Résumé
We review our results in Refs. [R. Albuquerque, S. Narison, D. Rabetiarivony and G. Randriamanatrika, Int. J. Mod. Phys. A33 (2018), 1850082; R. Albuquerque, S. Narison, F. Fanomezana, A. Rabemananjara, D. Rabetiarivony and G. Randriamanatrika, Int. J. Mod. Phys. A31 (2016) no. 36, 1650196.] for the masses and couplings of heavy-light D‾D(B‾B) -like molecules and (Qq‾)(Qq) -like four-quark states from relativistic QCD Laplace sum rules (LSR) where next-to-next-to-leading order (N2LO) PT corrections in the chiral limit, next-to-leading order (NLO) SU3 PT corrections and non-perturbative contributions up to dimension d = 6–8 are included. The factorization properties of molecule and four-quark currents have been used for the estimate of the higher order PT corrections. New integrated compact expressions of the spectral functions at leading order (LO) of perturbative QCD and up to dimensions d ≤ (6–8) non-perturbative condensates are presented. The results are summarized in Tables 5 to 10, from which we conclude, within the errors, that the observed XZ states are good candidates for being 1 ++ and 0 ++ molecules or/and four-quark states, contrary to the observed Y states which are too light compared to the predicted 1 −± and 0 −± states. We find that the SU3 breakings are relatively small for the masses (≤ 10 (resp. 3) %) for the charm (resp. bottom) channels while they are large (≤ 20 %) for the couplings which decrease faster ( 1/mb3/2 ) than 1/mb1/2 clearly separate (within the errors) molecules from four-quark states having the same quantum numbers. Results for the B‾K(D‾K) -like molecules and (Qq‾)(us) -like four-quark states from [R. Albuquerque, S. Narison, A. Rabemananjara and D. Rabetiarivony, Int. J. Mod. Phys. A31 (2016) no. 17, 1650093.] are also reviewed which do not favour the molecule or/and four-quark interpretation of the X (5568). We suggest to scan the charm (2327 ∼ 2444) MeV and bottom (5173 ∼ 5226) MeV regions for detecting the (unmixed) (cu‾)ds and (bu‾)ds via eventually their radiative or π +hadrons decays and reconsider more carefully the properties of the eventual Ds0⁎(2317) candidate. We expect that future experimental data and lattice results will check our predictions.