BESIII
detector operating at the BEPCII collider, a PWA of the
$J/\psi\to\phi\pi^{0}\eta$ decay is performed for the first time using the
covariant tensor amplitude method. Besides the well established vector
strangeonium meson $\phi(1680)$, an axial-vector meson $h_{1}(1900)$, with
mass M = (1911 $\pm$ 6 $\pm$ 14) $\mathrm{MeV}/c^{2}$ and width $\Gamma$ =
(149 $\pm$ 12 $\pm$ 23) $\mathrm{MeV}$, and a vector meson $X(2000)$, with
mass M = (1996 $\pm$ 11 $\pm$ 30) $\mathrm{MeV}/c^{2}$ and width $\Gamma$ =
(148 $\pm$ 16 $\pm$ 66) $\mathrm{MeV}$, are observed for the first time, with
statistical significances of 24$\sigma$ and 17$\sigma$, respectively. The
$h_{1}(1900)$ meson can be assigned as the $h_{1}(2P)$ strangeonium state,
since its mass and width agree well with the theoretical predictions
Barnes:2002mu ; Li:2020xzs . The $X(2000)$ state can be associated to the
$\phi(3S)$ or $\phi(2D)$ states, but its mass and width have large
discrepancies with the theoretical predictions Barnes:2002mu ; Li:2020xzs .
The observation of the new $h_{1}(1900)$ and $X(2000)$ states provides
important input to establish the strangeonium $s\bar{s}$ spectrum, and calls
for further theory work.

The decay branching fractions of $J/\psi$ $\to$ $\phi f_{0}(980)$ $\to\phi
a_{0}(980)^{0}$ and the corresponding EM process $J/\psi$ $\to$ $\phi
a_{0}(980)^{0}$ are measured with substantially improved precision. The mixing
intensity of $f_{0}(980)-a_{0}(980)^{0}$ ($\xi_{fa}$) is calculated to be
($0.85\pm 0.04\pm 0.25$)%, which is consistent with the destructive solution
in the previous measurement BESIII:2018ozj . It can be used to estimate the
coupling constants of the $f_{0}(980)$ and $a_{0}(980)^{0}$ resonances
Achasov:2016wll . Moreover, the two-fold ambiguity from the previous analysis
BESIII:2018ozj  is resolved here by performing the PWA of
$J/\psi\to\phi\pi^{0}\eta$. This provides crucial constraints for models
describing the internal structure of $a_{0}(980)^{0}$ and $f_{0}(980)$.

The BESIII Collaboration thanks the staff of BEPCII, the IHEP computing center
and the supercomputing center of USTC for their strong support. This work is
supported in part by National Key R&D Program of China under Contracts Nos.
2020YFA0406400, 2020YFA0406300; National Natural Science Foundation of China
(NSFC) under Contracts Nos. 11635010, 11735014, 11835012, 11935015, 11935016,
11935018, 11961141012, 12022510, 12025502, 12035009, 12035013, 12192260,
12192261, 12192262, 12192263, 12192264, 12192265, 11335008, 11625523,
12035013, 11705192, 11950410506, 12061131003, 12105276, 12122509, 12235017,
12205255; the Chinese Academy of Sciences (CAS) Large-Scale Scientific
Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP);
Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contract
No. U1832207, U1732263, U1832103, U2032111, U2032105; CAS Key Research Program
of Frontier Sciences under Contracts Nos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040;
100 Talents Program of CAS; The Institute of Nuclear and Particle Physics
(INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology;
European Union’s Horizon 2020 research and innovation programme under Marie
Sklodowska-Curie grant agreement under Contract No. 894790; German Research
Foundation DFG under Contracts Nos. 455635585, Collaborative Research Center
CRC 1044, FOR5327, GRK 2149; Istituto Nazionale di Fisica Nucleare, Italy;
Ministry of Development of Turkey under Contract No. DPT2006K-120470; National
Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National
Science and Technology fund of Mongolia; National Science Research and
Innovation Fund (NSRF) via the Program Management Unit for Human Resources &
Institutional Development, Research and Innovation of Thailand under Contract
No. B16F640076; Polish National Science Centre under Contract
No.2019/35/O/ST2/02907; The Swedish Research Council; U. S. Department of
Energy under Contract No. DE-FG02-05ER41374.

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# Confirmation of Water Absorption in the Thermal Emission Spectrum of the Hot
Jupiter WASP-77Ab with HST/WFC3

Megan Mansfield Steward Observatory, University of Arizona, 933 N. Cherry
Ave., Tucson, AZ 85719, USA  NHFP Sagan Fellow  Lindsey Wiser School of Earth
and Space Exploration, Arizona State University, Tempe, AZ 85281, USA  Kevin
B. Stevenson Johns Hopkins University Applied Physics Laboratory, Laurel, MD
20723, USA  Peter Smith  School of Earth and Space Exploration, Arizona State
University, Tempe, AZ 85281, USA  Michael R. Line  School of Earth and Space
Exploration, Arizona State University, Tempe, AZ 85281, USA  Jacob L. Bean
Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL
60637, USA  Jonathan J. Fortney  Department of Astronomy and Astrophysics,
University of California, Santa Cruz, CA 95064, USA  Vivien Parmentier
Department of Physics, University of Oxford, Oxford, OX1 3PU, UK  Eliza M.-R.
Kempton  Department of Astronomy, University of Maryland, College Park, MD
20742, USA  Jacob Arcangeli  Anton Pannekoek Institute for Astronomy,
University of Amsterdam, 1098 XH Amsterdam, The Netherlands  Jean-Michel
Désert Anton Pannekoek Institute for Astronomy, University of Amsterdam, 1098
XH Amsterdam, The Netherlands  Brian Kilpatrick  Space Telescope Science
Institute, Baltimore, MD 21218, USA  Laura Kreidberg  Max Planck Institute for
Astronomy, 69117 Heidelberg, Germany  Matej Malik  Department of Astronomy,
University of Maryland, College Park, MD 20742, USA

###### Abstract

Secondary eclipse observations of hot Jupiters can reveal both their
compositions and thermal structures. Previous observations have shown a
diversity of hot Jupiter eclipse spectra, including absorption features,
emission features, and featureless blackbody-like spectra. We present a
secondary eclipse spectrum of the hot Jupiter WASP-77Ab observed between $1-5$
$\mu$m with the Hubble Space Telescope (HST) and the Spitzer Space Telescope.
The HST observations show signs of water absorption indicative of a non-
inverted thermal structure. We fit the data with both a one-dimensional free
retrieval and a grid of one-dimensional self-consistent forward models to
confirm this non-inverted structure. The free retrieval places a $3\sigma$
lower limit on the atmospheric water abundance of
$\log(n_{\mathrm{H_{2}O}})>-4.78$ and can not constrain the CO abundance. The
grid fit produces a slightly super-stellar metallicity and constrains the
carbon-to-oxygen ratio to less than or equal to the solar value. We also
compare our data to recent high-resolution observations of WASP-77Ab taken
with the Gemini-South/IGRINS spectrograph and find that our observations are
consistent with the best-fit model to the high-resolution data. However, the
metallicity derived from the IGRINS data is significantly lower than that
derived from our self-consistent model fit. We find that this difference may
be due to disequilibrium chemistry, and the varying results between the models
applied here demonstrate the difficulty of constraining disequilibrium
chemistry with low-resolution, low wavelength coverage data alone. Future work
to combine observations from IGRINS, HST, and JWST will improve our estimate
of the atmospheric composition of WASP-77Ab.

Hot Jupiters (753), Extrasolar gaseous giant planets (509), Exoplanet
atmospheric composition (2021)

††journal: The Astronomical Journal††facilities: HST(WFC3),
Spitzer(IRAC)††software: batman (Kreidberg, 2015), emcee (Foreman-Mackey et
al., 2013), matplotlib (Hunter, 2007), numpy (van der Walt et al., 2011),
pymultinest (Buchner, 2016), pysynphot (STScI Development Team, 2013), scipy
(Virtanen et al., 2019)

##  1 Introduction

Thermal emission measurements taken during secondary eclipse have the
potential to reveal information on both the compositions and thermal
structures of hot Jupiter atmospheres. The compositions of hot Jupiter
atmospheres can be used to track their formation and migration conditions
(Venturini et al., 2016; Madhusudhan et al., 2017). For example, a key
prediction of the core accretion theory of planet formation is that
atmospheric metallicities should be inversely proportional to planet mass
(Fortney et al., 2013). Furthermore, the carbon-to-oxygen (C/O) ratio provides
information on the mechanisms through which hot Jupiters form and migrate to
their current locations (Öberg et al., 2011; Madhusudhan et al., 2014;
Mordasini et al., 2016; Ali-Dib, 2017; Espinoza et al., 2017; Schneider &
Bitsch, 2021).

In addition to constraining the composition, secondary eclipse observations
can provide information on the thermal structures of hot Jupiters. Theory
predicts a continuum of thermal structures and resulting secondary eclipse
spectra, which can be divided into three primary categories (Fortney et al.,
2008; Parmentier et al., 2018). The coolest hot Jupiters with dayside
temperatures ($T_{day}$) below $\approx 2100$ K are predicted to have non-
inverted temperature-pressure (T-P) profiles, which cause absorption features
in their emergent spectra. Hot Jupiters with intermediate temperatures between
$2100<T_{day}<2400$ K should have emission features resulting from inverted
T-P profiles. Such thermal inversions are predicted to be driven by the
presence of a variety of chemical species, such as TiO, VO, FeH, and metal
atoms (Hubeny et al., 2003; Lothringer et al., 2018). Finally, the ultra-hot
Jupiters with $T_{day}>2400$ K are expected to also have strongly inverted T-P
profiles, but display featureless secondary eclipse spectra in the HST/WFC3
bandpass ($1.1-1.7$ $\mu$m) due to molecular dissociation and H- opacity
(Parmentier et al., 2018; Lothringer et al., 2018; Kitzmann et al., 2018).

These predictions have been borne out through HST observations of absorption
features in low-temperature hot Jupiters (e.g., WASP-43b, Kreidberg et al.,
2014a; and HD 209458b, Line et al., 2016), subtle emission features in medium-
temperature hot Jupiters (e.g., WASP-121b, Evans et al., 2017; Mikal-Evans et
al., 2020; Mansfield et al., 2021; and WASP-76b, Edwards et al., 2020; Fu et
al., 2021; Mansfield et al., 2021) and blackbody-like spectra in the highest-
temperature ultra-hot Jupiters (e.g., WASP-18b, Arcangeli et al., 2018; and
WASP-103b, Kreidberg et al., 2018). However, not all observed hot Jupiters fit
neatly into these three categories. For example, ultra-hot Jupiter Kepler-13Ab
shows absorption features indicative of a non-inverted atmosphere, despite
having a high dayside temperature of $\approx 3000$ K (Beatty et al., 2017).
In general, the population of observed planets shows a scatter in the water
feature strengths at a given temperature, which may be caused by variations in
atmospheric composition (Mansfield et al., 2021).

In this paper we present the secondary eclipse spectrum of WASP-77Ab observed
with HST/WFC3 between $1.1-1.7$ $\mu$m and Spitzer/IRAC at 3.6 and 4.5 $\mu$m.
WASP-77Ab is a mid-temperature hot Jupiter with an equilibrium temperature of
$T_{eq}=1705$ K (Maxted et al., 2013), which is near the point where models
predict a transition from non-inverted T-P profiles creating absorption
features to inverted T-P profiles creating emission features (Mansfield et
al., 2021). The exact temperature of this transition, however, depends in
detail on parameters such as the planet’s atmospheric composition and the
amount of heat deposited in its interior. Our observations of WASP-77Ab have
double the signal-to-noise of any previous observations at temperatures near
this transition, giving us an opportunity to constrain the nature of this
transition. We describe our observations and data reduction in Section 2. In
Section 3, we perform a 1D free retrieval on our data and compare our data to
a set of 1D radiative-convective-thermochemical equilibrium models. Finally,
in Section 4 we compare our data to a recent Gemini-S/IGRINS high-resolution
thermal emission spectrum of WASP-77Ab, compare the water feature strength of
WASP-77Ab to the broader population, and discuss the results of our model
fits.

##  2 Observations and Data Reduction

All of the data presented in this paper were obtained from the Mikulski
Archive for Space Telescopes (MAST) at the Space Telescope Science Institute.
The specific observations analyzed can be accessed via
https://doi.org/10.17909/gjbj-r870 (catalog 10.17909/gjbj-r870).

###  2.1 HST/WFC3 Data

We observed two secondary eclipses of WASP-77Ab on 2020 November 7 and 2020
December 19 using the HST/WFC3+G141 grism between 1.1 and 1.7 $\mu$m as part
of program GO-16168. Each visit consisted of five consecutive orbits in which
WASP-77Ab was visible for approximately 52 minutes per orbit. At the beginning
of each orbit, we took a direct image of the target with the F126N filter for
wavelength calibration.

The observations were taken in the spatial scan mode with the $256\times 256$
subarray using the SPARS25, NSAMP $=5$ readout pattern, resulting in an
exposure time of 89.662 s. We used a scan rate of 0.195 arcsec s-1, which
produced spectra extending approximately 153 pixels in the spatial direction
and peak pixel counts of $\approx 37,000$ electrons per pixel. We used
bidirectional scans and observed 18 exposures per orbit.

We reduced the data using the data reduction pipeline described in Kreidberg
et al. (2014b). We used an optimal extraction procedure (Horne, 1986) and
masked cosmic rays. To subtract the background out of each frame, we visually
inspected the images to find a clear background spot on the detector and
subtracted the median of this background area. The uncertainties on the
measurements were determined by adding in quadrature the photon noise, read
noise, and median absolute deviation of the background.

Following standard procedure for HST/WFC3 eclipse observations, we discarded
the first orbit of each visit. The spectra were binned into 19 channels at a
resolution $R\approx 40-60$. Figure 1 shows an example extracted stellar
spectrum with the wavelength bins indicated. We also created a broadband white
light curve by summing the spectra over the entire wavelength range.

Figure 1: Example stellar spectrum extracted from one spatially scanned
exposure taken by HST/WFC3. Black and red lines indicate the extracted flux
before and after correcting for the flux of the companion star, WASP-77B,
respectively. The spectrum of WASP-77B appears redder in wavelength than that
of WASP-77A because its spectral trace was slightly offset in the spectral
direction on the detector. Vertical gray lines indicate the extent of the bins
for the spectroscopic light curve.

We fit both the white light curve and spectroscopic light curves with the
model described in Kreidberg et al. (2014b), which includes an eclipse model
(Kreidberg, 2015) and a systematics model based on Berta et al. (2012). For
the white light curves, the free parameters in the eclipse model were the mid-
eclipse time $T_{0}$ and the planet-to-star flux ratio $F_{p}$/$F_{s}$. For
the spectroscopic light curves, the mid-eclipse time was fixed to the best-fit
value from the white light curve
($T_{sec}=2455871.12983^{+0.00051}_{-0.00050}$ BJDTDB) and the only free
parameter in the eclipse model was $F_{p}$/$F_{s}$. In both cases, the period,
eccentricity, ratio of the semi-major axis to the stellar radius, inclination,
and planet-to-star radius ratio were fixed to $P=1.360030$, $e=0$,
$\frac{a}{R_{*}}=5.43$, $i=89.40$, and $\frac{R_{p}}{R_{*}}=0.13012$,
respectively (Stassun et al., 2017; Turner et al., 2016). The instrument
systematics model included an orbit-long ramp, whose amplitude and offset were
fixed to the same value for both visits, and a normalization constant, visit-
long slope, and correction for an offset between scan directions, which all
varied between visits. The white light curve fit thus contained a total of 10
free parameters, while the spectroscopic light curve fits had 9 free
parameters.

WASP-77A has a companion star, WASP-77B, which has a projected distance large
enough that their spectra do not overlap in stare mode. However, the spectra
of these two stars overlap during spatial scans. In order to correct for this
overlap, we observed a single 0.556 s stare mode exposure with the G141 grism
at the beginning of each of the two visits. For each visit, we used the same
optimal extraction procedure (Horne, 1986) to extract the stare mode spectra
of WASP-77A and WASP-77B. We then corrected the observed flux for the presence
of the companion star using the equation

$F_{*,corr}=F_{*,obs}\left(\frac{F_{A}}{F_{A}+F_{B}}\right),$ (1)

where $F_{*,corr}$ is the corrected flux in units of electrons, $F_{*,obs}$ is
the observed flux in units of electrons, and $F_{A}$ and $F_{B}$ are the
observed fluxes of the primary and companion star in that bandpass,
respectively.

We estimated the parameters with a Markov Chain Monte Carlo (MCMC) fit using
the emcee package (Foreman-Mackey et al., 2013). The best-fit white light
curve had $\chi^{2}_{\nu}=4.92$ and an average residual of 90 ppm, which is
typical for WFC3 observations of transiting planets orbiting bright host
stars. The spectroscopic light curves achieved photon-limited precision, with
$\chi^{2}_{\nu}$ values between $0.68-1.30$. The final secondary eclipse
spectrum is shown in Figure 2, and Table 1 lists the planet-to-star flux ratio
in each channel.

Figure 2: Left: Emission spectrum fits using the 1D free retrieval described in Section 3.1, and the Sc-CHIMERA 1D model grid described in Section 3.2. Dark lines represent the median fit, and dark and light shading show 1 and 2$\sigma$ regions, respectively. Black points show the observations. The inset shows a zoomed in view of the WFC3 segment of the spectrum. The models generally fit the data well, with the best fit models having reduced chi squared of $\chi^{2}_{\nu}=1.12$ for the free retrieval and $1.24$ for the grid fit. Right: Corresponding pressure-temperature profiles. Grid profiles within 1 and 2$\sigma$ are shown by dark and light purple lines, respectively. 1 and 2$\sigma$ regions for the free retrieval are shaded in dark and light yellow, respectively. Contribution functions are also plotted for each Spitzer point, and for in ($1.35-1.48$ $\mu$m) and out ($1.55-1.7$ $\mu$m) of the water feature in the WFC3 wavelength range. Wavelength [$\mu$m] |  $F_{p}$/$F_{s}$ [ppm]
---|---
$1.120-1.148$ | $192\pm 47$
$1.148-1.177$ | $297\pm 46$
$1.177-1.205$ | $384\pm 45$
$1.205-1.234$ | $359\pm 44$
$1.234-1.262$ | $324\pm 43$
$1.262-1.291$ | $354\pm 43$
$1.291-1.319$ | $359\pm 42$
$1.319-1.347$ | $348\pm 42$
$1.347-1.376$ | $313\pm 43$
$1.376-1.404$ | $283\pm 43$
$1.404-1.433$ | $273\pm 44$
$1.433-1.461$ | $271\pm 44$
$1.461-1.489$ | $313\pm 45$
$1.489-1.518$ | $315\pm 46$
$1.518-1.546$ | $346\pm 45$
$1.546-1.575$ | $402\pm 47$
$1.575-1.603$ | $436\pm 48$
$1.603-1.632$ | $499\pm 49$
$1.632-1.660$ | $486\pm 51$
$3.6$ | $2303\pm 62$
$4.5$ | $2904\pm 78$
Table 1: Secondary eclipse spectrum of WASP-77Ab.

###  2.2 Spitzer/IRAC Data

The Spitzer Space Telescope observed the WASP-77 system at 3.6 and 4.5 µm
under program 13038 (PI: Stevenson). Each phase curve observation lasted 39.5
hours (starting shortly before secondary eclipse and ending shortly after the
subsequent eclipse) and was subdivided into three Astronomical Observation
Requests (AORs). The first AOR consisted of a 24-minute settling period,
followed by a two science AORs lasting 23 and 16 hours each. The break between
science AORs occurred shortly after transit.

We used the Photometry for Orbits, Eclipses, and Transits (POET) data
reduction and analysis pipeline (Stevenson et al., 2012; Cubillos et al.,
2013; Bell et al., 2021) to derive the secondary eclipse depths reported in
this work. For these data, we utilized a $3\times 3$-pixel centroiding
aperture to minimize contamination from WASP-77A’s nearby binary companion
(WASP-77B) located roughly 2.5 Spitzer pixels away. The standard $5\times
5$-pixel centroiding aperture demonstrated a noticeable bias towards WASP-77B
and significant volatility in the measured values. At 3.6 µm, the pointing was
stable over the course of the phase curve observation. At 4.5 µm, we measured
a drift of 0.5 pixels over the first six hours of observing before
stabilizing. The 4.5 µm centroids do not overlap with the “sweet spot” mapped
out by May & Stevenson (2020) and, thus, we could not use their fixed
intrapixel sensitivity map to remove position-dependent systematics.

We tested a range of photometry aperture sizes from 2.0 to 4.75 pixels in
0.25-pixel increments. For each aperture size, we fit the transit, two
eclipses, and sinusoidal variation from the planet. Both Spitzer channels use
BLISS mapping (Stevenson et al., 2012) to fit the intrapixel sensitivity
variations. The 3.6 µm observation also requires a rising exponential plus
linear ramp to fit the time-dependent systematics and a linear function to fit
variations in PRF width along the $y$ direction (PRF detrending, Lanotte et
al., 2014). The 4.5 µm channel does not exhibit a time-dependent systematic.

The measured eclipse depths decrease systematically with increasing photometry
aperture size due to increasing contamination from WASP-77B within the
aperture. We use the mean image of each Spitzer observation to estimate the
companion flux fraction within each photometric aperture. This process
involves masking the flux from WASP-77A, computing the centroid of WASP-77B,
and performing aperture photometry on a Spitzer PRF situated at WASP-77B’s
centroid position. We then follow the methods describe by Stevenson et al.
(2014) to compute corrected eclipse depths. Using CatWISE (Marocco et al.,
2021), we estimate the dilution factor to be $0.410{\pm}0.013$ and
$0.405{\pm}0.012$ at 3.6 and 4.5 µm, respectively. This calculation is
possible since WISE1 and WISE2 have similar bandpasses to IRAC1 and IRAC2. As
validation to our methods, we find that the corrected eclipse depths are
independent of our choice of aperture size (i.e., they are all consistent
within 1$\sigma$). Using the apertures that yield the smallest standard
deviation of the normalized residuals (3.5 pixels at 3.6 µm and 4.5 pixels at
4.5 µm), we report our final eclipse depths in Table 1.

##  3 Analysis

We explore fitting the data with a variety of models to test how a gradient of
model assumptions impact the derived atmospheric parameters. Here we explore
the results from two common modeling philosophies. The first, described in
Section 3.1, is the ”free” retrieval methodology whereby we fit for the
constant-with-altitude abundances for water and carbon monoxide, (the dominant
species over the observed wavelengths) and a vertical temperature profile.
Within the free retrieval there are no physical/chemical constraints that
relate the gas abundances to each other or the temperature profile. The
second, described in Section 3.2, is the self-consistent 1D radiative
convective grid model fitting method. This method assumes thermochemical
equilibrium chemical abundances for all gases along the temperature pressure
profile, which in turn is dependent upon the opacities and gas abundances. In
this framework, rather than retrieving the gas abundances and T-P profile
independently, we instead retrieve intrinsic elemental abundances
(parameterized with a metalllicity and carbon to oxygen ratio) and a heat
redistribution (which sets the effective stellar flux on the planetary
dayside). We explore both of these models throughout this paper because their
differing levels of complexity allow us to better understand the nature of the
planet’s atmosphere than applying a single model framework alone.

###  3.1 1D Free Retrieval

We performed a 9-parameter free atmospheric retrieval, fitting directly for
the volume mixing ratios (constant with pressure) of H2O and CO, 6 parameters
describing the shape of an analytic temperature-pressure profile, and a scale
factor (see Table 2 for each model parameter and its prior range, which is
uniform for all parameters). The scale factor ($a$) accounts for any geometric
dilution of a dayside hotspot by multiplying the planet-to-star flux ratio by
a constant (e.g., Taylor et al., 2021). A value of $a$ close to 1 indicates a
more homogeneous dayside, while a smaller value of $a$ indicates a more
concentrated hotspot. The temperature-pressure profile is that given by
Madhusudhan & Seager (2009), which is a piecewise function of the form

$T(P)=T_{0}+\Bigg{(}\frac{\log(P/P_{0})}{\alpha_{1}}\Bigg{)}^{1/\beta_{1}},\
P_{0}<P<P_{1}$ (2)

$T(P)=T_{2}+\Bigg{(}\frac{\log(P/P_{2})}{\alpha_{2}}\Bigg{)}^{1/\beta_{2}},\
P_{2}<P<P_{3}$ (3)

$T(P)=T_{3},\ P>P_{3}$ (4)

for three atmospheric layers. Layer 1, the upper atmosphere, is between
pressures $P_{0}$ (the top of atmosphere) and $P_{1}$, and the T-P profile has
a slope determined by $\alpha_{1}$ and $\beta_{1}$. Layer 2, the middle
atmosphere, is between pressures $P_{1}$ and $P_{3}$ and has a slope
determined by $\alpha_{2}$ and $\beta_{2}$. At pressures greater than $P_{3}$,
the profile is isothermal. A third pressure point, $P_{2}$, can be either
above or below $P_{1}$, and if $P_{2}>P_{1}$, an inversion will occur. $T_{2}$
and $T_{3}$ are the temperatures at $P_{2}$ and $P_{3}$ (determined via
continuity), respectively, and $T_{0}$ is the top-of-atmosphere temperature.
We set $\beta_{1}=\beta_{2}=0.5$ to match empirical results, and are left with
6 free parameters: $T_{0}$, $P_{1}$, $P_{2}$, $P_{3}$, $\alpha_{1}$, and
$\alpha_{2}$. While an inversion is not expected for WASP-77Ab, we allow
$P_{2}$ to range both higher and lower than $P_{1}$.

For the planet’s thermal emission spectrum, we use a psuedo-line-by-line
radiative transfer code with absorption cross sections sampled at a resolution
$R=\lambda/\Delta\lambda$ of 20,000 (for an introduction to the forward
modelling and retrieval frameworks, see Line et al., 2013, 2021). We only
include opacities of H2-H2/He CIA, H2O, and CO. The stellar spectrum is
interpolated from the PHOENIX library of model stellar spectra (Husser et al.,
2013) and smoothed with a Guassian filter. Each model spectrum is then binned
onto the WFC3 wavelength grid and integrated through the IRAC throughput
curves. We used the Python wrapper PyMultiNest (Buchner, 2016) for the nested
sampling algorithm MULTINEST (Feroz et al., 2009) for Bayesian parameter
estimation.

Parameter | Prior
---|---
$\log(n_{\mathrm{H_{2}O}})$ |  $\mathcal{U}$(-12, 0)
$\log(n_{\mathrm{CO}})$ |  $\mathcal{U}$(-12, 0)
$T_{0}$ [K] |  $\mathcal{U}$(400,3000)
$\log P_{1}[\log$ bar] |  $\mathcal{U}$(-5.5, 2.5)
$\log P_{2}[\log$ bar] |  $\mathcal{U}$(-5.5, 2.5)
$\log P_{3}[\log$ bar] |  $\mathcal{U}$(-2, 2.5)
$\alpha_{1}$ |  $\mathcal{U}$(0.02, 1.98)
$\alpha_{2}$ |  $\mathcal{U}$(0.02, 1.98)
$\log(a)$ |  $\mathcal{U}$(-2, 4)
Table 2: Free parameters and their prior ranges (all uniform) for the free
retrieval.

Figure 2 shows the measured spectrum for WASP-77Ab with model spectra and T-P
profiles randomly drawn from the posterior distribution. Figure 3 contains a
corner plot showing the marginal posterior probability distribution of each
parameter. The best fit spectrum has a reduced chi-square metric
$\chi^{2}_{\nu}$ = 1.12. We are unable to constrain the abundance of H2O but
can place a robust lower limit at $\log(n_{\mathrm{H_{2}O}})>-4.78$ at
3$\sigma$, whereas CO (and therefore C/O) is entirely unconstrained due to the
lack of significant CO spectral features captured by WFC3. Consequently, we
can only place a lower limit on the metal content of the atmosphere at
[(C+O)/H] $>$ -1.69 at 3$\sigma$. The retrieved temperature-pressure profile
(Figure 2, right) is monotonically increasing with pressure and has a top-of-
atmosphere temperature of 1670${}^{+62}_{-68}$ K. The scale factor is 0.95
$\pm$ 0.04, indicative of a homogenous dayside with little to no clouds.

Figure 3: Posterior distributions of all parameters in the free retrieval
(Section 3.1). Off-diagonal plots show 2D posterior probabilities for pairs of
parameters, with 1, 2, and $3\sigma$ intervals indicated in dark, medium, and
light blue. Panels on the diagonal show 1D posterior probability distributions
for each parameter. The free parameters include volume mixing ratios of H2O
and CO, 6 parameters for the analytic T-P profile, and a scale factor.

###  3.2 Comparison to 1D Model Grid

In addition to performing a classic free retrieval, we used Sc-CHIMERA to
perform a 1D radiative-convective-thermochemical equilibrium (1D-RC) grid
model retrieval, following a similar methodology described in Arcangeli et al.
(2018) and Mansfield et al. (2018). We generated a WASP-77Ab specific model
grid with free parameters for the global heat redistribution ($f$),
metallicity ([M/H]), and carbon-to-oxygen ratio (C/O). We used the same 1D-RC
framework described in Mansfield et al. (2021), which is an upgrade to that
used in Arcangeli et al. (2018) and Mansfield et al. (2018). We also include
the scale factor ($a$), which can be included without an additional grid
dimension. The grid is coupled to the pymultinest nested sampler to perform
parameter estimation across $f$, [M/H], C/O, and $a$.

We defined prior ranges of 0.4 – 2.8 for $f$, -2.0 – 2.6 for [M/H], and 0.01 –
1.4 for C/O. The heat redistribution factor is defined as in Parmentier et al.
(2021) as a function of dayside and equilibrium temperature,
$f=(T_{d}/T_{*})^{4}$. As such, $f=1$ corresponds to full redistribution,
$f=2$ corresponds to dayside-only redistribution, and $f=2.67$ is the maximum
value allowed by energy conservation. The prior range for $f$ extends beyond
possible values to allow pymultinest to converge close to maximum and minimum,
if needed. The prior range for [M/H] encompasses the range of Solar System and
exoplanet observations and predictions presented in prior literature
(Thorngren et al., 2016; Mordasini et al., 2016; Kreidberg et al., 2014a;
Welbanks et al., 2019). The C/O prior range is also defined based on prior
literature expectations of C/O$<1$ (Mordasini et al., 2016).

Figure 2 shows the resulting spectrum and T-P profile for the grid fit, and
Figure 4 shows a corner plot for the full posterior. The best grid fit had a
reduced chi squared value of $\chi^{2}_{\nu}=1.24$ and showed a non-inverted
T-P profile. The value of $f=1.50\pm 0.09$ retrieved from the fit is
consistent with 3D models of cloud-free hot Jupiters at the temperature of
WASP-77Ab (Parmentier et al., 2021). The retrieved value of the scale factor
$a$ was close to 1, which is consistent with the constraint on $f$ because
with more heat redistribution we’d expect a less pronounced hotspot. The best
fit metallicity was [M/H]$=0.43^{+0.36}_{-0.28}$. We note that this
metallicity is significantly higher and less precise than the value derived
from recent high-resolution observations - see Section 4.2 for a full
discussion of these differences. The carbon-to-oxygen ratio is not well
constrained, as we do not observe any resolved features of carbon-bearing
molecules. However, the fit provides a $2\sigma$ upper limit of C/O$=0.78$,
indicating that the planet likely has a solar or sub-solar C/O.

Figure 4: Posterior distributions of free parameters in the 1D Sc-CHIMERA
model grid fit for the fit to the full data set (blue) and the fit to the data
with the bluest 4 points removed (red). For the full data set, 2D histograms
for pairs of parameters are shown in off-diagonal plots with 1, 2, and
3$\sigma$ regions shaded in light, medium, and dark blue, respectively.
Histograms on the diagonal show 1D posterior probability distributions for
each individual parameter.

##  4 Discussion

###  4.1 HST Water Feature Strength

In order to place our observations of WASP-77Ab in the broader context of
previous hot Jupiter secondary eclipse observations, we compared the observed
water feature strength and derived metallicity to HST/WFC3 observations of
other hot Jupiters. We computed the HST water feature strength $S_{H_{2}O}$
for WASP-77Ab following Equation 1 in Mansfield et al. (2021). The water
feature strength for WASP-77Ab is shown in Figure 5 compared to the feature
strengths for the data and models presented in Mansfield et al. (2021). We
find that the water feature strength of WASP-77Ab fits the previously observed
trend, and matches the expectations from the self-consistent models of
Mansfield et al. (2021). Additionally, the fact that this planet shows a water
feature in absorption at a dayside temperature of $\approx 1900$ K disfavors
models with high $\mathrm{C/O}\gtrsim 0.7$, low metallicity
$\mathrm{[M/H]}\lesssim-1.0$, or an amount of internal heating following
Thorngren et al. (2019), as such models predict a transition to inverted
atmospheres below this temperature.

Figure 5: HST water feature strength ($S_{H_{2}O}$) and dayside temperature
($T_{day}$) of WASP-77Ab (bold, diamond point) in the context of all other
planets observed between $1.1-1.7$ $\mu$m with HST/WFC3 (colored, circular
points; Mansfield et al., 2021; Fu et al., 2022). Both values are calculated
following the descriptions in Mansfield et al. (2021). Positive/negative
values of $S_{H_{2}O}$ indicate features observed in absorption/emission,
respectively, and a value of $S_{H_{2}O}=0$ indicates a featureless,
blackbody-like spectrum. The grey points and shaded region show predictions
from the 1D model grid presented in Mansfield et al. (2021). WASP-77Ab has
$S_{H_{2}O}=0.157\pm 0.049$, indicating the presence of a strong water
absorption feature in its spectrum. This value agrees with previously observed
trends that planets below $T_{day}\approx 2100$ K tend to have absorption
features due to non-inverted T-P profiles, but that the scatter in water
feature strengths for planets at similar temperatures suggests compositional
differences in their atmospheres (Fortney et al., 2008; Parmentier et al.,
2018; Mansfield et al., 2021).

###  4.2 Comparison to Gemini-S/IGRINS Results

Confidence in composition and thermal structure inferences is bolstered when
independent observations with different instruments arrive at the same
conclusions. WASP-77Ab was recently observed near secondary eclipse at high
resolution using the IGRINS spectrograph (R$\sim$45,000) on Gemini-South (Line
et al., 2021). These observations spanned a wavelength range of $1.45-2.55$
$\mu$m, which allowed them to precisely constrain abundances of both water and
carbon monoxide. Figure 6 compares our WFC3 spectrum to the best-fit model
from a high-resolution cross-correlation retrieval on these recent IGRINS
observations. This plot also shows an ensemble of 500 spectra reconstructed
from parameters drawn from the posterior probability distribution of that
retrieval.

Figure 6: Comparison of our HST/WFC3 and Spitzer emission spectrum of
WASP-77Ab (black points) with a fit of dayside emission from high-resolution
Gemini-S/IGRINS observation (Line et al., 2021). The blue line and points show
the median model fit to the IGRINS data, at full resolution and smoothed to
the resolution of the WFC3 data, respectively. Red lines show 500 random draws
from the posterior of the high-resolution fit smoothed to an R=100.

Figure 6 shows that the extrapolated IGRINS model spectra are remarkably
consistent with our WFC3 spectrum, providing cross-validation for these
ground- and space-based observations. However, the best fit to the high-
resolution observations retrieved a metallicity of
[M/H]$=-0.48^{+0.15}_{-0.13}$ and a carbon-to-oxygen ratio of C/O$=0.59\pm
0.08$ (Line et al., 2021). While their metallicity is consistent with the
lower limit from our free retrieval (which is the same retrieval paradigm used
in Line et al. (2021)), it is inconsistent with the metallicity we derive from
the grid fit at $1.8\sigma$.

Figure 7 shows the metallicities of WASP-77Ab derived from the free and grid
retrievals compared to the IGRINS result. We investigated what could be
driving the discrepancy in derived metallicities between our low-resolution
WFC3 and Spitzer data and the high-resolution IGRINS data and found that the
higher metallicity we derive with our grid fits is driven by the strong
downward slope of the bluest points in the WFC3 spectrum. We analyzed the two
WFC3 visits independently and found that the downward slope at the blue end of
the spectrum is consistent across both visits. We performed a grid fit to the
WFC3+Spitzer data with the bluest four points removed and derived a
metallicity of [M/H]$=0.10^{+0.43}_{-0.31}$, which is more consistent with the
high-resolution measurement. The results of this fit are shown in Figure 4.
This result may indicate that the bluest part of the spectrum, which is not
well fit by our equilibrium chemistry models, is influenced by disequilibrium
chemistry. However, the lack of precise abundance measurements from our free
retrieval demonstrates the difficulty of constraining chemistry in a non-
equilibrium model with only low-resolution, low wavelength coverage data.
Alternatively, this discrepancy may just be due to the sensitivity of low-
resolution retrieval results to slight changes in the spectral shape. We note
that our investigation here is not intended to provide a more accurate or
precise metallicity measurement than that derived from the IGRINS
observations, but rather to use a comparison of these two data sets to bolster
confidence in the high-resolution result and discuss the limitations of
deriving abundance constraints from low-resolution data alone. Additionally,
techniques for extracting abundance measurements from high-resolution data are
relatively new and have only been applied to a couple of data sets, so a
comparison to the low-resolution results we present here is useful for
assessing the validity of the high-resolution results, even if the low-
resolution composition measurements are less well constrained.

Figure 7: Atmospheric metallicity as a function of planet mass. Black points
show solar system planet metallicities, which are based on measurements of
[CH4/H] (Wong et al., 2004; Fletcher et al., 2009; Karkoschka & Tomasko, 2011;
Sromovsky et al., 2011). The black dashed line shows a fit to the solar system
trend, but plateauing at 1 when the planet metallicity equals the stellar
metallicity. Grey points show [H2O/H] for previously observed exoplanets
(Welbanks et al., 2019). We additionally compare four measurements of the
metallicity of WASP-77Ab: [M/H] from our grid retrieval described in Section
3.2 (red), [M/H] from the grid retrieval on the data with the bluest four
points removed (orange, see Section 4.2), [H2O/H] from our free retrieval
described in Section 3.1 (blue, lower limit only), and [C+O/H] from recent
high-resolution observations with Gemini-S/IGRINS (green, Line et al., 2021).

We leave a joint retrieval combining our low-resolution HST and Spitzer data
and the high-resolution Gemini-S/IGRINS data for a future paper (Smith et al.
in prep.). Although it is outside the scope of this paper, such combined high-
resolution and low-resolution fits can constrain the atmospheric composition
even more tightly than either data set alone (Brogi & Line, 2019).
Additionally, in the near future, (JWST) will measured the dayside emission
spectrum of WASP-77Ab from 2.87 to 5.10 $\mu$m (GTO 1274; PI Lunine). These
data will further illuminate the atmospheric composition of WASP-77Ab.

This work was based on observations made with the NASA/ESA Hubble Space
Telescope that were obtained from the data archive at the Space Telescope
Science Institute (STScI), which is operated by the Association of
Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555.
This work also used observations made with the Spitzer Space Telescope, which
is operated by the Jet Propulsion Laboratory, California Institute of
Technology under a contract with NASA. We acknowledge an anonymous reviewer
for helpful comments which improved the manuscript. Support for this work was
provided by NASA through the NASA Hubble Fellowship grant HST-HF2-51485.001-A
awarded by STScI. M. Mansfield acknowledges support from a NASA FINESST grant.
J.M.D acknowledges support from the Amsterdam Academic Alliance (AAA) Program,
and the European Research Council (ERC) European Union’s Horizon 2020 research
and innovation programme (grant agreement no. 679633; Exo-Atmos). This work is
part of the research programme VIDI New Frontiers in Exoplanetary Climatology
with project number 614.001.601, which is (partly) financed by the Dutch
Research Council (NWO).

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