In 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
+
)
.