Experimental Status of Conventional Charmonium Spectroscopy

. Based on data samples taken by the BESIII, Belle, KEDR and LHCb experiments, many measurements on conventional charmonium spectroscopy were ﬁnished in the past years. Some of recent results, such as precise measurements of J /ψ and ψ (2 S ) masses, the J /ψ decay width, the J /ψ and ψ (2 S ) electronic widths, two-photon width of χ c 0 , 2 meson, the χ c 1 , 2 resonance parameters with the decays χ c 0 , 2 → J /ψµ + µ − , the η c resonance parameters and observations of X (3823) and X ∗ (3860), were reported.

The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel. The acceptance of charged particles and photons is 93% over 4π solid angle. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for the electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end cap) region. The time resolution of the TOF barrel part is 68 ps, while that of the end cap part is 110 ps. The end cap TOF system is upgraded in 2015 with multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [6]. Figure 1 shows a schematic view of the BESIII detector. A detailed description of the BESIII detector is given in Ref. [7].

The Belle experiment
The Belle experiment is dedicated to search for CP violation and extends to the studies of rare decays of B meson at Υ(4S ) resonance [13]. The detector is a large solid-angle magnetic spectrometer that consists of a silicon vertex detector (VTX), a 50-layer central drift chamber, an array of aerogel threshold Cherenkov counters, a barrel-like arrangement of TOF scintillation counters, and an EMC comprised of CsI(Tl) crystals located inside a SSM that provides a 1.5 T magnetic field. An iron flux-return yoke instrumented with resistive plate chambers (KLM) located outside the coil is used to detect KL0 mesons and to identify muons. The Belle detector is described in detail elsewhere [14]. Figure 1 shows an overview of the Belle detector. The integrated luminosities [15] collected by the Belle detector are 100 fb −1 scan data, 6 fb −1 at Υ(1S ), 25 fb −1 at Υ(2S ), 3 fb −1 at Υ(3S ), 711 fb −1 at Υ(4S ) and 121 fb −1 at Υ(4S ).

The KEDR experiment
The KEDR experiment is dedicated to study the c, b-quarks physics region employed at the VEPP-4M e + e − collider [16,17]. The detector includes a tracking system consisting of a VTX and a MDC, a PID system of aerogel Cherenkov counters and TOF scintillation counters, and an EMC based on liquid krypton (barrel part) and CsI crystals (end cap part). The SSM provides a longitudinal magnetic field of 0.6 T. A muon system is installed inside the magnet yoke. The detector also includes a high-resolution tagging system for studies of two-photon processes. Figure 1 shows an overview of the KEDR detector.

The LHCb experiment
The LHCb experiment is dedicated to heavy flavor physics at the Large Hadron Collider (LHC) at CERN [18], its primary purpose is to look for indirect evidence of new physics in CP violation and rare decays of B hadrons. The detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5. It includes a high-precision tracking system consisting of a silicon-strip VTX surrounding the pp interaction region, a large-area siliconstrip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The LHCb detector is described in detail [19]. Figure 1 shows an overview of the LHCb detector. The integrated luminosities [20]   introduced compared to the TDR [4]. The material budget has been reduced by optimizing the thickness of the silicon sensors and the number of stations. The thickness of the sensors has been reduced from 300 to 220 µm, and the number of stations from 25 to 21 without significantly affecting its performance, as shown in this document.
The dipole magnet has not been modified from the TDR design [5] and its construction is advancing. Compared to the TP spectrometer layout, no shielding plate is placed upstream of the magnet. This change has been made in order to introduce magnetic field between the VELO and the magnet, i.e. in the region of RICH 1, for the Level-1 trigger improvement.
Compared to the TP, the number of tracking stations is reduced to four in order to reduce the material budget, without introducing performance losses, as demonstrated in this document 2 . The first station after the VELO, referred to as the Trigger Tracker (TT), is in front of the magnet and just behind RICH 1. It consists of four planes of silicon strip detectors. They are split into two pairs of planes separated by 30 cm. Together with 2 In the track reconstruction the VELO is now used as an integral part of the the tracking system. the VELO, the TT is used in the Level-1 trigger. Large impact parameter tracks found in the VELO are extrapolated to the TT and the magnetic field in the RICH 1 region allows their momenta to be measured. The three remaining stations are placed behind the magnet with equal spacing. Each station consists of an Inner Tracker (IT) close to the beam pipe and an Outer Tracker (OT) surrounding the IT. The OT is made of straw tubes and the IT of silicon strip detectors. Their designs remain unchanged from those described in the corresponding TDR's [6,2].
The RICH 1 material has been reduced, largely by changing the mirror material and redesigning the mirror support. The mirror will be made from either carbon-composite or beryllium. The mirror support has been moved outside of the acceptance. Further reduction of the material has been achieved by removing the entrance window, by connecting the front face of RICH 1 to the flange of the VELO exit window. Iron shielding boxes for the photon detectors have been introduced for two reasons. Firstly, they protect the photon detectors from the magnetic field. Secondly, they help to focus the magnetic field in the region where it is needed for the momentum measurement of the Level-1 trigger. Figure 1. Schematic drawing of the detectors for BESIII (Top left) [7], Belle (Top right) [14], KEDR (Bottom left) [17] and LHCb (Bottom right) [19] showing its main components.

Precise measurements of J/ψ and ψ(2S ) masses
The mass of a particle is its most fundamental characteristic, which should be known with the best possible accuracy. The masses of J/ψ and ψ(2S ) are usually used to calibrate the energy scales of accelerators and detectors operation in the charmonium region. The measurement precision of J/ψ and ψ(2S ) masses is helpful to determine the accuracy of masses of other charmonium states and the τ-lepton. In history, the J/ψ and ψ(2S ) masses were measured by many experiments [2], and achieved an accuracy of 17 MeV reported by KEDR experiment with the installment of the liquid krypton combined with data samples of additional three ψ(2S ) scans [21]. Recently, the KEDR experiment presented the best precise measurements for the J/ψ and ψ(2S ) masses, i.e. M J/ψ = (3096.900 ± 0.002 ± 0.006) MeV/c 2 , M ψ(2S ) = (3686.099±0.004±0.009) MeV/c 2 , based on data samples of six J/ψ scans and seven ψ(2S ) scans [22] using the resonance depolarization method. Figure 2 shows the fitted hadronic cross section for J/ψ scans and ψ(2S ) scans from different years.  [22]. The lines present the fit results.

Precise measurements of J/ψ and ψ(2S ) electronic widths
The electronic width of the J/ψ resonance is also an interesting and important parameter, which could reveal the basic structure of J/ψ resonance. It was measured first by BaBar [23] and CLEO-c [24] with the technique of initial state radiation (ISR). In 2015, the BESIII experiment performed additionally a search for the reaction e + e − → γ IS R X(3872) → γ IS R π + π − J/ψ via ISR technique [25]. No obvious significance of X(3823) was observed in this process, and an improved limit Γ X(3823) ee B(X(3823) → π + π − J/ψ) < 0.13 eV was given. Theoretically, the production of a resonance with quantum numbers J PC = 1 ++ , such as the X(3872), via single photon e + e − annihilation is forbidden, but is allowed by a next-to-leading order box diagram. Additionally, in this analysis, the ψ(2S ) electronic width was measured by fitting M(π + π − J/ψ) spectrum, i.e. Γ ψ(2S ) ee = (2213 ± 18 ± 99) eV, which is in agreement with the world average value [2] and updated the previous measurement [27]. Subsequently, the BE-SIII experiment measured the J/ψ electronic width with more precise accuracy using the ISR process e + e − → J/ψγ → µ + µ − γ by fitting m(µ + µ − ) spectrum in the range of 2.8 and 3.4 GeV/c 2 , i.e. Γ J/ψ ee = (5.58 ± 0.05 ± 0.08) keV [26]. Figure 3 shows the fitted mass spectra of µ + µ − and π + π − J/ψ.

Precise measurement of J/ψ width
The J/ψ width is an important parameter and reflect the internal interaction of J/ψ meson, which was predicted by various potential models and QCD. Thus, precise measurements of J/ψ decay widths may help validate these models and provide a better understanding of the underlying physics. In history, the J/ψ width was measured by many experiments [2] achieved an accuracy of 2.8 keV [2]. Recently, the BESIII experiment performed a more accurate measurement of J/ψ (lepton) width with processes e + e − →e + e − , µ + µ − at 15 CM energy points in the vicinity of the J/ψ resonance, i.e. Γ tot = (94.3 ± 2.1) keV and Γ ll = (5.64 ± 0.11) keV. These results are consistent with and of improved precision with respect to those from other experiments, but a bit less precise than the previous BESIII result obtained with the ISR technique. Figure 4 shows the comparison of full width and lepton width of J/ψ between this work and other measurements.

Precise measurement of χ c0,2 two-photon width
The two-photon decays of P-wave charmonia, such as the decays χ c0,2 → γγ, are helpful for understanding the nature of inter-quark forces and decay mechanisms, where the decay χ c1 → γγ is suppressed by Landau-Yang theorem [28]. In particular, the decays χ c0,2 → γγ offer the closest parallel between quantum electrodynamics (QED) and QCD, being analogous to the decays of the triplet states of positronium. One of interesting variables for χ c0,2 → γγ is the ratio of the two-photon decay widths Γ(χ c2 →γγ) Γ(χ c0 →γγ) , which is predicted by many theoretical models covering a wide range of values between 0.09 and 0.36 [29]. The two-photon decay widths of χ c0,2 were measured by many experiments [2]. Recently, the BESIII experiment performed an improved measurement of two-photon width of χ c0,2 and a helicity amplitude analysis of χ c2 → γγ based on 448 million ψ(2S ) events with the process ψ(2S ) → γχ cJ , χ cJ → γγ [30]. Figure 5 shows the fitted E(γ 1 ) spectrum. The measured ratio of two-photon width of χ c0,2 confirmed that helicity-zero component is highly suppressed. These results are more precise to data, and consistent with previous measurements [2].
Residual Pull

The η c (1S ) resonance parameter
The η c (1S ) state is the lowest-lying S-wave spin-singlet charmonium state and has been observed in various processes [2]. Recently, the KEDR experiment performed the measure-ments of decay rate Γ 0 γη c (1S ) = (2.98 ± 0.18 +0.15 −0.33 ) keV and resonance parameters M(η c (1S )) = (2983.5 ± 1.4 +1.6 −3.6 ) MeV/c 2 , Γ η c (1S ) = (27.2 ± 3.1 +5.4 −2.6 ) MeV, using the inclusive photon spectrum of a magnetic dipole radiative transition decay J/ψ → γη c (1S ) with consideration of an asymmetric photon line-shape [17]. The measured decay rate is significantly higher compared to those previous measurements [2], but is well consistent with the latest lattice QCD prediction [32]. It is noted that the measured parameters are sensitive to the line-shape of the photon spectrum in this decay and it was taken into account during analysis. Subsequently, the LHCb experiment also reported a measurement of η c (1S ) width by fitting M pp spectrum using the process B + → ppK + based on pp collision data, Γ η c (1S ) = (34±1.9±1.3) MeV [33]. Additionally, the η c (2S ) → pp was observed first with a total significance of 6.0σ, and the upper limits of relative branching fraction for other processes ψ(3773), X(3823) → pp were determined. Compared with the results obtained by radiative decays [17], the determinations of η c (1S ) parameters do not depend on the knowledge of the line shapes of the magnetic dipole transition. Figure 6 shows the fitted distributions of photon energy and M pp .

Observations of X(3823) and X * (3860)
In the charmonium family, the observation of D-wave cc meson and its decay modes would test phenomenological models predicted that the as-yet undiscovered 1 3 D 2 (ψ 2 ) has large decay width to γχ c1 and γχ c2 [34]. In 1994, the E705 experiment reported an indication of a 1 3 D 2 state with a mass of (3826 ± 13) MeV/c 2 and a statistical significance of 2.8 σ [35]. Recently, the Belle experiment reported a evidence of a new resonance in the γχ c1 final state using the process B ∓ → (γχ c1,2 )K ∓ with a mass of (3823.1 ± 1.8 ± 1.7) MeV/c 2 and a significance of 3.8 σ. The measured properties of the X(3823) are consistent with those expected for the ψ 2 (1 3 D 2 ) state [36]. Subsequently, the BESIII experiment reported the observation of X(3823) with a mass of (3821.7 ± 1.3 ± 0.7) MeV/c 2 and a significance of 6.2 σ using the process e + e − → π + π − X(3823) → π + π − γχ c1 based on data samples taken at CM energies of 4.230, 4.260, 4.360, 4.420 and 4.600 GeV [37]. These measurements are in good agreement with Belle's measurement and the assignment of the X(3823) state as the ψ 2 (1 3 D 2 ) charmonium state. Figure 7 shows the fitted distributions of M χ c1 γ and M recoil (π + π − ) from Belle and BESIII experiments.
Another new charmoniumlike state X * (3860) was observed by Belle experiment based on a full amplitude analysis using the process e + e − → J/ψDD (D ∈ D 0 or D + ) with a mass of (3860 +26 −32 +40 −13 ) MeV/c 2 and a width of (201 +154 −67

+88
−82 ) MeV [38]. The J PC = 0 ++ hypothesis is favored over the 2 ++ hypothesis at the level of 2.5σ. The X * (3860) seems to be a better candidate for the χ c0 (2P) charmonium state than the X(3915) according to the prediction of the potential model, since its properties are well matched to the expectations for the χ c0 (2P) resonance, where the X(3915) was identified as the χ c0 (2P) candidate in the previous PDG table [39]. Note that, the production amplitudes for the X * (3860) and χ c0 (2P) are in mutual agreement, but they do not agree with the NRQCD prediction [40]. Figure 8 shows the projection of the fit results onto M DD .  Figure 7. (Left) 2D UML fit projection of the M χ c1 γ distribution for the simultaneous fit of B ± → (χ c1 γ)K ∓ and B 0 → (χ c1 γ)K 0 S decays for M bc > 5.27 GeV/c 2 [35]. Simultaneous fit to the M recoil (π + π − ) distribution of γχ c1 events (Middle) and γχ c1 events (Right) [37]. Dots with error bar are for the data. The solid line denotes the fit results.

Summary
Using data samples taken by BESIII, Belle, KEDR and LHCb experiment, lots of recent progresses in the experimental study of CCS were reported, They include precise measurements of resonance parameters of J/ψ and ψ(2S ) mesons, two-photon width of χ c0,2 meson, resonance parameter of χ c1,2 meson, resonance parameter of η c meson and observations of X(3823) and X * (3860). In addition, the BESIII, Belle, KEDR and LHCb experiments will continue the study of CCS, and the Belle II at KEK are taking data now. It is hopeful that more progresses will be made in the experimental study of CCS in the future.