Four-quark states from functional methods

TL;DR

This paper reviews how functional methods like Dyson-Schwinger and Bethe-Salpeter equations are used to study four-quark states, providing insights into their internal structures without relying on model assumptions.

Contribution

It demonstrates the application of functional methods to analyze four-quark states, testing internal structure assumptions and identifying dominant clustering components in different meson sectors.

Findings

Chiral symmetry breaking influences light scalar mesons.

Heavy-light mesons show similar chiral effects.

Diquark-antidiquark components are negligible except in open-charm exotics.

Abstract

In this feature article we summarise and highlight aspects of the treatment of four-quark states with functional methods. Model approaches to those exotic mesons almost inevitably have to assume certain internal structures, e.g. by grouping quarks and antiquarks into (anti-)diquark clusters or heavy-light $q\bar{q}$ pairs. Functional methods using Dyson-Schwinger and Bethe-Salpeter equations can be formulated without such prejudice and therefore have the potential to put these assumptions to test and discriminate between such models. So far, functional methods have been used to study the light scalar-meson sector and the heavy-light sector with a pair of charmed and a pair of light quarks in different quantum number channels. For all these states, the dominant components in terms of internal two-body clustering have been identified. It turns out that chiral symmetry breaking plays an important role for the dominant clusters in the light meson sector (in particular for the scalar mesons) and that this property is carried over to the heavy-light sector. Diquark-antidiquark components, on the other hand, turn out to be almost negligible for most states with the exception of open-charm heavy-light exotics.