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

Abstract

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 D0D¯ ∗ 0S-wave. In terms of it we analyze the CDF data on inclusive pp¯ scattering to J/ ψπ+π-, and the Belle and BaBar data on B decays to KJ/ψπ+π- and KDD¯ ∗ 0 around the D0D¯ ∗ 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 D0D¯ ∗ 0 ranges from nearly 0 up to 1 in the different scenarios.