Possible $$D^{(*)}\bar{D}^{(*)}$$ D ( ∗ ) D ¯ ( ∗ ) and $$B^{(*)}\bar{B}^{(*)}$$ B ( ∗ ) B ¯ ( ∗ ) molecular states in the extended constituent quark models

Abstract The possible neutral $$D^{(*)}\bar{D}^{(*)}$$ D ( ∗ ) D ¯ ( ∗ ) and $$B^{(*)}\bar{B}^{(*)}$$ 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 $$D^{(*)}\bar{D}^{(*)}$$ D ( ∗ ) D ¯ ( ∗ ) with $$J^{PC}=1^{++},2^{++}$$ J P C = 1 + + , 2 + + and $$B^{(*)}\bar{B}^{(*)}$$ B ( ∗ ) B ¯ ( ∗ ) with $$J^{PC}=0^{++},1^{+-},1^{++},2^{++}$$ J P C = 0 + + , 1 + - , 1 + + , 2 + + are obtained. The molecular states $$D^{*}\bar{D}$$ D ∗ D ¯ with $$J^{PC}=1^{++}$$ J P C = 1 + + and $$B^{*}\bar{B}$$ B ∗ B ¯ with $$J^{PC}=1^{+-}$$ J P C = 1 + - are good candidates for X(3872) and $$Z^0_b(10610)$$ Z b 0 ( 10610 ) , respectively. The dependence of the results on the model parameters is also discussed.