Possible assignments of the X(3872), Zc(3900), and Zb(10610) as axial-vector molecular states

In this article, we construct both the color singlet-singlet type and the octet-octet type currents to interpolate X(3872), Z(c)(3900), and Z(b)(10610), and we calculate the vacuum condensates up to dimension-10 in the operator product expansion. Then we study the axial-vector hidden charm and hidden bottom molecular states with the QCD sum rules, explore the energy-scale dependence of the QCD sum rules for the heavy molecular states in details, and we use the formula root M-X/Y/Z(2) - (2M(Q))(2) with the effective masses M-Q to determine the energy scales. The numerical results support assigning X(3872), Z(c)(3900), and Z(b)(10610) as the color singlet-singlet type molecular states with J(PC) = 1(++), 1(+-), 1(+-), respectively, more theoretical and experimental work is still needed to distinguish the molecule and tetraquark assignments; while there are no candidates for the color octet-octet type molecular states.