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

Abstract

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.

An updated review of the new hadron states

“…Interested readers may consult Refs. [132,133,134,135,136,137,138,139,140,141,142,143,144,145] for systematical QCD sum rule studies on the light tetraquark and sexaquark/dibaryon currents.…”

Tetraquark-Adequate QCD Sum Rules

“…(It goes without saying that each such type of constraint may merely serve as a necessary but not sufficient condition for the factual participation of a given tetraquark state in any physical process under study.) Among others, this tool can then be used to confirm that the decay widths of any tetraquark states should be expected to be parametrically narrower than those of ordinary (quark-antiquark) mesons, or to point out directions towards a more adequate description of tetraquark mesons, by means of suitably adapted QCD sum rules, and has yet to be utilized in multiquark studies [28][29][30][31][32][33][34][35].…”

Measurement of e+e− → ωπ+π− cross section at $$ \sqrt{s} $$ = 2.000 to 3.080 GeV

“…This structure may correspond to φ(2170), ω (2205), ω(2290), and ω(2330), whose properties are poorly known in the particle data group (PDG) [20]. Many interpretations have been proposed for φ(2170), including a traditional ss state [21][22][23][24][25][26], an ssg hybrid [27,28], an sss d tetraquark state [29][30][31][32][33][34][35][36], a Λ Λ bound state [37][38][39][40][41], and an ordinary resonant state of φf 0 (980) produced by the interactions between the final state particles [42,43]. Recently, the φ(2170) state was examined through the BESIII experiment in the processes of e + e − → K + K − [44], K + K − π 0 π 0 [45], φη [46], ωη [47], K 0 S K 0 L [48], φη [49], and 2(K + K − ), φK + K − [50].…”