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

AbstractIn this work, we preform a systematic investigation about hidden heavy and doubly heavy molecular states from the $$D^{(*)}{\bar{D}}^{(*)}/B^{(*)}{\bar{B}}^{(*)}$$ D ( ∗ ) D ¯ ( ∗ ) / B ( ∗ ) B ¯ ( ∗ ) and $$D^{(*)}D^{(*)}/{\bar{B}}^{(*)}{\bar{B}}^{(*)}$$ D ( ∗ ) D ( ∗ ) / B ¯ ( ∗ ) 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 $$\pi $$ π , $$\eta $$ η , $$\rho $$ ρ , $$\omega $$ ω and $$\sigma $$ σ exchanges, as well as $$J/\psi $$ J / ψ or $$\varUpsilon $$ Υ 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 ( 3900 ) , $$Z_c(4020)$$ Z c ( 4020 ) , $$Z_b(10610)$$ Z b ( 10610 ) , and $$Z_b(10650)$$ Z b ( 10650 ) , can be related to the $$D{\bar{D}}^{*}$$ D D ¯ ∗ , $$D^*{\bar{D}}^{*}$$ D ∗ D ¯ ∗ , $$B{\bar{B}}^{*}$$ B B ¯ ∗ , and $$B^*{\bar{B}}^{*}$$ B ∗ B ¯ ∗ interactions with quantum numbers $$I^G(J^P)=1^+(1^{+})$$ I G ( J P ) = 1 + ( 1 + ) , respectively. The $$D{\bar{D}}^{*}$$ D D ¯ ∗ interaction is also attractive enough to produce a pole with $$0^+(0^+)$$ 0 + ( 0 + ) which is related to the X(3872). Within the same theoretical frame, the existence of $$D{\bar{D}}$$ D D ¯ and $$B{\bar{B}}$$ B B ¯ molecular states with $$0(0^+)$$ 0 ( 0 + ) are predicted. The possible $$D^*{\bar{D}}^*$$ D ∗ D ¯ ∗ molecular states with $$0(0^+, 1^+, 2^+)$$ 0 ( 0 + , 1 + , 2 + ) and $$1(0^+)$$ 1 ( 0 + ) and their bottom partners are also suggested by the calculation. In the doubly heavy sector, no bound state is produced from the $$DD/{\bar{B}}{\bar{B}}$$ D D / B ¯ B ¯ interaction while a bound state is found with $$0(1^+)$$ 0 ( 1 + ) from $$DD^*/{\bar{B}}{\bar{B}}^*$$ D D ∗ / B ¯ B ¯ ∗ interaction. The $$D^*D^*/{\bar{B}}^*{\bar{B}}^*$$ D ∗ D ∗ / B ¯ ∗ B ¯ ∗ interaction produces three molecular states with $$0(1^+)$$ 0 ( 1 + ) , $$0(2^+)$$ 0 ( 2 + ) and $$1(2^+)$$ 1 ( 2 + ) .