Implication of a negative effective range on the D D ¯ ∗ interaction and the nature of X (3872)

A recent analysis of the LHCb data [Esposito et al., Phys. Rev. D 105 L031503 (2022)PRVDAQ2470-001010.1103/PhysRevD.105.L031503] obtained a sizable negative effective range for the X(3872). This has attracted intensive discussions on whether X(3872) can be deemed as a DD¯∗ molecular state. This work explicitly demonstrates that the negative effective range of the X(3872) does not contradict the molecular picture, adopting an effective field theory formulation of the DD¯∗ interaction that can simultaneously reproduce the binding energy and effective range of the X(3872). We elaborate on the implications of the large negative effective range of X(3872) and the small binding energy on the underlying DD¯∗ interaction. Such results are relevant for a better understanding of hadronic molecules and their binding mechanism.