Molecular states from $$D^{(*)}{\bar{D}}^{(*)}/B^{(*)}{\bar{B}}^{(*)}$$ D ( ∗ ) D ¯ ( ∗ ) / B ( ∗ ) B ¯ ( ∗ ) and $$D^{(*)}D^{(*)}/{\bar{B}}^{(*)}{\bar{B}}^{(*)}$$ D ( ∗ ) D ( ∗ ) / B ¯ ( ∗ ) B ¯ ( ∗ ) interactions

In this work, we preform a systematic investigation about hidden heavy and doubly heavy molecular states from the $$D^{(*)}{\bar{D}}^{(*)}/B^{(*)}{\bar{B}}^{(*)}$$ and $$D^{(*)}D^{(*)}/{\bar{B}}^{(*)}{\bar{B}}^{(*)}$$ interactions in the quasipotential Bethe–Salpeter equation (qBSE) approach. With the help of Lagrangians with heavy quark and chiral symmetries, interaction potentials are constructed within the one-boson-exchange model in which we include the $$\pi $$ , $$\eta $$ , $$\rho $$ , $$\omega $$ and $$\sigma $$ exchanges, as well as $$J/\psi $$ or $$\varUpsilon $$ exchange. Possible bound states from the interactions considered are searched for as the pole of scattering amplitude. The results suggest that experimentally observed states, $$Z_c(3900)$$ , $$Z_c(4020)$$ , $$Z_b(10610)$$ , and $$Z_b(10650)$$ , can be related to the $$D{\bar{D}}^{*}$$ , $$D^*{\bar{D}}^{*}$$ , $$B{\bar{B}}^{*}$$ , and $$B^*{\bar{B}}^{*}$$ interactions with quantum numbers $$I^G(J^P)=1^+(1^{+})$$ , respectively. The $$D{\bar{D}}^{*}$$ interaction is also attractive enough to produce a pole with $$0^+(0^+)$$ which is related to the X(3872). Within the same theoretical frame, the existence of $$D{\bar{D}}$$ and $$B{\bar{B}}$$ molecular states with $$0(0^+)$$ are predicted. The possible $$D^*{\bar{D}}^*$$ molecular states with $$0(0^+, 1^+, 2^+)$$ and $$1(0^+)$$ and their bottom partners are also suggested by the calculation. In the doubly heavy sector, no bound state is produced from the $$DD/{\bar{B}}{\bar{B}}$$ interaction while a bound state is found with $$0(1^+)$$ from $$DD^*/{\bar{B}}{\bar{B}}^*$$ interaction. The $$D^*D^*/{\bar{B}}^*{\bar{B}}^*$$ interaction produces three molecular states with $$0(1^+)$$ , $$0(2^+)$$ and $$1(2^+)$$ .