Recent Results on Hadron Spectroscopy from BESIII

Hadron spectroscopy is one of the most important physics goals of BESIII. BESIII brings great opportunities to study the XYZ states of charmonium by directly producing the Y states up to 4.6 GeV. High statistics of charmonium decays collected at BESIII provide an excellent place for hunting gluonic excitations and studying the excited baryons. Recent results of light hadron spectroscopy and charmonium spectroscopy from BESIII will be reported.


INTRODUCTION
Hadron spectroscopy is a unique way to access Quantum Chromodynamics (QCD). QCD-motivated models for hadrons predict an assortment of "Exotic Hadrons" that have structures that are more complex than the quark-antiquark mesons and three-quark baryons of the original quark model, such as glueballs, hybrids and multi-quark states. Experimental search of these predictions and subsequent investigation of their properties would provide validation of and valuable input to the quantitative understanding of QCD.
BESIII (Beijing Spectrometer) is a general purpose 4π detector at the upgraded BEPCII (Beijing Electron and Positron Collider) that operated in the τ-charm threshold energy region [1]. Since 2009, it has collected the world's largest data samples of J/ψ, ψ(3686), ψ(3770) and ψ(4040) decays. More recently, data were taken in the energy region above 4 GeV, where energies up to about 4.6 GeV are accessible. These data are being used to make a variety of interesting and unique studies of light hadron spectroscopy, charmonium spectroscopy, high-statistics measurements of charmonium decays and D meson decays.

Charmonium spectroscopy
The quark model [2], which treats mesons as combinations of one quark and one anti-quark, is very successful in describing meson properties, particularly in the charmonium (cc) region below the open-charm threshold. [3]. The past decade, however, has seen the discovery of a number of new states (named the XYZ states) that do not fit within this model, and which perhaps point towards more complex systems. With its unique data samples at energies of 3.8-4.6 GeV, the BESIII experiment made a significant contribution to the study of charmonium and charmonium-like states.

Charged charmonum-like states: Z c 's
Recently, in the study of e + e − → J/ψπ + π − , a distinct charged structure, named the Z c (3900) ± , was observed in the J/ψπ ± spectrum by BESIII [4] and Belle [5]. Its existence was confirmed shortly thereafter with CLEO-c data [6]. The existence of the neutral partner in the decay Z c (3900) 0 → J/ψπ 0 has also been reported in CLEO-c data [6] and by BESIII [7], thus complementing the isospin-triplet representation of isospin one, I = 1, resonances. The Z c (3900) is a good candidate for an exotic state beyond simple quark models, since it contains a cc pair and is also electrically charged. Noting that the Z c (3900) has a mass very close to the D * D threshold (3875 MeV), BESIII analyzed the process e + e − → π ± (DD * ) ∓ , and a clear structure in the (DD * ) ∓ mass spectrum is seen, called the Z c (3885). The measured mass and width are (3883.9 ± 1.5 ± 4.2) MeV/c 2 and (24.8 ± 3.3 ± 11.0) MeV, respectively, and quantum numbers J P = 1 + are favored [8]. A neutral structure in the DD * system around the DD * mass threshold is observed with a statistical significance greater than 10σ in the processes e + e − → D + D * − π 0 + c.c. and e + e − → D 0D * 0 π 0 + c.c. at √ s = 4.226 and 4.257 GeV in the BESIII experiment [10]. Assuming the Z c (3885) → DD * and the Z c (3900) → J/ψπ signals are from the same source, the ratio of partial widths Γ(Z c (3885)→DD * ) Γ(Z c (3900)→J/ψπ) is determined to be 6.2±1.1±2.7. This ratio is much smaller than typical values for decays of conventional charmonium states above the open charm threshold. BESIII also searched for the decay mode of Z c with the annihilation of cc in the reaction e + e − → ωπ + π − [9]. The upper limits of the Born cross section are determined to be 0.26 and 0.18 pb, at E CM = 4.23 and 4.26 GeV, respectively. Figure 1 shows the Z c (3900) ± → π ± J/ψ and its isospin-partner, Z c (3900) 0 → π 0 J/ψ. The results of Z c (3885) → (DD * ) observed in e + e − → π(DD * ) processes are shown in Fig. 2. Table 1 lists corresponding masses and widths of the Z c states near the D * D threshold. BESIII analyzed the reaction e + e − → π + π − h c , at E CM = 4.23, 4.26 and 4.36 GeV [11]. Corresponding π ± h c invariant mass distribution, when all energy points are combined, is shown in Fig. 3. The Z c (4020) ± signal has 8.9σ significance. And the inset represents a search for the Z c (3900) → πh c , at E CM = 4.23 and 4.26 GeV. At the 90% confidence level (C.L.), the upper limits on the production cross-sections are set to σ(e + e − → π ± Z c (4020) ∓ → π + π − h c ) < 13 pb at 4.23 GeV and < 11 pb at 4.26 GeV. These are lower than those of Z c (4020) → π ± J/ψ [4]. BESIII also observed e + e − → π 0 π 0 h c at √ s = 4.23, 4.26, and 4.36 GeV [12], confirming the isospin of Z c (4020) to be one. Similarly to the case of the Z c (3900), the mass of the Z c (4020) is near the threshold for D * D * production. BESIII studied two reactions: e + e − → (D * D * ) ± π ∓ , at E CM = 4.26 GeV [14], and e + e − → (D * D * ) 0 π 0 , at E CM = 4.23 and 4.26 GeV [15].
A structure that couples to D * D * is evident, in both charged and neutral decays, denoted as Z c (4025). Fig. 4 shows the results of Z c (4025). Assuming the Z c (4020) and the Z c (4025) signals are from the same source, the ratio of partial widths Γ(Z c (4025)→D * D * ) Γ(Z c (4020)→h c π) is determined to be 12 ± 5. Table 1 lists corresponding masses and widths of the Z c states near the D * D * threshold.     . Z c (4020) → πh c production in e + e − → ππh c processes: (a)charged mode [11], (b) neutral mode [12].
The production cross-sections of σ B (e + e − → π + π − X(3823)) · B(X(3823) → γχ c1 , γχ c2 ) were also measured at these c.m. energies. The cross-sections of e + e − → π + π − X(3823) were fitted with the Y(4360) shape or the ψ(4415) shape, as shown in Fig. 6 (c). Both the Y(4360) and ψ(4415) hypotheses are accepted at a 90% C.L.  Structures in e + e − → charmonium + hadrons The e + e − → ωχ c0 process was observed at √ s = 4.23 and 4.26 GeV for the first time [19]. By examining the ωχ c0 cross section as a function of center-of-mass energy as shown in Fig. 7 (a), we find that it is inconsistent with the line shape of the Y(4260) observed in e + e − → π + π − J/ψ. Assuming the ωχ c0 signals come from a single resonance, we extract mass and width of the resonance to be (4230 ± 8 ± 6) MeV/c 2 and (38 ± 12 ± 2) MeV, respectively, and the statistical significance is more than 9σ.
BESIII analyzed e + e − → ηJ/ψ [20]. Statistically significant η signals were observed, and the corresponding Born cross-sections were measured. The Born cross-sections σ(e + e − → ηJ/ψ) in this measurement are well consistent with previous results [21,22]. The measured Born cross-sections were also compared to those of e + e − → π + π − J/ψ obtained from the Belle experiment [23], as shown in Fig. 7 (b). Different line shapes can be observed in these two processes, indicating that the production mechanism of ηJ/ψ differs from that of π + π − J/ψ in the vicinity of √ s = 4.1-4.6 GeV. This could indicate the existence of a rich spectrum of the Y states in this energy region with different coupling strengths to various decay modes.

Light meson spectroscopy
Glueballs and other resonances with large gluonic components are predicted as bound states by QCD. The lightest (scalar) glueball is estimated to have a mass in the range from 1 to 2 GeV/c 2 ; pseudoscalar and tensor glueballs are expected at higher masses. Radiative decays of the charmonium provide a gluon rich environment and are therefore regarded as one of the most promising hunting grounds for glueballs and hybrids.  Observation and Spin-Parity Determination of the X(1835) in J/ψ → γK 0 S K 0 S η X(1835) was first observed in J/ψ → γη ′ π + π − by BESII [25]; this observation was subsequently confirmed by BE-SIII [26]. In addition, an enhancement in the invariant pp mass at threshold, X(pp), was first observed by BESII in the decay J/ψ → γpp [27], and was later also seen by BESIII [28] and CLEO [29]. In a partial wave analysis(PWA), BESIII determined the J PC of the X(pp) to be 0 −+ [30]. The mass of the X((pp) is consistent with X(1835), but the width of the X(pp) is significantly narrower. To understand the nature of the X(1835), it is crucial to measure its J PC and to search for new decay modes. Fig. ?? (a) shows the scatter plot of the invariant mass of K 0 S K 0 S versus that of K 0 S K 0 S η, indicating the structure around 1.85 GeV/c 2 is strongly correlated with f 0 (980). A partial wave analysis (PWA) of J/ψ → γK 0 S K 0 S η has been performed in the mass range M K 0 [31]. Fig. 8 (b) and (c) are the invariant mass distributions of K 0 Overlaid on the data are the PWA fit projections, as well as the individual contributions from each component. The PWA fit requires a contribution from X(1835) → K 0 S K 0 S η with a statistical significance greater than 12.9σ, where the X(1835) → K 0 S K 0 S η is dominated by f 0 (980) production. The spin parity of the X(1835) is determined to be 0 −+ . The mass and width of the X(1835) are measured to be 1844 ± 9(stat) +16 −25 (syst) MeV/c 2 and 192 +20 −17 (stat) +62 −43 (syst) MeV, respectively. The corresponding product branching fraction B X(1835) is measured to be (3.31 +0. 33 −0.30 (stat) +1.96 −1.29 (syst)) × 10 −5 . The mass and width of the X(1835) are consistent with the values obtained from the decay J/ψ → γη ′ π + π − by BESIII [26]. These results are all first-time measurements and provide important information to further understand the nature of the X(1835). Another 0 −+ state, the X(1560), also is observed in data with a statistical significance larger than 8.9σ. The mass and width of the X(1560) are consistent with those of the η(1405) and η(1475) as given in Ref. [32] within 2.0σ and 1.4σ, respectively. Amplitude analysis of the π 0 π 0 system produced in radiative J/ψ decays A mass independent amplitude analysis of the π 0 π 0 system in radiative J/ψ decays is performed [33]. This analysis uses the world's largest data sample of its type, collected with the BESIII detector, to extract a piecewise function that describes the scalar and tensor ππ amplitudes in this decay. While the analysis strategy employed to obtain results has complications, namely ambiguous solutions, a large number of parameters, and potential bias in subsequent analyses from non-Gaussian effects, it minimizes systematic bias arising from assumptions about ππ dynamics, and, consequently, permits the development of dynamical models or parameterizations for the data. The intensities and phase differences for the amplitudes in the fit are presented as a function of M π 0 π 0 in Ref. [33]. Additionally, in order to facilitate the development of models, the intensities and phases for each bin of M π 0 π 0 are given in supplemental materials of Ref. [33]. These results may be combined with those of similar reactions for a more comprehensive study of the light scalar meson spectrum. Finally, the branching fraction of radiative J/ψ decays to π 0 π 0 is measured to be (1.15 ± 0.05) × 10 −3 , where the error is systematic only and the statistical error is negligible. This is the first measurement of this branching fraction.

Partial Wave Analysis of J/ψ → γφφ
The low lying pseudoscalar glueball is predicted to be around 2.3−2.6 GeV/c 2 by Lattice QCD [34,35,36]. Aside from the η(2225), very little is known in the pseudoscalar sector above 2 GeV/c 2 . A partial wave analysis of the decay J/ψ → γφφ is performed in order to study the intermediate states. The most remarkable feature of the PWA results is that 0 −+ states are dominant. The existence of the η(2225) is confirmed and two additional pseudoscalar states, η(2100) with a mass 2050 +30 The three tensors f 2 (2010), f 2 (2300) and f 2 (2340) observedin π − p → φφn [37] are also observed in J/ψ → γφφ. Recently, the production rate of the pure gauge tensor glueball in J/ψ radiative decays has been predicted by Lattice QCD [38], which is compatible with the large production rate of the f 2 (2340) in J/ψ → γφφ and J/ψ → γηη [39]. Fig. 9 shows the PWA fit results with comparison of data.

Summary
With the worlds largest samples of J/ψ, ψ(3686), ψ(3770), Y(4260) .etc from e + e − production, the BESIII experiment made a significant contribution to the study of the charmonium spectroscopy, light meson spectroscopy and light baryon spectroscopy. BESIII will continue to run 6-8 years. Complementary to other experiments, with various production mechanisms, BESIII will continue shedding light on the the nature of hadrons.