Nature of $X(3872)$ from the line shape

Using a general parameterization of two-body scattering amplitude, we systematically analyze the corresponding data on $X(3872)$, more explicitly, the CDF data on inclusive $p\bar{p}$ scattering to $J/\psi \pi^+\pi^-$, and the Belle and BaBar data on $B$ decays to $K\, J/\psi \pi^+\pi^-$ and $K D\bar{D}^{*0}$ around the $D^0\bar{D}^{*0}$ threshold. We achieve a good reproduction of data and find that the $X(3872)$ can be interpreted as a bound and/or virtual state, or even higher-order (double or triple) virtual sate pole. The latter point was not realized previously in the literature. % The latter point has not been realized in other literatures. As a result, the compositeness of the $X(3872)$ can vary largely from nearly 0 to 1. More higher-precision data is needed to discriminate its pole structure and nature.