From the lineshape of the $X(3872)$ to its structure

TL;DR

Analysis of the $X(3872)$ lineshape suggests it is likely a compact tetraquark rather than a loosely bound molecule, based on effective range measurements and theoretical criteria.

Contribution

The paper links lineshape analysis to the internal structure of $X(3872)$, proposing it is a tetraquark rather than a molecular state, based on effective range and Weinberg's criterion.

Findings

Negative effective range incompatible with shallow bound state

$X(3872)$ likely has a compact tetraquark structure

Supports emerging pattern for exotic mesons

Abstract

From a study of the lineshape of the $X(3872)$, the LHCb collaboration measures a sizeable negative effective range. This cannot be reconciled with a shallow $D\bar{D}^*$ bound state hypothesis. Based on Weinberg's compositeness criterion, together with a theorem by Smorodinsky, it follows that the $X$ has to have a compact hidden charm structure, most likely a tetraquark, interacting with unbound $D\bar{D}^*$ pairs via short-distance color forces. This conclusion is strengthened by the general pattern recently emerging for exotic mesons.