---
abstract: 'In recent years, lots of studies of charmonium decays have been performed at BESIII based on large data samples of $J/\psi$, $\psi(3686)$ and $\psi(3770)$. Recent results in searches for radiative transitions of $\psi(3770)$ and rare phenomena in charmonium decays, and studies of light hadrons structures and properties will be presented.'
author:
- 'X. C. Ai on behalf of the BESIII Collaboration'
bibliography:
- 'proceeding.bib'
nocite: '[@*]'
title: Studies of Charmonium at BESIII
---

INTRODUCTION
============

The BESIII detector at the BEPCII collider has accumulated the world’s largest data samples of $e^+e^-$ collisions in the $\tau$-charm region, including $J/\psi$, $\psi(3686)$, $\psi(3770)$ and the XYZ data. These data samples provide a clean and simple environment to study the production and decay mechanisms of charmonium states including not only $J/\psi$, $\psi(3686)$, $\psi(3770)$, but also $\eta_c$, $\eta_c(2S)$ and $\chi_{cJ}$ which are available by the $\gamma$ transition of $\psi(3686)$ and $\psi(3770)$.

Results in this presentation are based on 2.92 fb$^{-1}$ data sample taken at $\sqrt{s}$ = 3.773 GeV, 1.06 $\times$ $10^8$ $\psi(3686)$ events and 1.31 $\times$ $10^9$ $J/\psi$ events.

SEARCH FOR $\psi(3770)$ RADIATIVE TRANSITIONS
=============================================

The nature of the excited $J^{PC}$ = $1^{--}$ $c\bar{c}$ bound states above the $D\bar{D}$ threshold is of interest but still not well known. The $\psi(3770)$ resonance, as the lightest charmonium state lying above the open charm threshold, is generally assigned to be a dominant $1^3 D_1$ momentum eigenstate with a small $2^3 S_1$ admixture [@bib1]. It has been thought almost entirely to decay to $D\bar{D}$ states [@bib2; @bib3]. Unexpectedly, the BES Collaboration found a large inclusive non-$D\bar{D}$ branching fraction, (14.7 $\pm$ 3.2)%, by utilizing various methods [@bib4; @bib5; @bib6; @bib7]. A later work by the CLEO Collaboration found a contradictory non-$D\bar{D}$ branching fraction,(3.3 $\pm$ 1.4$_{-4.8}^{+6.6}$)% [@bib8]. The BES results suggest substantial non-$D\bar{D}$ decays, although the CLEO result finds otherwise. In the exclusive analyses, various non-$D\bar{D}$ decay modes have been observed, including hadronic transitions $\psi(3770)\rightarrow J/\psi\pi^+\pi^-$ [@bib9; @bib10], $\pi^0\pi^0J/\psi$, $\eta J/\psi$  [@bib10], the $E1$ transitions $\gamma \chi_{cJ}$ (J = 0, 1) [@bib11; @bib12], and the decay to light hadrons $\phi\eta$ [@bib13]. The sum of the observed non-$D\bar{D}$ exclusive components still makes up less than 2% of all decays [@pdg], which motivates the search for other exclusive non-$D\bar{D}$ final states.

Search for $\psi(3770)\rightarrow\gamma\eta_c$ and $\gamma\eta_c(2S)$
---------------------------------------------------------------------

The radiative transitions $\psi(3770)\rightarrow\gamma\eta_c(\eta_c(2S))$ are supposed to be highly suppressed by selection rules, considering the $\psi(3770)$ is predominantly the $1^3D_1$ state. However, due to the non-vanishing photon energy in the decay, higher multipoles beyond the leading one could contribute [@bib15]. Recently, the partial decay widths $\Gamma(\psi(3770)\rightarrow\gamma\eta_c(\eta_c(2S))$ have been calculated in Ref. [@bib15] by considering contributions from the intermediate meson loop (IML) mechanism.

Using the $\psi(3770)$ data sample, the radiative transitions $\psi(3770)\rightarrow\gamma\eta_c(\eta_c(2S))$ through the decay process $\psi(3770)\rightarrow K_S^0 K^{\pm}\pi^{\mp}$ have been searched for [@bibetac]. Figure  \[fig:mkskpi\] shows the invariant-mass spectrum of $K_S^0 K^{\pm}\pi^{\mp}$ for selected candidates, together with the estimated backgrounds in the $\eta_c$ mass region (Fig. \[fig:mkskpi\](a)) and in the $\chi_{c1}$ $-$ $\eta_c(2S)$ mass region (Fig. \[fig:mkskpi\](b)). No significant $\eta_c$ and $\eta_c(2S)$ signals are observed. The upper limits on the branching fractions at a 90% C.L. have been set: ${\mathcal B}(\psi(3770)\rightarrow\gamma\eta_c) < 6.8 \times 10^{-4}$ and ${\cal B}(\psi(3770)\rightarrow\gamma\eta_c(2S)) < 2.0 \times 10^{-3}$. The upper limit for $\Gamma(\psi(3770)\rightarrow\gamma\eta_c)$ is within the error range of the theoretical predictions of IML [@bib15] and lattice QCD calculations [@bib16]. However, the upper limit for $\Gamma(\psi(3770)\rightarrow\gamma\eta_c(2S))$ is much larger than the prediction and is limited by statistics and the systematic error.

![Invariant-mass spectrum for $K_S^0 K^{\pm}\pi^{\mp}$ from data with the estimated backgrounds and best-fit results superimposed in the (a) $\eta_c$ and (b) $\chi_{c1}$ and $\eta_c(2S)$ mass regions. Dots with error bars are data. The shaded histograms represent the background contributions and the solid lines show the total fit results.[]{data-label="fig:mkskpi"}](fit1.png "fig:"){width="200pt"} ![Invariant-mass spectrum for $K_S^0 K^{\pm}\pi^{\mp}$ from data with the estimated backgrounds and best-fit results superimposed in the (a) $\eta_c$ and (b) $\chi_{c1}$ and $\eta_c(2S)$ mass regions. Dots with error bars are data. The shaded histograms represent the background contributions and the solid lines show the total fit results.[]{data-label="fig:mkskpi"}](fit2.png "fig:"){width="200pt"}

Measurement of the Branching Fraction for $\psi(3770)\rightarrow\gamma\chi_{cJ}$
--------------------------------------------------------------------------------

Within an S-D mixing model [@bib1], Refs. [@bib17; @bib18; @bib19] predict the partial widths for $\psi(3770)$ $E1$ radiative transitions, but with large uncertainties. Up to now, the transition $\psi(3770)\rightarrow\gamma\chi_{c2}$ has not been observed. Precision measurements of partial widths of the $\psi(3770)\rightarrow\gamma\chi_{c1,2}$ processes are critical to test the theoretical predictions, and to better understand the nature of the partial widths of the $\psi(3770)$, as well as to find the origin of the non-$D\bar{D}$ decays of $\psi(3770)$.

Using the $\psi(3770)$ data sample, the $\psi(3770)$ $E1$ transitions $\psi(3770)\rightarrow\gamma\chi_{c1,2}$ have been studied [@bibchicJ] by reconstructing $\chi_{cJ}$ using the decay $\chi_{cJ}\rightarrow\gamma J/\psi$. Figure \[fig:mgjpsi\] shows the invariant-mass distribution of the higher energetic photon and $J/\psi$. Clear peak corresponding to the $\chi_{c1}$ signal is observed while there is no significant signal of $\chi_{c2}$. The branching fraction of $\psi(3770)\rightarrow\gamma\chi_{c1}$ is measured to be ${\cal B}(\psi(3770)\rightarrow\gamma\chi_{c1}) = (2.48\pm0.15\pm0.23)\times 10^{-3}$ , which is the most precise measurement to date. The upper limit on the branching fraction of $\psi(3770)\rightarrow \gamma\chi_{c2}$ at 90% C.L. is ${\cal B}(\psi(3770)\rightarrow\gamma\chi_{c2})<0.64\times10^{-3}$.

![Invariant mass spectrum of higher energetic photon and $J/\psi$ selected from data. The dots with error bars represent the data. The solid (red) line shows the fit. The dashed (blue) line shows the smooth background. The long-dashed (green) line is the sum of the smooth background and the contribution from $e^+e^-\rightarrow(\gamma_{ISR})\psi(3686)$ production.[]{data-label="fig:mgjpsi"}](mgjpsi.png){width="200pt"}

SEARCH FOR RARE PHENOMENA IN CHARMONIUM DECAYS
==============================================

Search for Isospin-violating Transition $\chi_{c0,2}\rightarrow\pi^0\eta_c$
---------------------------------------------------------------------------

Based upon an effective-field theoretical approach, theoretical calculations give qualitative insights in the isospin-breaking mechanisms in charmonium decays below $D\bar{D}$ threshold [@bib25]. Currently, for such a theory, quantitative predictions of individual branching fractions of isospin-forbidden decays of charmonium require more constraints from experimental data.

Using the $\psi(3686)$ data sample, the hadronic isospin-violating transitions $\chi_{c0,2}\rightarrow\pi^0\eta_c$ have been searched for through $\eta_c\rightarrow K_S^0 K^{\pm}\pi^{\mp}$ decays [@bibpi0etac]. No statistically significant signal is observed and upper limits on the branching fractions for the processes $\chi_{c0,2}\rightarrow\pi^0\eta_c$ have been obtained. The results are ${\cal B}(\chi_{c0}\rightarrow \pi^0\eta_c) < 1.6\times 10^{-3}$ and ${\cal B}(\chi_{c2}\rightarrow \pi^0\eta_c) < 3.2\times 10^{-3}$. These are the first upper limits on ${\cal B}(\chi_{c0,2}\rightarrow \pi^0\eta_c)$ that have been reported so far. These limits might help to constrain non-relativistic field theories and provide insight in the role of charmed-meson loops to the various transitions in charmonium and charmonium-like states.

Search for $C$-parity Violation in $J/\psi\rightarrow\gamma\gamma$, $\gamma\phi$
--------------------------------------------------------------------------------

In the Standard Model (SM), $C$ invariance is held in strong and electromagnetic (EM) interactions. Until now, no $C$-violating processes have been observed in EM interactions. Any evidence for $C$ violation in the EM sector would immediately indicate physics beyond the SM.

Using the $\psi(3686)$ data sample, the decays of $J/\psi\rightarrow\gamma\gamma$ and $\gamma\phi$ have been searched for via $\psi(3686)\rightarrow J/\psi\pi^+\pi^-$ [@bibgggphi]. No significant signal is observed for $J/\psi\rightarrow\gamma\gamma$ and $J/\psi\rightarrow\gamma\phi$. The upper limits for the branching fractions of $J/\psi\rightarrow \gamma\gamma$ and $J/\psi\rightarrow\gamma\phi$ are set to be ${\cal B}(J/\psi\rightarrow \gamma\gamma) < 2.7 \times 10^{-7}$ and ${\cal B}(J/\psi\rightarrow \gamma\phi) < 1.4 \times 10^{-6}$, respectively. The upper limit on ${\cal B}(J/\psi\rightarrow \gamma\gamma)$ is one of magnitude more stringent than the previous upper limit [@bib26], and ${\cal B}(J/\psi\rightarrow \gamma\phi)$ is the first upper limit for this channel.

Observation of OZI-suppressed Decay $J/\psi \rightarrow \pi^0 \phi$
-------------------------------------------------------------------

A full investigation of $J/\psi$ decaying to a vector meson ($V$) and a pseudoscalar meson ($P$) can provide rich information about SU(3) flavor symmetry and its breaking, probe the quark and gluon content of the pseudoscalar mesons, and determine the electromagnetic amplitudes [@bib27; @bib28; @bib29].

Using the $J/\psi$ data sample, the first evidence for a doubly OZI suppressed electromagnetic $J/\psi$ decay $J/\psi\rightarrow \pi^0\phi \rightarrow K^+K^-\gamma\gamma$ has been reported [@bib30]. A clear structure in the $K^+K^-$ invariant mass spectrum around 1.02 GeV/$c^2$ is observed, which can be attributed to interference of $J/\psi\rightarrow \pi^0\phi$ and $J/\psi\rightarrow K^+K^-\pi^0$ decays. Figure \[fitmkk\] shows the fit to the invariant mass spectrum of $K^+K^-$ with the background events estimated with $\pi^0$ sidebands subtracted. Due to the interference, two possible solutions are found. The corresponding measured values of the branching fraction of $J/\psi \rightarrow \pi^0 \phi$ are ($2.94\pm0.16\pm0.16$) $\times$ $10^{-6}$ and ($1.24\pm0.33\pm0.30$) $\times$ $10^{-7}$, respectively.

![Fit to $M(K^+K^-)$ spectrum after sideband subtraction for Solution I (a) and Solution II (b). The red dotted curve denotes the $\phi$ resonance; the blue dashed curve is the non-$\phi$ contribution; the green dot-dashed curve represents their inter-ference; the blue solid curve is the sum of them.[]{data-label="fitmkk"}](fitmkk.png){width="200pt"}

STUDIES OF LIGHT HADRON STRUCTURES AND PROPERTIES
=================================================

Study of $J/\psi\rightarrow \phi \pi^0 f_0(980)$
------------------------------------------------

The nature of the scalar meson $f_0(980)$ is a long-standing puzzle [@pdg]. In the study of $J/\psi$ radiatively decaying into $\pi^+\pi^-\pi^0$ and $\pi^0\pi^0\pi^0$, BESIII observed the decay of $\eta(1405)\rightarrow\pi^0 f_0(980)$ with a large isospin violation and an anomalously narrow width of $f_0(980)$ [@bib1405]. One proposed explanation for these phenomena is the triangle singularity mechanism [@tsm1; @tsm2].

Using the $J/\psi$ data sample, the decays $J/\psi\rightarrow \phi\pi^0\pi^0\pi^0$ with $\phi\rightarrow K^+K^-$ are investigated [@bib14052]. The isospin-violating decay $J/\psi\rightarrow \phi \pi^0 f_0(980)$ is observed for the first time. Figure \[fig:mpipi\_980\] shows the invariant mass spectrum of $\pi^+\pi^-$ (Fig. \[fig:mpipi\_980\](a)) and $\pi^0\pi^0$ (Fig. \[fig:mpipi\_980\](b)). A clear $f_0(980)$ exists for the $\pi^+\pi^-$ mode. The width obtained from the dipion mass spectrum is ($15.3\pm4.7$) MeV/$c^2$, which is consistent with that in the study of $J/\psi\rightarrow \gamma \eta(1405)\rightarrow \gamma \pi^0 f_0(980)$ [@bib1405] and the prediction of a theoretical work [@bibtsm3] based on the triangle singularity mechanism [@tsm1; @tsm2]. In the invariant mass spectra of $f_0(980)\pi^0$, there is evidence of a resonance around 1.28 GeV/$c^2$ for the $f_0(980)\rightarrow \pi^+\pi^-$ mode, which was identified as the axial-vector meson $f_1(1285)$.

![The spectra (a) $M(\pi^+\pi^-)$ and (b) $M(\pi^0\pi^0)$ (three entries per event) with $K^+K^-$ in the $\phi$ signal region (black dots) and in the $\phi$ sideband regions (hatched histogram). The solid curve is the full fit, the long-dashed curve is the $f_0(980)$ signal, the dotted line is the non-$\phi$ background, and the short-dashed line is the total background.[]{data-label="fig:mpipi_980"}](f0_pippim.png "fig:"){width="200pt"} (-35,115)[(a)]{} ![The spectra (a) $M(\pi^+\pi^-)$ and (b) $M(\pi^0\pi^0)$ (three entries per event) with $K^+K^-$ in the $\phi$ signal region (black dots) and in the $\phi$ sideband regions (hatched histogram). The solid curve is the full fit, the long-dashed curve is the $f_0(980)$ signal, the dotted line is the non-$\phi$ background, and the short-dashed line is the total background.[]{data-label="fig:mpipi_980"}](f0_pi0pi0.png "fig:"){width="200pt"} (-35,115)[(b)]{}

Study of $\chi_{cJ}\rightarrow \eta'K^+K^-$
-------------------------------------------

Until now, $K_0^*(1430)$ has been observed in $K_0^*(1430)\rightarrow K\pi$ only, but it is also expected to couple to $\eta'K$ [@etapk1; @etapk2]. $\chi_{c1}\rightarrow\eta'K^+K^-$ is a promising channel to search for $K_0^*(1430)$ and study its properties while decays of $\chi_{c0,2}\rightarrow K_0^*(1430)K$ are forbidden by spin-parity conservation.

Using the $\psi(3686)$ data sample, the decay $\chi_{cJ}\rightarrow \eta'K^+K^-$ with $\eta'\rightarrow \gamma \rho^0$ and $\eta'\rightarrow\eta\pi^{+}\pi^{-}$, $\eta\rightarrow\gamma\gamma$ is studied for the first time [@etapkk]. Abundant structures on the $K^+K^-$ and $\eta K^{\pm}$ invariant mass spectra are observed for $\chi_{c1}$ candidate events, and a partial wave analysis is performed for the decay $\chi_{c1}\rightarrow \eta'K^+K^-$. Figure \[fig:metapk\] shows the comparisons of data and fit projections in terms of the invariant mass spectra of $\eta'K^{\pm}$ for $\chi_{c1}$ candidate events. The partial branching fractions of $\chi_{c1}$ decay processes with intermediate states $f_0(980)$, $f_0(1710)$, $f_2'(1525)$ and $K_0^*(1430)$ are measured for the first time.

![image](project_etapkk_1.png){width="200pt"} (-30,155)[(a)]{} ![image](project_etapkk_2.png){width="200pt"} (-30,155)[(b)]{}

Study of $\chi_{cJ}$ Decaying into $\phi K^*(892)\bar{K}$
---------------------------------------------------------

The nature of the axial-vector candidate, $h_1(1380)$ is still controversial [@13801; @13802]. The direct observation of the $h_1(1380)$ in experiments and the precise measurement of its resonance parameters may shed light on its nature and aid in identifying the ground state axial-vector meson nonet in the quark model.

Using the $\psi(3686)$ data sample, the first measurement of $\chi_{cJ}\rightarrow \phi K_S^0 K^{\pm} \pi^{\mp}$ and $\chi_{cJ}\rightarrow \phi K^+ K^- \pi^0$ has been reported [@k892]. The decays are dominated by the three-body reaction $\chi_{cJ}$ decaying into $\phi K^*(892)\bar{K}$. The branching fractions for this reaction via neutral and charged $K^*(892)$ are measured for the first time. Figure \[fig:1380\] shows the invariant mass spectrum of $K\bar{K}\pi$, a significant excess of events above the phase space expectation is observed near the $K^*(892)\bar{K}$ mass threshold in the decays of $\chi_{c1,2}$ with a significance greater than $10\sigma$. The observed structure has negative $C$ parity, and is expected to be the $h_1(1380)$ state, considering its mass, width and decay through $K^*(892)\bar{K}$. The mass and width of the $h_1(1380)$ are determined to ($1412\pm4\pm8$) MeV/c$^2$ and ($84\pm12\pm40$) MeV, respectively. This is the first evidence of the $h_1(1380)$ in its decay to $K^*(892)\bar{K}$. Evidence is also found for the decays $\chi_{cJ}\rightarrow \phi\phi(1680)$ and $\chi_{cJ}\rightarrow \phi\phi(1850)$,but with significances less than $5\sigma$.

![The sum of $K_S^0 K^{\pm} \pi^{\mp}$ and $K^{\pm} \pi^{\mp}\pi^0$ mass spectra in the $\chi_{c1}$ and $\chi_{c2}$ mass regions. The markers with error bars represent the data; the dash curve the $h_1(1380)$ signal; the dash-dot-dot curve the $\phi(1680)$ signal; and the dash-dot curve the $\phi(1850)$ signal.[]{data-label="fig:1380"}](1380.png){width="200pt"}

SUMMARY
=======

Based on 2.92 fb$^{-1}$ data sample taken at $\sqrt{s}$ = 3.773 GeV, 1.06$\times10^8$ $\psi(3686)$ events and 1.31$\times10^9$ $J/\psi$ events collected with BESIII detector at the BEPCII collider, studies have been performed to search for the radiative transitions of $\psi(3770)$ and rare decays of charmonium, and study light hadron structures and properties. The upper limits on branching fractions are set for radiative transitions of $\psi(3770)$, $\psi(3770)\rightarrow \gamma \eta_c(\eta_c(2S))$ and $\psi(3770)\rightarrow \gamma \chi_{c2}$, the isospin-violating decay $\chi_{c0,2}\rightarrow\pi^0\eta_c$, and $C$-violation decay $J/\psi\rightarrow\gamma\gamma$, $\gamma\phi$. The OZI-suppressed decay $J/\psi\rightarrow \pi^0\phi$ is observed for the first time. The isospin-violating decay $J/\psi\rightarrow \phi\pi^0 f_0(980)$, $f_0(980)\rightarrow\pi^+\pi^-$ is observed with the width of the $f_0(980)$ obtained from the dipion mass spectrum found to be much smaller than the world average value. The decay $\chi_{c1,2}\rightarrow \eta'K^+K^-$ is studied for the first time. Intermediate process $\chi_{c1}\rightarrow \eta'f_0(980)$, $\chi_{c1}\rightarrow\eta'f_0(1710)$, $\chi_{c2}\rightarrow\eta'f_2'(1525)$ and $\chi_{c1}\rightarrow
K_0^*(1430)^{\pm}K^{\mp}$ are observed and their branching fractions are measured. The branching fractions of decay $\chi_{cJ}$ decaying into $\phi K^*(892)\bar{K}$ are measured for the first time and the first evidence of the $h_1(1380)$ in its decay to $K^*(892)\bar{K}$ is obtained. These measurements provide important information to understand the nature of $\psi(3770)$, the isospin-violation mechanism and properties of light hadrons, such as $f_0(980)$, $K_0^*(1430)$ and $h_1(1380)$.
