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Using the pictures for \(X(3872)\) as a mixture of charmonium and molecular \(D^{*0}D^0\) states; \(Y(3940)\) as a mixture of \(\chi _{c0}\) and \(D^*D^{\prime *}\) states, and \(Y(4260)\) as a mixture of the tetra-quark state with charmonium states, the corresponding mixing angles are estimated within the QCD sum rules. We find that our predictions for the mixing angles of the \(X(3872)\), \(Y(4260)\), and \(Y(3940)\) states are considerably smaller compared to work in which the mixing angles are estimated from the condition in reproducing the mass of these states. Our conclusion is that the considered pictures for the \(X(3872)\), \(Y(4260)\), and \(Y(3940)\) states are not successful in describing these states.

Determination of the mixing angle between new charmonium states