Implication of a negative effective range on the $D\bar{D}^*$ interaction and the nature of $X(3872)$

TL;DR

This paper shows that a negative effective range for the $X(3872)$ does not rule out its interpretation as a $D\bar{D}^*$ molecular state, using an effective field theory approach to match experimental data.

Contribution

It explicitly demonstrates that the negative effective range is compatible with the molecular picture of $X(3872)$ through an effective field theory model.

Findings

Negative effective range does not contradict the molecular interpretation.

The model reproduces the binding energy and effective range of $X(3872)$.

Implications for understanding hadronic molecules and their binding mechanisms.

Abstract

A recent analysis of the LHCb data [Phys. Rev. D 105 (2022) 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 $D\bar{D}^*$ 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 $D\bar{D}^*$ 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 $D\bar{D}^*$ interaction. Such results are relevant for a better understanding of hadronic molecules and their binding mechanism.