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We present a numerical solution of the four-quark Bethe–Salpeter equation for ground-state scalar tetraquarks with J P C = 0 + + . We find that the four-body equation dynamically generates pseudoscalar-meson poles in the Bethe–Salpeter amplitude. The resulting tetraquarks are genuine four-quark states that are dominated by pseudoscalar meson–meson correlations. Diquark–antidiquark contributions are subleading because of their larger mass scale. In the light quark sector, the sensitivity of the tetraquark wave function to the pion poles leads to an isoscalar tetraquark mass M σ ∼ 350 MeV which is comparable to that of the σ / f 0 ( 500 ) . The masses of its multiplet partners κ and a 0 / f 0 follow a similar pattern. This provides support for a tetraquark interpretation of the light scalar meson nonet in terms of ‘meson molecules’. [ABSTRACT FROM AUTHOR]

Abstract: We determine the mass of tetraquark bound states from a coupled system of covariant Bethe–Salpeter equations. Similar in spirit to the quark–diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark–gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion–pion constituents. Both results are in agreement with a meson molecule picture for the . Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5–6 GeV. [Copyright &y& Elsevier]

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. 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. [ABSTRACT FROM AUTHOR]

We present results for single pseudoscalar meson pole contributions and pion box contributions to the hadronic light-by-light (LBL) correction of the muon's anomalous magnetic moment. We follow the recently developed dispersive approach to LBL, where these contributions are evaluated with intermediate mesons on-shell. However, the space-like electromagnetic and transition form factors are not determined from analytic continuation of time-like data, but directly calculated within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. This strategy allows for a systematic comparison with a strictly dispersive treatment and also with recent results from lattice QCD. Within error bars, we obtain excellent agreement for the pion electromagnetic and transition form factor and the resulting contributions to LBL. In addition, we present results for the η and η ′ pole contributions and discuss the dynamical effects in the η − η ′ mixing due to the strange quarks. Our result for the total pseudoscalar pole contributions is a μ PS-pole = 91.6 (1.9) × 10 − 11 and for the pion-box contribution we obtain a μ π − box = − 16.6 (1) (7) × 10 − 11. [ABSTRACT FROM AUTHOR]