In the framework of QCD sum rules, we investigate the $q{q}^{\prime }\overline{Q}\overline{Q}$ tetraquark structure with quantum number $J^P=1^{+}$, which is embedded in two types of configurations, the $[8_c{]}_{q\overline{Q}}\otimes [8_c{]}_{q^{\prime }\overline{Q}}$ and $[1_c{]}_{q\overline{Q}}\otimes [1_c{]}_{q^{\prime }\overline{Q}}$ with $Q=b$, $c$, $q=u$, and $q^{\prime }=d$, $s$. Our finding confirms the lattice QCD result that the bottom tetraquark states could exist and their masses are evaluated. In the calculation, the nonperturbative condensate contributions up to dimension eight in operator product expansion are considered, and those terms linear to the strange quark mass $m_s$ are kept. It is found that for octet-octet configuration the masses of potential tetraquark states are about 11.28 GeV for the $ud\overline{b}\overline{b}$ system, and 11.36 and 11.39 GeV for the $us\overline{b}\overline{b}$ system, which are above the corresponding two-meson thresholds. For molecular configuration, the corresponding masses are found below the thresholds, that is, 10.36 GeV and 10.51 GeV, respectively. The possible tetraquark decay channels are analyzed and the strong decay rates are evaluated. The mass dependence on the radiative correction and the condensates is estimated. Moreover, the doubly charmed tetraquark states are also considered.

In this paper, we study the $B_c$-meson exclusive decays to S-wave charmonia and light pseudoscalar or vector mesons, i.e., $\pi$, $K$, $\rho$, and $K^{*}$ at the next-to-leading order (NLO) in the QCD coupling. The nonfactorizable contribution is included, which is absent in traditional naive factorization. Numerical results show that NLO QCD corrections markedly enhance the branching ratio with a $K$ factor of 1.75 for $B_c^{\pm }\to {\eta }_c{\pi }^{\pm }$ and 1.31 for $B_c^{\pm }\to J/\psi {\pi }^{\pm }$ using certain input parameters. And the theoretical uncertainties for their branching ratios are reduced compared with that of direct tree-level calculation. In order to investigate the asymptotic behavior, the analytic form is obtained in the heavy quark limit, i.e., $m_b\to \infty$. We note that annihilation topologies contribute trivia in this limit, and the corrections at leading order in $z=m_c/m_b$ expansion come from form factors and hard spectator interactions. At last, some related phenomenologies are also discussed.

Very recently, the LHCb Collaboration observed distinct structures with the $$cc{\bar{c}}{\bar{c}}$$c c c ¯ c ¯ in the $$J/\Psi $$J / Ψ -pair mass spectrum. In this work, we construct four scalar ( $$J^{PC} = 0^{++}$$J PC = 0 + + ) $$[8_c]_{Q\bar{Q^\prime }}\otimes [8_c]_{Q^\prime {\bar{Q}}}$$[ 8 c ] Q Q ′ ¯ ⊗ [ 8 c ] Q ′ Q ¯ type currents to investigate the fully-heavy tetraquark state $$Q Q^\prime {\bar{Q}} \bar{Q^\prime }$$Q Q ′ Q ¯ Q ′ ¯ in the framework of QCD sum rules, where $$Q=c, b$$Q = c , b and $$Q^\prime = c, b$$Q ′ = c , b . Our results suggest that the broad structure around 6.2-6.8 GeV can be interpreted as the $$0^{++}$$0 + + octet–octet tetraquark states with masses $$6.44\pm 0.11$$6.44 ± 0.11 GeV and $$6.52\pm 0.10$$6.52 ± 0.10 GeV, and the narrow structure around 6.9 GeV can be interpreted as the $$0^{++}$$0 + + octet–octet tetraquark states with masses $$6.87\pm 0.11$$6.87 ± 0.11 GeV and $$6.96\pm 0.11$$6.96 ± 0.11 GeV, respectively. Extending to the b-quark sector,the masses of their fully-bottom partners are found to be around 18.38-18.59 GeV. Additionally, we also analyze the spectra of the $$[8_c]_{c{\bar{c}}}\otimes [8_c]_{b {\bar{b}}}$$[ 8 c ] c c ¯ ⊗ [ 8 c ] b b ¯ and $$[8_c]_{c{\bar{b}}}\otimes [8_c]_{b {\bar{c}}}$$[ 8 c ] c b ¯ ⊗ [ 8 c ] b c ¯ tetraquark states, which lie in the range of 12.51–12.74 GeV and 12.49–12.81 GeV, respectively.

In this perspective, we outline that a space borne gravitational wave detector network combining LISA and Taiji can be used to measure the Hubble constant with an uncertainty less than 0.5% in ten years, compared with the network of the ground based gravitational wave detectors which can measure the Hubble constant within a 2% uncertainty in the next five years by the standard siren method. Taiji is a Chinese space borne gravitational wave detection mission planned for launch in the early 2030 s. The pilot satellite mission Taiji-1 has been launched in August 2019 to verify the feasibility of Taiji. The results of a few technologies tested on Taiji-1 are presented in this paper.

By using QCD Sum Rules, we found that the charged hidden charm tetraquark \([c u][\bar{c} \bar{d}]\) states with \( J^P = 1^-\) and \( 2^+\) , which are possible quantum numbers of the newly observed charmonium-like resonance \(Z_c(4025)\) , have masses of \(m_{1^-}^c = (4.54 \pm 0.20) \, \text {GeV}\) and \(m_{2^+}^c = (4.04 \pm 0.19) \, \text {GeV}\) . The contributions up to dimension eight in the operator product expansion were taken into account in the calculation. The tetraquark mass of \(J^{P} \,{=}\, 2^{+}\) state was consistent with the experimental data of \(Z_c(4025)\) , suggesting the \(Z_c(4025)\) state to possess the quantum number of \(J^P \,{=}\, 2^+\) . Extending to the b-quark sector, the corresponding tetraquark masses \(m_{1^-}^b = (10.97 \pm 0.25) \, \text {GeV}\) and \(m_{2^+}^b = (10.35 \pm 0.25) \, \text {GeV}\) were obtained, which values are testable in future B-factories.

Recently, a hadronic state named ${\eta }_1(1855)$, about 1.86 GeV, was observed in the BESIII experiment. This finding has a peculiar interest due to its exotic quantum number $J^{\mathrm{PC}}=1^{-+}$. In this paper, we examine the tetraquark interpretation for the structure of ${\eta }_1(1855)$ in the configurations of $[1_c{]}_{\overline{s}s}\otimes [1_c{]}_{\overline{q}q}$ and $[1_c{]}_{\overline{s}q}\otimes [1_c{]}_{\overline{s}q}$, and perform a mass spectrum calculation in the framework of QCD sum rules. The results show that the observed ${\eta }_1(1855)$ could be embedded into the $[1_c{]}_{\overline{s}s}\otimes [1_c{]}_{\overline{q}q}$ configuration. The possible tetraquark and hybrid decay modes are analyzed, which are critical in decoding its inner structure. In the same way, we evaluate as well the $\overline{s}s\overline{s}s$ molecular state with $1^{-+}$ quantum number and find that there might exist two such ground states.