Exotic hadrons from BESIII

. We report the progress in the study of the exotic hadrons, also called XYZ states, at BESIII experiment with its unique data samples in e + e − annihila-tion at center-of-mass energies of 3.8–4.6 GeV. The talk covers the observation of the Z c (3900) and Z c (4020) and new measurements related to them; updated measurement of the resonant parameters of the Y (4260) in e + e − → π + π − J /ψ and discovery of its new decay modes π + π − ψ (2 S ), ωχ c 0 , π + π − h c , and D D ∗− π + + c . c . ; and observation of X in e + e − annihilation.


Introduction
In the conventional quark model, mesons are composed of one quark and one anti-quark, while baryons are composed of three quarks. Although this picture is very simple, it describes almost all the hadrons observed so far [1]. However, many charmonium-like states were discovered at two B-factories BaBar and Belle in the first decade of this century [2]. Whereas some of these are good candidates of charmonium states, many other states have exotic properties, which may indicate that exotic states, such as multi-quark state, hadronic molecule, or hybrid, have been observed [3]. Experimentally, these states are also called XYZ states, to indicate their nature is still unclear.
BaBar and Belle experiments finished their data taking in 2008 and 2010, respectively, and the data are still used for various physics analyses. In 2008, the BESIII [4], a τ-charm factory experiment at the BEPCII e + e − collider, started data taking, and contributed to the study of the XYZ particles ever since. In this article, we focus on the measurements of the three mostly studied XYZ states, i.e., the X(3872), the Y(4260), and the Z c (3900), at BESIII [5]. µ + µ − . The J/ψ signal is selected by requiring the invariant mass of the lepton pair is consistent with the J/ψ, and a sample of 1595 π + π − J/ψ events with a purity of 90% is obtained. The intermediate states are studied by examining the Dalitz plot (shown in Fig. 1) of the selected candidate events. A structure at around 3.9 GeV/c 2 was observed in the π ± J/ψ invariant mass distribution with a statistical significance larger than 8σ, which is referred to as the Z c (3900). A fit to the π ± J/ψ invariant mass spectrum with a constant width Breit-Wigner (BW) function ( Fig. 1), neglecting interference with other amplitudes, results in a mass of (3899.0±3.6±4.9) MeV/c 2 and a width of (46 ± 10 ± 20) MeV. The Z c (3900) state was reported shortly after at Belle [7] with initial state radiation (ISR) data and with CLEO-c data at a c.m. energy of 4.17 GeV [8], and the mass and width agreed very well with the BESIII measurement.

Spin-parity of the Z c (3900)
BESIII determines the spin-parity of the Z c (3900) based on a partial wave analysis (PWA) of e + e − → π + π − J/ψ events at √ s = 4.23 and 4.26 GeV [9]. Following the event selection reported in Ref. [6], the numbers of selected candidate events are 4154 at √ s = 4.23 GeV and 2447 at √ s = 4.26 GeV, with 365 and 272 background events, respectively, estimated by using the J/ψ mass sidebands.

Observation of
With the data sample at √ s = 4.26 GeV, the BESIII experiment studied e + e − → π ± (DD * ) ∓ with single-tag method (only one of the two D mesons is reconstructed) and observed the open-charm decay Z c (3900) ± → (DD * + c.c.) ± [10]. The analysis is refined with double-tag method (both D mesons are reconstructed) and more luminosity [11]. In this analysis, both e + e − → π + D 0 D * − + c.c. and π + D − D * 0 + c.c. are measured with data samples at √ s=4.23 and 4.26 GeV. The double D tag technique allows the use of more D decay modes and the background level is greatly suppressed.
The double-tag analysis only has ∼9% events in common with the single-tag analysis, so the two analyses are almost statistically independent and the results can be combined to have a better measurement. The combined pole mass and width are (3882.2±1.1±1.5) MeV/c 2 and (26.5±1.7±2.1) MeV, respectively. The combined production rate σ(e + e − → π ∓ Z c (3900 23 GeV which is from double-tag method only.

Evidence for Z c (3900) → ρη c
BESIII searches for e + e − → π + π − π 0 η c and intermediate states decay into ρη c with data collected at 4.23, 4.26, and 4.36 GeV [12]. The recoil mass of one charged pion (equivalent to the invariant mass of ρ ± η c ) is shown in Fig. 2 for the data at √ s = 4.23 GeV, the Z c (3900) ± signal is found while there is no significant Z c (4020) ± signal. The ρ ± η c invariant mass distribution is fitted with the contributions from Z c (3900) and Z c (4020) together with a smooth background. 240 ± 56 Z c (3900) ± events is observed with a statistical significance of 4.3σ (3.9σ including the systematical uncertainty). The Z c (3900) signals at other c.m. energies and the Z c (4020) signals at all the c.m. energies are not statistically significant.  Figure 2. The π ± recoil mass distribution in e + e − → π ± ρ ∓ η c at √ s = 4.23 GeV and the fit with Z c (3900/4020) ± signals (left panel); and the same plot with background subtracted (right panel). Dots with error bars are data, shaded histogram is from η c sidebands, normalized to the number of backgrounds from the fit, the solid lines are total fit and the dotted line is background.
Using the results from Ref. [9], the ratio of the branching fractions of different Z c (3900) ± decays is calculated as 23 GeV and less than 6.4 at √ s = 4.26 GeV at the 90% C.L. The theoretical predictions for this ratio varies depending on model assumptions and ranges from a few per cent to a few hundreds [13][14][15][16][17][18].

Observation of the Z c (4020)
The partner state of the Z c (3900) close to the D * D * is searched in e + e − → π + π − h c and e + e − → (D * D * ) ± π ∓ . BESIII measures cross sections of e + e − → π + π − h c at c.m. energies of 3.90-4.42 GeV [19]. Intermediate states are studied by examining the Dalitz plot of the selected π + π − h c candidate events. There is distinct signal for an exotic charmonium-like structure in the π ± h c system (Fig. 3). The mass and width of the Z c (4020) are measured to be (4022.9±0.8±2.7) MeV/c 2 and (7.9±2.7±2.6) MeV, respectively. The statistical significance of the Z c (4020) signal is found to be greater than 8.9σ. The study of e + e − → (D * D * ) ± π ∓ process using data at √ s =4.26 GeV [20] indicates the open-charm decay Z c (4020) → (D * D * ) ± in the π ∓ recoil mass spectrum (see Fig. 3). The measured mass and width of the structure are (4026.3 ± 2.6 ± 3.7) MeV/c 2 and (24.8 ± 5.6 ± 7.7) MeV, respectively, and the statistical significance is 13σ.

e + e − → π + π − J/ψ
The cross sections of e + e − → π + π − J/ψ are measured precisely at c.m. energies from 3.77 to 4.60 GeV using 9 fb −1 of BESIII data [24]. Figure 4 shows the measured cross sections, one can see clearly the Y(4260) structure observed by BaBar and Belle experiments, but it is peaked at around 4.22 GeV rather than 4.26 GeV from the previous fits [7,25].
Two resonant structures in the Y(4260) peak region are needed in a fit to the cross sections. The first one has a mass of (4222.0 ± 3.1 ± 1.4) MeV/c 2 and a width of (44.1 ± 4.3 ± 2.0) MeV, while the second one has a mass of (4320.0 ± 10.4 ± 7.0) MeV/c 2 and a width of (101.4 +25.3 −19.7 ± 10.2) MeV. The mass of first resonance is lower than that of the Y(4260) and it is much narrower. The second resonance is observed in e + e − → π + π − J/ψ for the first time, with a statistical significance larger than 7.6σ.
It is worth pointing out that the lower mass structure (called Y(4220) hereafter) is the main component of the Y(4260) structure but with improved measurement of the resonant parameters thanks to the high luminosity data from BESIII.
As the BESIII data can only reach 4.6 GeV, the parameters of the Y(4660) are fixed to Belle measurement [30] in the fit to the e + e − → π + π − ψ(2S ) cross sections. The data require a lower-mass resonance with a mass M = (4209.5 ± 7.4 ± 1.4) MeV/c 2 and a width Γ = (80.1 ± 24.6 ± 2.9) MeV with a statistical significance of 5.8σ, this is the first observation of the new decay mode Y(4220) → π + π − ψ(2S ). The fit results are also presented in Fig. 6.

e + e − → ωχ c0
The process e + e − → ωχ c0 is observed for the first time and the cross sections or the upper limits on the cross sections (when the signal is not significant) at the 90% C.L. are determined [28,32]. By assuming the ωχ c0 signals come from a single resonance, the mass is determined to be (4226 ± 8 ± 6) MeV/c 2 , and width (39 ± 12 ± 2) MeV (shown in Fig. 6).
In fact, it is in the e + e − → ωχ c0 mode that the Y(4220) (or Y(4230)) structure was first reported [28].

e
BESIII reported measurements of the cross section of e + e − → D 0 D * − π + +c.c. at c.m. energies from 4.05 to 4.60 GeV [33] (shown in Fig. 6), which is a significant improvement over the Belle measurement [34] with ISR technique. A fit to the cross section is performed to determine the parameters of the resonant structures. The fit yields a mass of (4228.6±4.1±5.9) MeV/c 2 and a width of (77.1±6.8±6.9) MeV for the lower mass structure, and a mass of (4400.1 ± 9.3) MeV/c 2 and a width of (181.7 ± 16.9) MeV for the higher mass one. Here for the higher mass state, the errors are statistical only. This is the first observation of the Y(4220) decays into open-charm final state D 0 D * − π + + c.c..

Resonant parameters of the Y(4260) from combined fit
As the cross sections of different final states have some common features, and some of the final states have been measured by different experiments, these data are used to do combined fit to extract more information about the resonant structures [35,36].
The X(3872) signal is shown in Fig. 7 (left), the mass is measured as (3871.9 ± 0.7 ± 0.2) MeV/c 2 and the width is less than 2.4 MeV at the 90% C.L. The statistical significance of X(3872) is 6.3σ. The energy-dependent cross sections (Fig. 7 (right)) can be described with the Y(4260) resonance well, which supports the existence of radiative transition Y(4260) → γX(3872). Together with the hadronic transition of the Y(4260) → πZ c (3900) [6][7][8], these suggest that there might be some commonality in the nature of X(3872), Y(4260), and Z c (3900), and so the model developed to interpret any one of them should also consider the other two.

Summary and Perspectives
BESIII has achieved a lot in the study of the XYZ states. There are still some data at BESIII not analyzed and data at more energy points will be taken [42]. More analyses with these data samples will allow many improved understanding of the XYZ states, especially the X(3872), Y(4260), Z c (3900), and Z c (4020). BEPCII is upgrading the maximum c.m. energy from 4.6 to 4.9 GeV in two years, this will enable a full coverage of the Y(4660) [23] and Y(4630) [43] resonances, improved measurements of their properties are expected.