Different pole structures in line shapes of the $X(3872)$

Understand

We introduce a near-threshold parameterization that is more general than the effective-range expansion up to and including the effective-range because it can also handle with a near-threshold zero in the $D^0\bar{D}^{*0}$ $S$-wave.

• In terms of it we analyze 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.
• It is shown that data can be reproduced with similar quality for the $X(3872)$ being a bound {\it and/or} a virtual state.
• We also find that the $X(3872)$ might be a higher-order virtual-state pole (double or triplet pole), in the limit in which the small $D^{*0}$ width vanishes.