Why static bound-state calculations of tetraquarks should be met with scepticism

TL;DR

Static bound-state calculations of tetraquarks are unreliable and often misleading, as they ignore important dynamical effects and coupling to two-meson states, casting doubt on the existence of these states.

Contribution

This paper critically examines the validity of static bound-state models for tetraquarks, emphasizing the need to consider dynamical effects and unitarity.

Findings

Static models ignore coupling to two-meson states

Predicted tetraquark masses are highly unreliable

Many claimed tetraquark states lack solid theoretical support

Abstract

Recent experimental signals have led to a revival of tetraquarks, the hypothetical $q^2\bar{q}^2$ hadronic states proposed by Jaffe in 1976 to explain the light scalar mesons. Mesonic structures with exotic quantum numbers have indeed been observed recently, though a controversy persists whether these are true resonances and not merely kinematical threshold enhancements, or otherwise states not of a true $q^2\bar{q}^2$ nature. Moreover, puzzling non-exotic mesons are also often claimed to have a tetraquark configuration. However, the corresponding model calculations are practically always carried out in pure and static bound-state approaches, ignoring completely the coupling to asymptotic two-meson states and unitarity, especially the dynamical effects thereof. In this short paper we argue that such static predictions of real tetraquark masses are highly unreliable and provide little evidence of the very existence of such states.