We apply the method of QCD sum rules to study the structure X newly observed by the BESIII Collaboration in the φη mass spectrum in 2.0-2.1 GeV region in the J/ψ → φηη decay. We construct all the ssss tetraquark currents with J PC = 1 +− , and use them to perform QCD sum rule analyses. One current leads to reliable QCD sum rule results and the mass is extracted to be 2.00 +0.10 −0.09 GeV, suggesting that the structure X can be interpreted as an ssss tetraquark state with J PC = 1 +−. The Y (2175) can be interpreted as its ssss partner having J PC = 1 −− , and we propose to search for the other two partners, the ssss tetraquark states with J PC = 1 ++ and 1 −+ , in the η f 0 (980), η KK , and η KK * mass spectra.

We use the method of light-cone sum rules to study S-wave decays of the SU (3) flavor 6F P -wave heavy baryons into ground-state heavy baryons accompanied by vector mesons ρ and K * . In Ref. [1] we have studied their mass spectrum and pionic decays, and found that the Σ b (6097) ± and Ξ b (6227) − can be well interpreted as P -wave bottom baryons of J P = 3/2 − . In this paper we further studied their decays accompanied by vector mesons, and we propose to search for a new state Ξ b (5/2 − ), that is thebaryons into ground-state heavy baryons accompanied by a vector meson (ρ or K * ). We shall further apply the obtained results to investigate the Σ b (6097) ± and Ξ b (6227) − [7,8]. Our sum rule results obtained in Ref. [1] suggest that they can be well interpreted as P -wave bottom baryons of J P = 3/2 − . This conclusion is supported by Refs. [61-67], and we refer to for more discussions. Our results also suggest that they belong to the bottom baryon doublet [6 F , 2, 1, λ] (its definition will be given below), which contains altogether six bottom baryons,We predicted the mass and decay width of the Ω b (3/2 − ) state to beand masses of the three J P = 5/2 − states to be

Some errors have been detected when studying P-wave bottom baryons of the SUð3Þ flavor 6 F with the spin-parity quantum number J P ¼ 5=2 −. We present the correct results below. To do this, we need the full expression of the J ¼ 5=2 propagator [1]: Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published articles title, journal citation, and DOI.

The heavy baryon system bounded by the strong interaction has a rich internal structure, so its mass spectra can have the fine structure similar to the line spectra of atom bounded by the electromagnetic interaction. We systematically study the internal structure of P-wave Ω b baryons and calculate their D-wave decay properties. The present study, together with our previous studies on their mass spectra and S-wave decay properties, suggest that all the four excited Ω b baryons recently discovered by LHCb can be well explained as P-wave Ω b baryons, and their beautiful fine structure is directly related to the rich internal structure of P-wave Ω b baryons.