Different pole structures in line shapes of the

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 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 X(3872) being a bound and/or a virtual state. We also find that 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. Once the latter is restored the corrections to the pole position are non-analytic and much bigger than the $$D^{*0}$$ width itself. The X(3872) compositeness coefficient in $$D^0\bar{D}^{*0}$$ ranges from nearly 0 up to 1 in the different scenarios