We study the P -wave bottom baryons using the method of QCD sum rule and heavy quark effective theory. Our results suggest that Λ b (5912) 0 and Λ b (5920) 0 can be well described by the baryon doublet [3F , 1, 1, ρ], and they belong to the SU (3)3F multiplets of J P = 1/2 − and 3/2 − . Their SU (3) flavor partners, Ξ b (1/2 − ) and Ξ b (3/2 − ), have masses 6.06 ± 0.13 GeV and 6.07 ± 0.13 GeV, respectively, with mass splitting 9 ± 4 MeV. The results obtained using baryon doublet [3F , 1, 0, λ] are similar and also consistent with the experimental data. We also study the SU (3) 6F multiplets by using the baryon multiplets [6F , 0, 1, λ], [6F , 1, 0, ρ] and [6F , 2, 1, λ], and our results suggest that the P -wave bottom baryons Σ b , Ξ ′ b and Ω b have (averaged) masses about 6.0 GeV, 6.2 GeV and 6.4 GeV, respectively.

We have used QCD sum rules to study the newly observed charged state Z c (4025) as a hidden-charm D * D * molecular state with the quantum numbers I G (J P ) = 1 + (1 + ). Using a D * D * molecular interpolating current, we have calculated the two-point correlation function and the spectral density up to dimension eight at leading order in α s . The extracted mass is m X = (4.04 ± 0.24) GeV. This result is compatible with the observed mass of Z c (4025) within the errors, which implies a possible molecule interpretation of this new resonance. We also predict the mass of the corresponding hidden-bottom B * B * molecular state: m Z b = (9.98 ± 0.21) GeV.

We study the exotic bcqq, bcss and qcqb, scsb systems by constructing the corresponding tetraquark currents with J P = 0 + and 1 + . After investigating the two-point correlation functions and the spectral densities, we perform QCD sum rule analysis and extract the masses of these open-flavor tetraquark states. Our results indicate that the masses of both the scalar and axial vector tetraquark states are about 7.1 − 7.2 GeV for the bcqq system and 7.2 − 7.3 GeV for the bcss system. For the qcqb tetraquark states with J P = 0 + and 1 + , their masses are extracted to be around 7

in a systematic way, we investigate the two-point correlation functions to extract the masses of the charmonium-like states with QCD sum rule. For the 1 −− qcqc charmonium-like state, mX = 4.6 ∼ 4.7 GeV, which implies a possible tetraquark interpretation for the state Y (4660). The masses for both the 1 ++ qcqc and scsc charmonium-like states are around 4.0 ∼ 4.2 GeV, which are slightly above the mass of X(3872). For the 1 −+ and 1 +− qcqc charmonium-like states, the extracted masses are around 4.5 ∼ 4.7 GeV and 4.0 ∼ 4.2 GeV respectively. As a byproduct, the bottomonium-like states are also studied. We also discuss the possible decay modes and experimental search of the charmonium-like states.

We have extended the calculation of the correlation functions of heavy quarkonium hybrid operators with various J P C quantum numbers to include QCD condensates up to dimension six. In contrast to previous analyses which were unable to optimize the QCD sum-rules for certain J P C , recent work has shown that inclusion of dimension six condensates stabilizes the hybrid sum-rules and permits reliable mass predictions. In this work we have investigated the effects of the dimension six condensates on the remaining channels. After performing the QCD sum-rule analysis, we update the mass spectra of charmonium and bottomonium hybrids with exotic and non-exotic quantum numbers. We identify that the negative-parity states with J P C = (0, 1, 2) −+ , 1 −− form the lightest hybrid supermultiplet while the positive-parity states with J P C = (0, 1) +− , (0, 1, 2) ++ belong to a heavier hybrid supermultiplet, confirming the supermultiplet structure found in other approaches. The hybrid with J P C = 0 −− has a much higher mass which may suggest a different excitation of the gluonic field compared to other channels. In agreement with previous results, we find that the J P C = 1 ++ charmonium hybrid is substantially heavier than the X(3872), which seems to preclude a pure charmonium hybrid interpretation for this state.