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

TL;DR

This paper introduces a generalized near-threshold parameterization to analyze the $X(3872)$ line shape, revealing it can be a bound, virtual, or higher-order virtual state, with implications for its compositeness.

Contribution

It develops a more general parameterization for near-threshold states and applies it to $X(3872)$ data, exploring various pole structures and their effects on the state’s nature.

Findings

Data can be fitted with $X(3872)$ as bound or virtual state.

$X(3872)$ may be a higher-order virtual-state pole.

The compositeness coefficient varies from nearly 0 to 1.

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 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. 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.