Study of the hidden charm <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mo>*</mml:mo></mml:msup></mml:math> interactions in chiral effective field theory

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