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There has recently been a dramatic renewal of interest in hadron spectroscopy and charm physics. This renaissance has been driven in part by the discovery of a plethora of charmonium-like XYZ states at BESIII and B factories, and the observation of an intriguing proton-antiproton threshold enhancement and the possibly related X(1835) meson state at BESIII, as well as the threshold measurements of charm mesons and charm baryons. We present a detailed survey of the important topics in tau-charm physics and hadron physics that can be further explored at BESIII during the remaining operation period of BEPCII. This survey will help in the optimization of the data-taking plan over the coming years, and provides physics motivation for the possible upgrade of BEPCII to higher luminosity.

We study e+e-→π+π-hc at center-of-mass energies from 3.90 to 4.42 GeV by using data samples collected with the BESIII detector operating at the Beijing Electron Positron Collider. The Born cross sections are measured at 13 energies and are found to be of the same order of magnitude as those of e+e-→π+π-J/ψ but with a different line shape. In the π±hc mass spectrum, a distinct structure, referred to as Zc(4020), is observed at 4.02  GeV/c2. The Zc(4020) carries an electric charge and couples to charmonium. A fit to the π±hc invariant mass spectrum, neglecting possible interferences, results in a mass of (4022.9±0.8±2.7)  MeV/c2 and a width of (7.9±2.7±2.6)  MeV for the Zc(4020), where the first errors are statistical and the second systematic. The difference between the parameters of this structure and the Zc(4025) observed in the D*D[over ¯]* final state is within 1.5σ, but whether they are the same state needs further investigation. No significant Zc(3900) signal is observed, and upper limits on the Zc(3900) production cross sections in π±hc at center-of-mass energies of 4.23 and 4.26 GeV are set.

We study the process e+ e- →(D* D*)± π∓ at a center-of-mass energy of 4.26 GeV using a 827  pb(-1) data sample obtained with the BESIII detector at the Beijing Electron Positron Collider. Based on a partial reconstruction technique, the Born cross section is measured to be (137±9±15)  pb. We observe a structure near the (D* D*)± threshold in the π∓ recoil mass spectrum, which we denote as the Zc±(4025). The measured mass and width of the structure are (4026.3±2.6±3.7)  MeV/c2 and (24.8±5.6±7.7)  MeV, respectively. Its production ratio σ(e+ e- → Zc±(4025)π∓ → (D* D*)± π∓)/σ(e+ e- → (D* D*)± π∓) is determined to be 0.65±0.09±0.06. The first uncertainties are statistical and the second are systematic.

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