Four-Quark States from Functional Methods
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Gernot Eichmann · Christian S. Fischer Nico Santowsky · Paul C. Wallbott
· Walter Heupel ·
Four-Quark States from Functional Methods
Received: 30 July 2020 / Accepted: 28 September 2020 © The Author(s) 2020
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 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. Diquarkantidiquark components, on the other hand, turn out to be almost negligible for most states with the exception of open-charm heavy-light exotics.
1 Introduction One of the spectacular successes of this millennium’s hadron spectroscopy experiments is the discovery of many ’exotic’ meson states in the heavy-quark energy region that do not seem to fit into the conventional q q¯ picture, see e.g. [1–8] for recent review articles. Some of these carry net electromagnetic charge and thus ¯ q¯ (with q = u, d, s and Q = c, b). As a consequence, may be naturally explained as four-quark states Q Qq four-quark states are generally considered as promising candidates to explain the structure and properties of these exotic hadrons. On the other hand, four-quark states may also play an important role in the low-energy spectrum of QCD. The lightest multiplet of scalar mesons has been under debate for a long time. Its experimental situation G. Eichmann LIP Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisbon, Portugal E-mail: [email protected] G. Eichmann Departamento de Física, Instituto Superior Técnico, 1049-001 Lisbon, Portugal C. S. Fischer (B)· W. Heupel · N. Santowsky · P. C. Wallbott Institut für Theoretische Physik, Justus-Liebig Universität Gießen, 35392 Giessen, Germany E-mail: [email protected] C. S. Fischer Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Campus Gießen, 35392 Giessen, Germany
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Fig. 1 Dyson equation (1) and onshell Bethe–Salpeter equation (3) in graphical form
appeared questionable and its place in the Review of Particle Physics [9] has been firmly established only in this century. Since t
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