4
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 Xinyang Normal University, Xinyang 464000, People’s Republic of China
78 Yantai University, Yantai 264005, People’s Republic of China
79 Yunnan University, Kunming 650500, People’s Republic of China
80 Zhejiang University, Hangzhou 310027, People’s Republic of China
81 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 AlsoatFrontiersScienceCenterforRareIsotopes, LanzhouUniversity, Lanzhou 730000, People’s RepublicofChina
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
(Dated: September27, 2023)
Based on a data sample of (27.08 0.14) 108 ψ(3686) events collected with the BESIII de-
tector at the BEPCII collider, the M± 1 trans× ition ψ(3686) γηc(2S) with ηc(2S) KK¯π is
studied, where KK¯π is K+K−π0 or K S0K±π∓. The mass→ and width of the ηc(2S→ ) are mea-
sured to be (3637.8 0.8(stat) 0.2(syst)) MeV/c2 and (10.5 1.7(stat) 3.5(syst)) MeV, re-
spectively. The prod± uct branchi± ng fraction (ψ(3686) γηc(2S± )) (ηc(2± S) KK¯π) is deter-
mined to be (0.97 ±0.06(stat) ±0.09(syst))B ×10−5. U→ sing B(ηc(2× S)B
→
KK¯π→ ) = (1.86+ −0 0. .6 48 9)%,
we obtain the branching fraction of the radiative transition to be (ψ(3686) γηc(2S)) =
(5.2 0.3(stat) 0.5(syst)+1.9(extr)) 10−4, where the third uncertB ainty is due→ to the quoted
(ηc±
(2S)
KK¯±
π).
−1.4 ×
B →
I. INTRODUCTION served by the Belle collaboration in the B meson decay,
B± K±η (2S),withη (2S) K0K±π∓ in2002[10].
→ c c → S
However,knowledgeaboutthisparticleisstillverylimit-
Charmonia, comprising bound states of a charmed
ed. Forexample,thesumofitsbranchingfractions(BFs)
quarkanditsantiquark(cc¯),provideauniqueopportuni-
measuredexperimentallyisonlyabout3%[11]. Sincethe
tytostudythestronginteractionsintheτ-charmenergy
η (2S)isapseudo-scalarparticlewithquantumnumbers
regime,wherenon-perturbativecontributionsarecompa- c
JPC =0−+, it cannotbe produceddirectly via electron-
rable to perturbative ones. In the low energy region,the
positron annihilation. The production of the η (2S)
large coupling of the strong interaction (α ) makes first- c
s
throughψ(3686)radiativetransitionrequiresacharmed-
principle calculations extremely difficult. Thus, various
quark spin-flip and, thus, proceeds via a magnetic tran-
theoretical models have been developed [1–4], and good
sition. The partial width Γ(ψ(3686) γη (2S)) [1–
agreement has been achieved for the mass spectrum of → c
3] and the BF (ψ(3686) γη (2S)) [12] have been
charmonia below the open-charm threshold. However, B → c
calculated in different theoretical frameworks, as shown
long-standing puzzles in charmonium physics still exist,
such as the ρ π puzzle [5–7] and substantial non-DD¯ in Table I. These include the non-relativistic potential
− model (NR model) [1, 2], the Godfrey-Isgur relativized
decays of the ψ(3770)[8, 9]. Further studies of the char-
potential model (GI model) [1, 2], the light-front quark
moniumsystemaredesired,both theoreticalandexperi-
model [3], and effective field theory [12], among others.
mental, to resolve these puzzles and consequently better
Significant discrepancies exist among the predictions.
understand the strong interaction.
Thecharmoniumspin-singletstateη (2S)wasfirstob- On the experimental side, the first observation of the
c