Possible D ( ∗ ) ¯ D ( ∗ ) and B ( ∗ ) ¯ B ( ∗ ) molecular states in the extended constituent quark models

The possible neutral D ( ∗ ) ¯ D ( ∗ ) and B ( ∗ ) ¯ B ( ∗ ) molecular states are studied in the framework of the constituent quark models, which is extended by including the s channel one-gluon exchange. Using different types of quark– quark potentials, we solve the four-body Schrödinger equation by means of the Gaussian expansion method. The bound states of D ( ∗ ) ¯ D ( ∗ ) with J PC = 1 ++ , 2 ++ and B ( ∗ ) ¯ B ( ∗ ) with J PC = 0 ++ , 1 +− , 1 ++ , 2 ++ are obtained. The molecular states D ∗ ¯ D with J PC = 1 ++ and B ∗ ¯ B with J PC = 1 +− are good candidates for X ( 3872 ) and Z 0 b ( 10610 ) , respectively. The dependence of the results on the model parameters is also discussed.