QCD sum rule studies on the $$s s {\bar{s}} {\bar{s}}$$ tetraquark states of $$J^{PC} = 0^{-+}$$

We apply the method of QCD sum rules to study the $$s s {\bar{s}} {\bar{s}}$$sss¯s¯ tetraquark states of $$J^{PC} = 0^{-+}$$JPC=0-+. We construct all the relevant $$s s {\bar{s}} {\bar{s}}$$sss¯s¯ tetraquark currents, and find that there are only two independent ones. We use them to further construct two weakly-correlated mixed currents. One of them leads to reliable QCD sum rule results and the mass is extracted to be $$2.51^{+0.15}_{-0.12}$$2.51-0.12+0.15 GeV, suggesting that the X(2370) or the X(2500) can be explained as the $$ss{\bar{s}}{\bar{s}}$$sss¯s¯ tetraquark state of $$J^{PC} = 0^{-+}$$JPC=0-+. To verify this interpretation, we propose to further study the $$\pi \pi /K {\bar{K}}$$ππ/KK¯ invariant mass spectra of the $$J/\psi \rightarrow \gamma \pi \pi \eta ^\prime /\gamma K {\bar{K}} \eta ^\prime $$J/ψ→γππη′/γKK¯η′ decays in BESIII to examine whether there exists the $$f_0(980)$$f0(980) resonance.

Nucleon form factors at threshold

The pp¯invariant mass spectra in the processes e+e−→ pp¯, e+e−→ nn¯, J/ψ → pp¯ω, J/ψ → pp¯ρ, and J/ψ → pp¯γ close to the pp¯is discussed. The optical potentials for NN¯pair in the superposition of S and D waves (due to tensor forces) at spin unity of the pair, as well as for NN¯pair in the S wave at spin zero of the pair, are proposed. The parameters of the potentials are obtained by fitting the cross sections of NN¯scattering together with the pp¯invariant mass spectra in e+e−→ pp¯annihilation and J/ψ decays. Good agreement with the available experimental data is achieved. Using our potential and the Green’s function approach we also describe the cross section of e+ e−→ 6π and the η’π+ π− invariant mass spectrum in the decay J/ψ → γη’π+π− in the energy region near the NN¯threshold.

The initial single chiral particle emission mechanism and its predictions of charmonium-like structures

We propose a new mechanism, named as the initial single chiral particle emission mechanism, to explain the charged Zb(10610) and Zb(10650) observed in the ϒ(5S) → π+π-ϒ(nS), π+π-hb(mP), (n = 1 ~ 3, m = 1, 2) processes. After successfully interpreting the charge Zb structures, we extend this mechanism to study the process of the dipion transitions between the higher charmonia/charmonium-like state and the lower charmonia. In these transitions process, we predict two charmonium analogs of the charged Zb. After the observations of Zc(3900) by the BESIII and the Belle Collaborations, we reproduce the dipion and the J/ψπ invariant mass distributions simultaneously with the initial single chiral particle emission mechanism. In addition, we predict some enhancements in the J/ψK invariant mass spectra in the dikaon decay of the higher charmonium and the charmonium like states.