Charmonium and Charmoniumlike States at the BESIII Experiment
aa r X i v : . [ h e p - e x ] F e b Charmonium and Charmoniumlike States at the BESIII Experiment
Chang-Zheng Yuan
1, 2, ∗ Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China
Abstract
Charmonium is a bound state of a charmed quark and a charmed antiquark, and a charmoniumlike state isa resonant structure that contains a charmed quark and antiquark pair but has properties that are incompat-ible with a conventional charmonium state. While operating at center-of-mass energies from 2 to 4.9 GeV,the BESIII experiment can access a wide mass range of charmonium and charmoniumlike states, and hascontributed significantly in this field. We review BESIII results involving conventional charmonium states,including the first observation of M1 transition ψ (2 S ) → γη c (2 S ) and the discovery of the ψ (3823) ;and report on studies of charmoniumlike states, including the discoveries of the Z c (3900) and Z c (4020) tetraquark candidates, the resolution of the fine structure of the Y (4260) , the discovery of the new produc-tion process e + e − → γX (3872) , and the uncovering of strong evidence for the commonality among the X (3872) , Y (4260) , and Z c (3900) states. The prospects for further research at BESIII and proposed futurefacilities are also presented. Keywords: charmonium states, charmoniumlike states, exotic hadrons, e + e − annihilation ∗ Electronic address: [email protected] . INTRODUCTION In the conventional quark model, mesons are comprised of a quark and anti-quark pair, whilebaryons are comprised of three quarks. A bound state of a charmed quark ( c ) and a charmedantiquark ( ¯ c ) is named charmonium. The first charmonium state, the J/ψ , was discovered atBNL [1] and at SLAC [2] in 1974, and since then, all the charmonium states below the open-charm threshold and a few vector charmonium states above the open-charm threshold have beenestablished [3]; the measured spectrum of states agrees well with theoretical calculations based onQCD-inspired potential models [4–6].In addition to the charmonium states, the conventional quark model describes almost all of theother hadrons that have been observed to date quite well, including baryons and other mesons [3].Since the very beginning of the quark model, exotic hadronic states with configurations not lim-ited to two or three quarks have been the subject of numerous theoretical proposals and experi-mental searches [7, 8]. These proposed exotic hadrons include hadron-hadron molecules, diquark-diantiquark tetraquark states, hadro-quarkonia, quark-antiquark-gluon hybrids, multi-gluon glue-balls, and pentaquark baryons.Many charmonium and charmoniumlike states were discovered at the BaBar [9] and Belle [10] B -factories during the first decade of this century [11]. Whereas some of these are good candidatesfor conventional charmonium states, there are other states that have properties that do not matchthose of any of the unassigned c ¯ c states, which may indicate that exotic states have already beenobserved [12]. These candidate exotic meson states are collectively called the XYZ particles, toindicate their underlying nature is still unclear. Although this is not fully accepted within the highenergy physics community, practitioners in the field use Z Q (xxxx) to denote a quarkoniumlikestate with mass roughly xxxx MeV/ c that contains a heavy quark pair Q ¯ Q and with non-zeroisospin; Y (xxxx) for a vector quarkoniumlike state, and X (xxxx) for states with other quantumnumbers.Although the BaBar [9] and Belle [10] experiments finished data taking in 2008 and 2010,respectively, the data are still used for various physics analyses. In 2008, two new experiments:BESIII [13], a τ -charm factory experiment at the BEPCII e + e − collider; and LHCb [14], a B -factory experiment at the LHC pp collider, started data taking, and have been contributing to thestudy of charmonium and charmoniumlike states ever since.The BESIII experiment at the BEPCII double ring e + e − collier observed its first collisions inthe τ -charm energy region in July 2008. The BESIII detector [13] is a magnetic spectrometerwith an effective geometrical acceptance of 93% of π and state-of-the-art subdetectors for highprecision charged and neutral particle measurements. After a few years of running at center-of-mass (c.m.) energies for its well-defined physics programs [15], i.e., at the J/ψ and ψ (2 S ) peaksin 2009 and the ψ (3770) peak in 2010 and 2011, the BESIII experiment began to collect data forthe study of the XYZ particles, a program that was not described in the BESIII Yellow Book [15].The first data sample was collected at the ψ (4040) resonance in May 2011 with an integratedluminosity of about . − . This sample was used to search for the production of the X (3872) and the excited P -wave charmonium spin-triplet states via ψ (4040) radiative transitions. The sizeof the sample was limited by the brief, one-month running time following the ψ (3770) data takingin the 2010–2011 run.In summer 2012, the LINAC of the BEPCII was upgraded so that the highest beam energy wasincreased from . to . , which made it possible to collect data at higher c.m. energies(up to . ). A data sample of
525 pb − was collected at a c.m. energy of .
26 GeV from2ecember 14, 2012 to January 14, 2013, with which the Z c (3900) charged charmoniumlike statewas discovered [16]. This observation changed the data collection plan for the 2012–2013 runand had considerable impact on the subsequent running schedule of the experiment; more datapoints between . and .
60 GeV dedicated to the
XYZ related analyses were recorded [17].The highest beam energy was further increased from . to .
45 GeV in summer 2019, making itpossible to collect data at even higher c.m. energies (up to . ).The data samples used for the XYZ study cover the energy range between 4.0 and 4.7 GeV,with a typical integrated luminosity of
500 pb − at each energy point. These data were also usedfor charmonium studies together with a 448 million ψ (2 S ) event sample. Data samples with atotal
826 pb − integrated luminosity at 104 energy points between . and . [18] was alsoused for the XYZ study.In this article, we review studies of charmonium and charmoniumlike states from the BE-SIII [13] experiment. We first introduce the study of conventional charmonium states and then the
XYZ states. Finally, we discuss prospects for future studies with the BESIII experiment, and alsopoint out possible studies at next generation facilities.
II. CONVENTIONAL CHARMONIUM STATES
The search for new charmonium states has always been a high priority topic. With the datataken at c.m. energies above 4 GeV, it is possible to search for states predicted by the potentialmodels that are still unobseved [4–6]. These states include the excited P -wave spin-triplet states χ cJ (2 P ) ( J = 0 , , ), the excited P -wave spin-singlet state h c (2 P ) , the D -wave spin-triplet states ψ J (1 D ) ( J = 2 , ; J = 1 state, the ψ (3770) , was observed many years ago [3]), and the D -wavespin-singlet state η c (1 D ) .The predicted mass of the D -wave charmonium states (excluding the ψ (3770) , which is, infact, a mixture of the D and S vector states) is in the . ∼ . GeV/ c range predictedby several phenomenological calculations [4–6, 19]. Since the mass of ψ (1 D ) is above the D ¯ D threshold but below the D ¯ D ∗ threshold, and ψ (1 D ) → D ¯ D violates parity, the ψ (1 D ) is ex-pected to be narrow and its dominant decay mode is ψ (1 D ) → γχ c [19, 20]. The ψ (1 D ) state,also called the ψ (3823) , was discovered at BESIII [21] in this final state, and the ψ (1 D ) statewas observed by LHCb in its decay into D ¯ D final state [22].The spin-triplet charmonium states are produced copiously in e + e − annihilation and in B de-cays and, thus, they are understood much better than the spin-singlet charmonium states, includingthe lowest lying S -wave state, the η c , its radial excited partner the η c (2 S ) , and the P -wave spin-singlet state the h c . Since these three states are all produced in ψ (2 S ) decays, the world largest ψ (2 S ) data sample at BESIII made it possible to study their properties with improved precision.In addition, the unexpected large production cross section for e + e − → π + π − h c in BESIII energyregion [23] opened a new mechanism of studying the h c and η c (from h c → γη c ), and BESIIIcontributed world best measurements of the properties of these states [24]. We report here the ob-servation of the M1 transition ψ (2 S ) → γη c (2 S ) at BESIII [25], a transition that has been soughtfor since the first generation BES experiment in 1980’s.3 . Discovery of M1 transition ψ (2 S ) → γη c (2 S ) The production of the η c (2 S ) through a radiative transition from the ψ (2 S ) involves a charmed-quark spin-flip and, thus, proceeds via a magnetic dipole (M1) transition. The branching fractionhas been calculated by many authors, with predictions in the range B ( ψ (2 S ) → γη c (2 S )) =(0 . − . × − [26–28]. Experimentally, this transition has been searched for by CrystalBall [29], BES [30, 31], and CLEO [32]. No convincing signal was observed by any of theseexperiments.With a sample of 106 million ψ (2 S ) events collected at BESIII, the process ψ (2 S ) → γη c (2 S ) was observed for the first time with η c (2 S ) → K S K ± π ∓ and K + K − π modes. The final K ¯ Kπ mass spectra and the fit results are shown in Fig. 1. The fit yields for the number of the η c (2 S ) signal events are ± for the K S K ± π ∓ mode and ± for the K + K − π mode; the overallstatistical significance of the signal is larger than σ [25]. ) (GeV/c ± π ± K K m ) E v e n t s / ( . G e V / c ) (GeV/c π ± K K m ) E v e n t s / ( . G e V / c
10 ) ± π ± K data (Kfitting results cJ χ (2S) c η background ) (GeV/c π - K + K m ) E v e n t s / ( . G e V / c ) (GeV/c π - K + K m ) E v e n t s / ( . G e V / c
10 ) π - K + data (Kfitting results cJ χ (2S) c η background FIG. 1: The fit to the invariant-mass spectra for K S K ± π ∓ (left panel) and K + K − π (right panel). Dotswith error bars are data, and the curves are total fit and each component. The lowest peaks correspond tothe η c (2 S ) signals. The mass of the η c (2 S ) is measured to be (3637 . ± . ± . MeV/ c , the width (16 . ± . ± . MeV, in good agreement with the PDG world average values [3], and the product branchingfractions B ( ψ (2 S ) → γη c (2 S )) × B ( η c (2 S ) → K ¯ Kπ ) = (1 . ± . ± . × − . Combiningthis result with a BaBar measurement of B ( η c (2 S ) → K ¯ Kπ ) , the M1 transition rate is determinedto be B ( ψ (2 S ) → γη c (2 S )) = (6 . ± . stat ± . sys ) × − . This agrees with theoreticalcalculations [26–28] and naive estimates based on the J/ψ → γη c transition [32].This study benefited from the BESIII detector’s high resolution electromagnetic calorimeter,which makes the detection of the radiative photon with 50 MeV energy possible [13]. Given thetiny transition rate and the low photon energy, it is understandable why this transition was notobserved in previous studies [29, 30, 32]. This is the third M1 transition observed in a charmo-nium system (the other two are J/ψ → γη c and ψ (2 S ) → γη c observed in 1980 [33]); improvedmeasurements of these transitions and discovery of more M1 transitions would improve the un-derstanding of the high order effects involved in these transitions [6].4 . Observation of ψ (3823) The processes of e + e − → π + π − γχ c , are studied at BESIII experiment using . − datasamples collected at c.m. energies from . to .
60 GeV [21]. The χ c , are reconstructed viatheir decays into γJ/ψ , with J/ψ to ℓ + ℓ − ( ℓ = e, µ ). A clear signal is observed as a ± eventpeak in the γχ c invariant mass distribution that is evident in Fig. 2(1eft); its mass is determinedto be (3821 . ± . ± .
7) MeV /c , and its properties are in good agreement with the ψ (1 D ) charmonium state. The statistical significance of the ψ (3823) signal is . σ . The upper limit onthe intrinsic width of the ψ (3823) is determined as
16 MeV at the 90% confidence level (C.L.).This observation is in good agreement with the . σ “evidence” in B decays reported by Belle [34].For the γχ c mode, no significant ψ (3823) signal is observed (Fig. 2(right)), and an upper limiton its production rate is determined. BESIII obtains the ratio B [ ψ (3823) → γχ c ] B [ ψ (3823) → γχ c ] < . at the 90%C.L., which also agrees with expectations for the ψ (1 D ) state [20]. ) ) (GeV/c - π + π ( recoil M3.6 3.7 3.8 3.9 E v en t s / M e V / c DataFitBackgroundSideband ) ) (GeV/c - π + π ( recoil M3.6 3.7 3.8 3.9 E v en t s / M e V / c DataFitBackgroundSideband
FIG. 2: Simultaneous fit to the M recoil ( π + π − ) distribution of γχ c events (left) and γχ c events (right),respectively [21]. The small peak in the left panel is the ψ (3823) signal. Dots with error bars are data,red solid curves are total fit, dashed blue curves are background, and the green shaded histograms are J/ψ mass sideband events.
With the observation of three D -wave spin-triplet states, their center-of-gravity, 3822 MeV/ c ,is a good estimation of the mass of the D -wave spin-singlet state, η c (1 D ) . Since it cannot decayinto open charm final states, the η c (1 D ) is expected to be very narrow, and the identification ofit should be clear, if it is produced with large enough rate, in e + e − → γη c (1 D ) or e + e − → π + π − h c (2 P ) → π + π − γη c (1 D ) . III. EXOTIC CHARMONIUMLIKE STATES
A revival of the study of charmonium spectroscopy occurred in the early 21st century whenthe BaBar and Belle B -factories started accumulating large data samples at Υ(4 S ) peak. Thehigh luminosity at these B -factories enabled studies of charmonium states that are produced in avariety of ways, including B decays, initial-state-radiation (ISR) processes, double-charmoniumproduction, two-photon processes, etc. While the discovery of the conventional charmonium statessuch as η c (2 S ) and χ c (2 P ) were more-or-less rountine, the observations of the X (3872) by Bellein 2003 [35] and the Y (4260) by BaBar in 2005 [36], the first of the XYZ mesons, came as big5urprises; although these new states decay to final states that contain both a c - and a ¯ c -quark, theyhave properties that do not match those of any c ¯ c meson [12].All studies of XYZ states at the B -factories suffer from low statistics and limited precision. Incontrast, BESIII can tune the c.m. energy to match the peaks of the Y states, where event rates arehigh enough to facilitate precise measurements of their resonance parameters and search for newstates among their decay products. A. New insights into the Y states The Y states, such as the Y (4260) [36], the Y (4360) [37, 38] and the Y (4660) [38], are pro-duced directly or via the ISR process in e + e − annihilation and, thus, are vectors with quantumnumbers J P C = 1 −− . These states have strong couplings to hidden-charm final states in con-trast to the established vector charmonium states in the same mass region, such as the ψ (4040) , ψ (4160) , and ψ (4415) , which dominantly couple to open-charm meson pairs [39, 40].In potential models, five vector charmonium states are expected to be in the mass region be-tween 4.0 and 4.7 GeV/ c , namely the ψ (3 S ) , ψ (2 D ) , ψ (4 S ) , ψ (3 D ) , and ψ (5 S ) [19], withthe first three identified with the well-established ψ (4040) , ψ (4160) , and ψ (4415) charmoniummesons; the masses of the as yet undiscovered ψ (3 D ) and ψ (5 S ) are expected to be higher than4.4 GeV/ c . However, six vector states in this mass region have been identified, as listed above.These makes the Y (4260) , Y (4360) and perhaps the Y (4660) states good candidates for new typesof exotic particles and this stimulated many theoretical interpretations, including tetraquark states,molecular states, hybrid states, or hadro-charmonia [12].The Y (4260) was first observed at the B -factories as a distinct peak in the π + π − J/ψ invariantmass distribution for ISR-produced e + e − → γ ISR π + π − J/ψ events [36, 41]. Improved measure-ments from both BaBar [42] and Belle [43] with their full data samples confirmed the existence ofboth the Y (4260) and a non- Y (4260) component in e + e − → π + π − J/ψ around . , but theline-shape was parameterized with different models. The parameters of the Y (4260) determinedby fit to the combined data from the two B -factory experiments and the CLEO measurements [44]are M Y (4260) = (4251 ±
9) MeV /c and Γ Y (4260) = (120 ±
12) MeV [45]. High precisionBESIII measurements of the direct cross section for the Y (4260) production in different finalstates supply new insight into its nature. These measurements include: e + e − → π + π − J/ψ [46], e + e − → π + π − h c [23], e + e − → ωχ cJ [47, 48], e + e − → D D ∗− π + + c.c. [49], and so on [50].Figure 3 shows the measured cross sections for each of these final states. The Y (4260) structureis evident, but its line shape is, in fact not well described by a single Breit-Wigner (BW) resonancefunction. Instead, its line-shape is peaked at around .
22 GeV , which is substantially lower thanthe average value from previous measurements [45], and a distinct shoulder is observed on itshigh-mass side that is especially pronounced in the π + π − J/ψ mode. In order to describe this lineshape, two resonant structures in the Y (4260) peak region are needed. The lower one has a massof (4222 . ± . ± .
4) MeV /c and a width of (44 . ± . ± .
0) MeV , while the higher onehas a mass of (4320 . ± . ± .
0) MeV /c and a width of (101 . +25 . − . ± .
2) MeV . The massof the first resonance is ∼
30 MeV /c lower than the world average value at that time [45] forthe Y (4260) and its width is about a factor of three narrower. The second resonance is observedin the e + e − → π + π − J/ψ process for the first time. The resonance parameters for the Y (4260) structures are also measured in other decay channels and listed in Table I.Since the resonant structure around . /c is present in all of the above channels with6 σ ( π + π - J / ψ ) ( pb ) PRL118, 0920010255075100 σ ( π + π - h c ) ( pb ) PRL118, 0920020255075100 σ ( ω χ c ) ( pb ) PRL114, 092003PRD 99, 091103020040060080010004 4.1 4.2 4.3 4.4 4.5 4.6Ecm (GeV) σ ( D D * - π + ) ( pb ) PRL122, 102002
FIG. 3: From top to bottom are the measured cross sections of e + e − → π + π − J/ψ [46], e + e − → π + π − h c [23], e + e − → ωχ c [47, 48], and e + e − → D D ∗− π + + c.c. [49]. Dots with error bars arethe data and the dotted vertical line is the peak of the Y (4220) . similar resonance parameters, the authors of Ref. [51] applied a combined fit to the measured crosssections to determine the resonance parameters of the low-mass Y (4220) peak with a resultantmass of (4219 . ± . ± .
1) MeV /c and width of (56 . ± . ± .
9) MeV . These values arevery different from those obtained from previous experiments [45]. The fit also gives the productof the leptonic decay width and the decay branching fraction to the considered final state. After7
ABLE I: Resonance parameters of the Y (4220) from different modes measured at BESIII. The crosssections measured at c.m. energy of 4.226 GeV are also listed.Mode Mass (GeV/ c ) Width (MeV) σ at √ s = 4 . GeV (pb) e + e − → π + π − J/ψ . ± . ± . . ± . ± . . ± . ± . e + e − → π + π − h c . +5 . − . ± . . +12 . − . ± . . ± . ± . e + e − → ωχ c . ± . ± . . ± . ± . . ± . ± . e + e − → π + D D ∗− + c.c. . ± . ± . . ± . ± . ± ± accounting for the unmeasured isospin partners of the measured channels, a lower limit on theleptonic partial width of the Y (4220) is determined to be Γ e + e − > (29 . ± .
4) eV , where theerror is the combined fit error and those from different fit scenarios. The authors of Ref. [52]analyzed BESIII, Belle, and BaBar data on charmonium as well as open charm final states, anda leptonic width of O (0 . ∼ keV is obtained. This partial width is much larger than LQCDpredictions for a hybrid vector charmonium state [53].In spite of the limited experimental information that had been available between the time ofits discovery in 2005 and the recent BESIII measurements, the Y (4260) has attracted consider-able attention. The BESIII measurements of its production, decay, and line shape in a varietyof final states enable more sophisticated theoretical investigations and some analyses have beenperformed, such as those in Ref. [52] and those quoted in Ref. [12]. The presence of the nearby D ∗ + s D ∗− s , D ¯ D (2420) , and ωχ cJ production thresholds, and its mass overlap with the ψ (4160) and ψ (4415) conventional charmonium states complicate its interpretation. Joint experimentaland theoretical efforts will likely be required to gain a full understanding of the nature of this state. B. Discovery of the iso-triplet charmoniumlike Z c (3900) and Z c (4020) states Searching for charged charmoniumlike states is one of the most promising ways of establishingthe existence of the exotic hadrons, since such a state must contain at least four quarks and, thus,could not be a conventional meson. These searches have been concentrated on decay final statesthat contain one charged pion and a charmonium state, such as the
J/ψ , ψ (2 S ) , and h c , since theyare narrow and their experimental identification is relatively unambiguous.The first reported charged charmoniumlike state, the Z c (4430) − , was found in the π − ψ (2 S ) invariant mass distribution in B → Kπ − ψ (2 S ) decays by the Belle experiment in 2008 [54, 55]. Itwas confirmed by the LHCb experiment seven years later [56]. The Z c (3900) − was observed in the π − J/ψ invariant mass distribution in the study of e + e − → π + π − J/ψ at BESIII [16] and Belle [43]experiments, and the Z c (4020) − was observed in the π − h c system in e + e − → π + π − h c [57] onlyat BESIII.
1. Observation of the Z c (3900) The BESIII experiment studied the e + e − → π + π − J/ψ process using a
525 pb − data sampleat a c.m. energy of .
26 GeV [16]. About signal events were observed and the cross sectionwas measured to be (62 . ± . ± . pb, which agrees with the previous existing results from the8elle [41] and BaBar [42] experiments. The intermediate states in this three-body system werestudied by examining the Dalitz plot of the selected candidate events, as shown in Fig. 4. ) ) (GeV/c ψ J/ + π ( M
10 11 12 13 14 15 16 17 18 19 20 ) ) ( G e V / c - π + π ( M ) ) (GeV/c ψ J/ ± π ( max M E v en t s / . G e V / c ) ) (GeV/c ψ J/ ± π ( max M E v en t s / . G e V / c ) ) (GeV/c ψ J/ ± π ( max M E v en t s / . G e V / c DataTotal fitBackground fit
PHSP MCSideband
FIG. 4: Dalitz plot for selected e + e − → π + π − J/ψ events in the
J/ψ signal region (left, the inset showbackground events from the
J/ψ mass sidebands) and the Z c (3900) signal in the M max ( πJ/ψ ) (right).Points with error bars are data, the curves are the best fit, the dashed histograms are the phase space distri-butions and the shaded histograms are the non- π + π − J/ψ background estimated from the normalized
J/ψ sidebands.
In addition to the known f (500) and f (980) structures in the π + π − system, a structure ataround . /c was observed in the π ± J/ψ invariant mass distribution with a statistical sig-nificance larger than σ , which is referred to as the Z c (3900) . A fit to the π ± J/ψ invariant massspectrum (see Fig. 4) determined its mass to be (3899 . ± . ± .
9) MeV /c and its width to be (46 ± ±
20) MeV .An article from the Belle experiment that was released subsequent to the BESIII paper reportedthe observation of the Z c (3900) state (referred to as Z (3900) + in the Belle paper) produced viathe ISR process with a mass of (3894 . ± . ± .
5) MeV /c and a width of (63 ± ±
26) MeV with a statistical significance larger than . σ [43]. These observations were later confirmed by ananalysis of CLEO-c data at a c.m. energy of .
17 GeV [58], with a mass and width that agree withthe BESIII and Belle measurements.BESIII studied the spin-parity of the Z c (3900) with a partial wave analysis (PWA) of about6000 e + e − → π + π − J/ψ events at √ s = 4 . and .
26 GeV [59]. The fit indicated that the spin-parity J P = 1 + assignment for the Z c (3900) is favored over other quantum numbers ( − , − , − ,and + ) by more than 7 σ .The Z c (3900) mass determined from its πJ/ψ invariant mass distribution is slightly above the D ¯ D ∗ mass threshold. The open-charm decay Z c (3900) ± → ( D ¯ D ∗ ) ± was observed with muchlarger rate than that to πJ/ψ [60, 61], and the pole mass and width were determined with highprecision to be (3882 . ± . ± .
5) MeV /c and (26 . ± . ± .
1) MeV , respectively.In both the QCD tetraquark and the molecular pictures, the Z c (3900) ± states are the I = ± members of an isospin triplet. BESIII confirmed this by observing their neutral, isospin I = 0 partners: the Z c (3900) , in both the π J/ψ [62] and ( D ¯ D ∗ ) [63] decay modes. These ob-servations establish the Z c (3900) as isovector states with even G -parity. From a PWA to the e + e − → π π J/ψ data in the vicinity of the Y (4260) resonance, it is found that the cross sectionline shape of e + e − → π Z c (3900) → π π J/ψ is in agreement with that of the Y (4220) (see9ig. 5) [64]. (GeV)s ) ( pb ) ψ J / π π → c Z π → - e + ( e σ − dataFitY(4220)expo.interference/ndf = 8.45/ 5 χ ± = (41.2 Γ FIG. 5: The cross sections of e + e − → π Z c (3900) → π π J/ψ [64]. Points with error bars are data,the red solid curve is the total fit result, the red-dashed (blue-dotted) curve is the resonant (non-resonant)component, and the magenta dash-dotted line represents the interference of the two components.
BESIII also searched for the Z c (3900) isospin violating decay mode ηJ/ψ [65] as well as tothe light hadron final states ωπ [66], K ¯ Kπ and K ¯ Kη [67], these were not observed and the upperlimits of the decay rates are one order of magnitude or even smaller than that for Z c (3900) → πJ/ψ , as naively expected.
2. Observation of the Z c (4020) The process e + e − → π + π − h c was observed at c.m. energies of . − .
42 GeV [57] with crosssection that is similar to that for e + e − → π + π − J/ψ [46]. Intermediate states of this three-bodysystem were studied by examining the Dalitz plot of the selected π + π − h c candidate events, similarto what was done for e + e − → π + π − J/ψ process [16]. Although there are no clear structures in the π + π − system, there is distinct evidence for an exotic charmoniumlike structure in the π ± h c system,as clearly evident in the Dalitz plot shown in Fig. 6. This figure also shows projections of the M ( π ± h c ) (two entries per event) distribution for the signal events as well as the background eventsestimated from normalized h c mass sidebands. There is a significant peak at around .
02 GeV /c (the Z c (4020) ), and there are also some events at around . /c that could be due to the Z c (3900) . The mass and width of the Z c (4020) were measured to be (4022 . ± . ± .
7) MeV /c and (7 . ± . ± .
6) MeV , respectively. The statistical significance of the Z c (4020) signal isgreater than . σ .In an analysis of e + e − → π π h c process, the Z c (4020) , the neutral isospin partner of the Z c (4020) ± was observed in π h c system. This indicates that the Z c (4020) is an isovector state [68].The open charm decay of the Z c (4020) was observed in e + e − → ( D ∗ ¯ D ∗ ) π , with a rate that is muchlarger than that for its decay into πh c [69, 70].10 ) (GeV/c - π + π M0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ) ( G e V / c π c h M ) (GeV/c c h ! (cid:85) M3.95 4.00 4.05 4.10 4.15 4.20 4.25 ) E v e n t s / ( . G e V / c ) (GeV/c c h + (cid:85) M3.8 3.9 4.0 4.1 ) E v e n t s / ( . G e V / c FIG. 6: Dalitz plot ( M π + h c vs. M π + π − ) for selected e + e − → π + π − h c events (left) and the Z c (4020) signalobserved in πh c invariant mass spectrum (right). Points with error bars are data, the solid curves are the bestfit, the shaded histograms are the non- π + π − h c background estimated from the normalized h c sidebands.
3. Nature of the Z c states Although many measurements have been performed on the Z c (3900) and Z c (4020) , the ex-perimental information is still not very precise. From the experience of the Z c (4430) , we knowthat the resonance parameters determined from a simple one-dimensional fit to the invariant massdistribution [54] may differ from those based on a full amplitude analysis with the interferenceeffects between different amplitudes considered properly [55]. The same thing may happen withthe Z c (3900) and Z c (4020) . Amplitude analyses that are applied to the relevant final states thatextract the resonant parameters as well as the couplings to different modes are essential to obtainmore refined information for understanding the nature of these states. In addition, PWA also canprovide measurements of Argand plots of the Z c amplitudes, which can be used to discriminatebetween different models for the Z c states.The production of Z c states at a variety of c.m. energies can reveal whether these states are fromresonance decays or continuum production. So far only the Z c (3900) has been observed both in e + e − annihilation [16] and in B -hadron decays [71, 72]. Searches for these states in differentproduction modes is of great importance.These states seem to indicate that a new class of hadrons has been observed. Since there are atleast four quarks within each of these Z c states, they have been alternatively interpreted as compacttetraquark states, molecular states of two charmed mesons ( D ¯ D ∗ + D ∗ ¯ D , D ∗ ¯ D ∗ , etc.), hadro-quarkonium states, or other multiquark configurations; in some phenomenological studies theyhave been attributed to purely kinematical effects [12]. Since many of these models suffer fromassumptions that are hard to prove, it is essential that non-perturbative studies such as lattice QCD(LQCD) provide a way to understand their underlying nature; if the Z c structures are not purelykinematical effects, they should appear on the lattice since they are strong interaction phenomena.The currently available LQCD calculations that are relevant to the Z c (3900) suffer from anumber of uncertainties, as has been recently reviewed in Ref. [73]. These include the latticespacing, the volume, the physical π mass, and the channels that are considered in the calculation.An early lattice study performed by Prelovsek et al. investigated the energy levels of two-meson systems including πJ/ψ , πψ (2 S ) , ρη c , D ¯ D ∗ , D ∗ ¯ D ∗ , etc., as well as tetraquark operators.11owever, no convincing signals for extra new energy levels apart from the almost free scatteringstates of the two mesons were identified [74]. Taking D ¯ D ∗ as the main relevant channel, theCLQCD collaboration performed a calculation that was based on the single-channel L¨uscher finite-size formalism and found a slightly repulsive interaction between the two charmed mesons [75,76]. The results therefore do not support the possibility of a shallow bound state for the two mesonsfor the pion mass values of 300, 420, and 485 MeV/ c . A preliminary study using staggered quarksfinds no J P C = 1 + − state distinct from the noninteracting scattering states either, but the authorsalso pointed out that future calculations with a larger interpolating operator basis may be able toresolve this state [77].The HALQCD collaboration studied the problem using an approach where an effective poten-tial is extracted from the lattice data and then used to solve the Schr¨odinger-like equations [78, 79].A fully coupled-channel potential for πJ/ψ , ρη c , and D ¯ D ∗ interactions is obtained, and a strongoff-diagonal transition between πJ/ψ and D ¯ D ∗ indicates that the Z c (3900) can be explained as athreshold cusp within their current configuration ( m π = 400 − MeV/ c ). In order to establisha definite conclusion on the structure of the Z c (3900) in the real world, full QCD simulations nearthe physical point are being carried out [78, 79].Recently, in order to clarify the mismatch between these two approaches, CLQCD performed atwo-channel lattice study using the two-channel Ross-Shaw effective range expansion [80]. Theyconsidered the πJ/ψ and D ¯ D ∗ channels that are most strongly coupled to Z c (3900) and foundthat the parameters of the Ross-Shaw matrix do not seem to support the HALQCD scenario. Theparameters turn out to be large and the Ross-Shaw M matrix is far from singular, which is requiredfor a resonance close to the threshold. However, since only two channels are studied, it is stillnot a direct comparison with the HALQCD approach, in which three channels were studied. InRef. [73], the same three channels that the HALQCD collaboration analyzed were considered,namely πJ/ψ , ρη c , and D ¯ D ∗ . However, the final results will not come very soon.Whatever the nature of the Z c states turn to be, they will teach us a lot about the hadronicstructures. Unless all these structures are purely kinematical effects (in which case it would haveto be an as yet unknown kinematic effect), they will suggest a new category of hadrons beyondthe conventional meson and baryon picture. Recent discoveries of structures with two pairs ofcharm-anticharm quarks [81] and with a minimal 4-quark configuration cs ¯ u ¯ d [82] confirm this ex-pectation. Additional searches for other conceivable states should be performed and the theoreticalconsequences of these new types of hadrons should be investigated. C. Comprehensive study of the X (3872) in e + e − collision The X (3872) was first observed in B ± → K ± π + π − J/ψ decays 17 years ago by Belle [35].It was confirmed subsequently by several other experiments [83–86]. Prior to 2014, the X (3872) was only observed in B meson decays and hadron collisions. Since the quantum numbers of X (3872) are J P C = 1 ++ , it can be produced via radiative decays of excited vector charmoniumor charmoniumlike states such as the ψ s and the Y s.The X (3872) was observed at BESIII in the process e + e − → γX (3872) → γπ + π − J/ψ , J/ψ → ℓ + ℓ − [87] (see the left panel of Fig. 7) and this first measurement was subsequentlyimproved with more data [88]. The c.m. energy dependence of the product of the cross section σ [ e + e − → γX (3872)] and the branching fraction B [ X (3872) → π + π − J/ψ ] is shown in the rightpanel of Fig. 7, where the red curve shows the results of a fit to a BW resonance line shape with12 mass of (4200 . +7 . − . ± .
0) MeV /c and a width of (115 +38 − ±
12) MeV . These resonanceparameters are consistent with those of the ψ (4160) charmonium states [3] or the Y (4220) (seeSec. III A) within errors. ) ) (GeV/c ψ J/ - π + π M( E v en t s / M e V / c DataTotal fitBackground (GeV)s4 4.2 4.4 4.6 ) ( pb ) ψ J / - π + π γ → X ( ) γ ( σ DataBESIII 2014Fit
FIG. 7: (Left panel) Fit to the M ( π + π − J/ψ ) distribution [87] and (right panels) fit to σ B [ e + e − → γX (3872)] × B [ X (3872) → π + π − J/ψ ] [88]. Dots/triangles with error bars are data, and the curvesare the best fits. Using all the data samples available at c.m. energies between . and . , BESIII is able toobserve for the first time significant signals of X (3872) → ωJ/ψ [88] and X (3872) → π χ c [89],and search for other possible decays.BESIII confirmed earlier observations of a large X (3872) → D ∗ ¯ D + c.c. branching frac-tion and finds evidence for X (3872) → γJ/ψ with a significance of . σ [90]. No evidenceis found for the decays X (3872) → γψ (2 S ) . The upper limit on the ratio B ( X (3872) → γψ (2 S )) / B ( X (3872) → γJ/ψ ) < . is obtained at the 90% C.L. [90], which is inconsis-tent with LHCb [91] and BaBar measurements [92] but consistent with a Belle upper limit [93].No significant X (3872) → π χ c , signals are observed.The hadronic transitions of the X (3872) to low mass charmonum states via a single pion or arho meson violate isospin, and the large decay rates of X (3872) → π χ c and ρJ/ψ → π + π − J/ψ relative to the isospin-conserved mode X (3872) → ωJ/ψ indicate that X (3872) is very unlikelyto be a pure charmonium state, such as the χ c (2 P ) . The order of magnitude larger decay rateto D ∗ ¯ D + c.c. than to charmonium final state favors the D ∗ ¯ D + c.c. molecule interpretation ofthe X (3872) , as is the relatively smaller production rate of X (3872) → γψ (2 S ) compared with X (3872) → γJ/ψ , or at least that there is a large fraction of molecular component in its wavefunction in addition to a charmonium component.BESIII measured the ratios of branching fractions for X (3872) → γJ/ψ , γψ (2 S ) , ωJ/ψ , π χ c , D ∗ ¯ D + c.c. , π D ¯ D , and γD ¯ D to that for X (3872) → π + π − J/ψ . By combining thesewith the measurements of the X (3872) properties from the B -factories, the authors of Ref. [94]obtained the absolute branching fractions of the X (3872) decays into six modes by globally fittingthe measurements provided by Belle, BaBar, BESIII, and LHCb experiments (see Table II). Thebranching fraction for X (3872) → π + π − J/ψ is determined to be (4 . +1 . − . )% , which is in goodagreement with earlier estimates in Refs. [95] and [96]. By combining the branching fractionsof all of the observed modes, the fraction of the unknown decays of the X (3872) is found to be (31 . +18 . − . )% , which is an important challenge for future experimental studies of X (3872) decays.13 ABLE II: The fitting results of the absolute branching fractions of the X (3872) decays [94]. The branchingfraction of X (3872) decays into unknown modes is calculated from the fit results.Parameter index Decay mode Branching fraction1 X (3872) → π + π − J/ψ (4 . +1 . − . )% X (3872) → D ∗ ¯ D + c.c. (52 . +25 . − . )% X (3872) → γJ/ψ (1 . +0 . − . )% X (3872) → γψ (2 S ) (2 . +1 . − . )% X (3872) → π χ c (3 . +2 . − . )% X (3872) → ωJ/ψ (4 . +2 . − . )% X (3872) → unknown (31 . +18 . − . )% With a very large sample of X (3872) → π + π − J/ψ events, the LHCb experiment reportedan improved measurement of its mass and a first measurement of its width [97]. Limited by itscapability of D ∗ reconstruction and mass resolution, it is still not possible for LHCb to measurethe line shape of the resonance. D. Commonality between the X (3872) , Y (4260) , and Z c (3900) With data taken with c.m. energy at and near the Y (4260) resonance peak, BESIII discov-ered a clear signal for X (3872) production in association with a γ -ray [87], as shown in Fig. 7,and a clear signal for Z c (3900) production in association with a π meson [64], as shown inFig. 5. The c.m.-energy-dependence of the e + e − → γX (3872) cross section is suggestive of a Y (4260) → γX (3872) decay process, and that of e + e − → π Z c (3900) cross section is sugges-tive of a Y (4260) → πZ c (3900) decay process, these indicate that there might be some commonfeatures to the internal structures of the Z c (3900) , Y (4260) , and X (3872) .Many of the models developed to interpret the nature of one of these three states do not considerthe possibility of a connection between them. With data supplied by the BESIII experiments, someof these models may be ruled out and others may need to be revisited in the light of these newobservations. IV. SUMMARY AND PERSPECTIVES
With the capability of adjusting the e + e − c.m. energy to the peaks of resonances, combinedwith the clean experimental environments due to near-threshold operation, BESIII is uniquely ableto perform a broad range of critical measurements of charmonium physics, and the production anddecays of many of the nonstandard XYZ states, as discussed above in the context of the studiesof the X (3872) , Y (4220) , Z c (3900) and Z c (4020) . Table III shows the operating times associatedthe discoveries of the XYZ states at BESIII and other experiments, including the previous gener-ation B -factories BaBar and Belle, and the new generation super- B -factories LHCb and Belle II.BESIII’s special advantages for studying the XYZ states are evident.We emphasize here that BESIII measured all the known decay modes of the X (3872) anddiscovered its new decay modes even though the numbers of produced X (3872) events are much14 ABLE III: The numbers of observed events of discovery modes of the
XYZ states at the BESIII andother experiments. Here the states are detected with X (3872) → π + π − J/ψ , Y (4260) → π + π − J/ψ , Z c (3900) ± → π ± J/ψ , Z c (4020) → π ± h c , and Y (4660) → π + π − ψ (2 S ) . The numbers for Belle II ex-periments are a simple scale according to those of Belle experiment. “–” means no measurement available.BESIII can detect other decay modes of these states while other experiments can barely do.Experiment Data taking time X (3872) Y (4260) Z c (3900) Z c (4020) Y (4660) BESIII 3 months 20 6,000 1,300 180 250BaBar 1999-2008 90 270 80 – 45Belle 1999-2010 170 550 160 – 90LHCb 2011-12 ( B decays) 4,000 – – – –2011-18 ( pp collision) 16,000 – – – –Belle II 2019-30 8,000 28,000 8,000 – 5,000 smaller than those of other experiments. This is because the very clean experimental environmentof e + e − collisions in the τ -charm threshold energy region uniquely facilitates the isolation ofsignals for X (3872) decays into final states with one or more photons with high efficiency. Thisis especially true for final states that contain an h c charmonium state like the BESIII discovery ofthe Z c (4020) state and measurements of Y (4220) and Y (4390) → π + π − h c decays. Neither theBaBar and Belle B -factory nor the LHCb experiment has ever seen an h c signal.BESIII has produced a considerable amount of information about the XYZ and the conventionalcharmonium states. In addition, there are still data that are still being analyzed and more data thatwill be accumulated at other c.m. energies [50, 98]. Analyses with these additional data sampleswill provide an improved understanding of the
XYZ states, especially the X (3872) , Y (4260) , Z c (3900) , and Z c (4020) . The maximum c.m. energy accessible at BEPCII was upgraded from 4.6to 4.9 GeV in 2019, and a 3.5 fb − sample of data between 4.6 and 4.7 GeV was accumulated inthe 2019-20 running period, with more data planned for the future. This will enable a full coverageof the Y (4660) [38] resonance and a search for possible higher mass vector mesons and states withother quantum numbers, as well as improved measurements of their properties.At the same time, other experiments will also supply information on these states. At the LHCb,in addition to the 3 fb − data at 7 and 8 TeV that have been used for most of their publishedanalyses, there is a 6 fb − data sample at 13 TeV that is being used for improved analyses of manyof the topics discussed above such as the X (3872) decay properties and the searches for the Y and Z c (3900) states in B decays.Belle II [99] has collected about 70 fb − data by mid-2020, and will accumulate 50 ab − dataat the Υ(4 S ) peak by the end of 2030. These data samples can be used to study the XYZ andcharmonium states in many different ways [11], among which ISR can produce events in thesame energy range covered by BESIII. A 50 ab − Belle II data sample will correspond to 2.0–2.8 fb − data for every 10 MeV from 4–5 GeV. Similar statistics will be available for modeslike e + e − → π + π − J/ψ at Belle II and BESIII (after considering the fact that Belle II has lowerefficiency). Belle II has the advantage that data at different energies will be accumulated at thesame time, making the analysis much simpler than at BESIII.There are two super τ -charm factories proposed, the STC in China [100] and the SCT in Rus-sia [101]. Both machines would run at c.m. energies of up to 5 GeV or higher with a peakluminosity of cm − s − which is a factor of 100 improvement over the BEPCII. This would15nable systematic studies of the XYZ and charmonium states with unprecedented precision.
Acknowledgments
I thank my BESIII collaborators for producing these fantastic results presented in this re-view, I thank Steve Olsen for comments and suggestions on the manuscript. This work is sup-ported in part by National Key Research and Development Program of China under ContractNo. 2020YFA0406300, National Natural Science Foundation of China (NSFC) under contractNos. 11961141012, 11835012, and 11521505; and the CAS Center for Excellence in ParticlePhysics (CCEPP).
Note added:
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