Study of the hidden charm $D\bar{D}^*$ interactions in chiral effective field theory

TL;DR

This paper investigates the interactions of hidden charm $Dar{D}^*$ mesons using chiral effective field theory, revealing potential molecular states including the $X(3872)$ and predicting new structures near the $Dar{D}^*$ threshold.

Contribution

It constructs chiral Lagrangians incorporating symmetries and calculates interaction potentials up to second order, providing insights into the molecular nature of certain charmonium-like states.

Findings

Identifies a hierarchy of interaction strengths among channels.

Supports $X(3872)$ as a $0^+(1^{++})$ molecular state.

Predicts additional molecular states near the $Dar{D}^*$ threshold.

Abstract

We study the chiral interactions of the hidden charm $D\bar{D}^*$ system within chiral effective field theory. Chiral Lagrangians are constructed by incorporating the chiral symmetry, heavy quark symmetry as well as proper charge conjugation properties of the heavy mesons. The interacting potentials of the $S$-wave $D\bar{D}^*$ are calculated up to second chiral order at 1-loop level, where complete two-pion exchange interactions are included. We further investigate the behaviors of the potentials in coordinate space, as well as their bound state properties. Our studies indicate that there exists a interacting strength ordering among considered four channels: $\text{str.}[0^+(1^{++})]>\text{str.}[0^-(1^{+-})] > \text{str.}[1^+(1^{+-})] > \text{str.}[1^-(1^{++})]$ where str. stands for the strength of the $D\bar{D}^*$ interaction. Moreover, we find that $X(3872)$ can be treated as a good candidate of $0^+(1^{++})$ molecular state. There also tends to form $0^-(1^{+-})$ and $1^+(1^{+-})$ molecular states and we expect the experiments to search for the predicted multi-structures around the $D\bar{D}^*$ mass region.