The $$\pi f_0(500)$$ decay of the $$a_1(1260)$$

We evaluate the $$a_1(1260) \rightarrow \pi \sigma (f_0(500))$$ a 1 ( 1260 ) → π σ ( f 0 ( 500 ) ) decay width from the perspective that the $$a_1(1260)$$ a 1 ( 1260 ) resonance is dynamically generated from the pseudoscalar–vector interaction and the $$\sigma $$ σ arises from the pseudoscalar–pseudoscalar interaction. A triangle mechanism with $$a_1(1260) \rightarrow \rho \pi $$ a 1 ( 1260 ) → ρ π followed by $$\rho \rightarrow \pi \pi $$ ρ → π π and a fusion of two pions within the loop to produce the $$\sigma $$ σ provides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of 13–22 MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the $$\pi \sigma $$ π σ channel in recent lattice QCD calculations of the $$a_1$$ a 1 .

Beam Asymmetries from Light Scalar Meson Production on the Proton at GlueX

The GlueX facility, featuring a linearly polarised 9 GeV real photon beam delivered to a large-acceptance detector system, has recently completed its first phase of running, and analysis efforts of this dataset are well underway. It has been suggested that at GlueX energies, quark systems beyond the three quark and quark-antiquark systems of baryons and mesons, such as hybrid mesons, tetraquarks and glueballs, should exist, and studies of these systems could shed new light on how quarks combine under the strong force, particularly the role played by gluons. Meticulous study of the spectrum of hadronic states is required to understand the strong force in the non-perturbative energy regime, and the light scalar meson sector is an area that remains poorly understood. GlueX data encompasses final states at energies where photoproduction of the a0 (980) and f 0 (980) mesons can provide discriminatory evidence between various models, manifested in experimental observables such as the cross section and beam asymmetry, and performing detailed measurements of these quantities is considered a priority of the ongoing research program. The work presented showcases efforts to measure the beam asymmetry of the reaction γp→pηπ whose mass spectrum encompasses several mesons, including the a 0(980) light scalar, and the a 2(1320) tensor. Future prospects for related analyses in the light scalar meson sector, informed by this measurement, will also be discussed.

Four-Quark States from Functional Methods

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 $$q{\bar{q}}$$ 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.

Inverse mass hierarchy of light scalar mesons driven by anomaly-induced flavor breaking

We propose a novel mechanism to reproduce the observed mass hierarchy for scalar mesons lighter than 1 GeV (called the inverse hierarchy), regarding them as mesons made of a quark and an anti-quark ($q\bar{q}$ mesons). The source is provided by the SU(3) flavor-symmetry breaking induced by the U(1) axial anomaly. In particular, the anomaly term including the explicit chiral symmetry breaking plays a significant role in the light scalar meson spectrum. To be concrete, we construct a linear sigma model for scalar mesons of $q\bar{q}$ type together with their pseudoscalar chiral partners, including an anomaly-induced explicit chiral symmetry-breaking term. We find that, due to the proposed mechanism, the inverse hierarchy, i.e., $m\left[ a_0 (980) \right] \simeq m\left[ f_0 (980) \right] > m \left[ K_0^\ast (700) \right] > m \left[ f_0(500) \right]$, is indeed realized. Consequently, the quark content of $f_0 (500)$ is dominated by the isoscalar $\bar uu+ \bar dd$ component, and $f_0 (980)$ by the strange quark bilinear one, $s\bar{s}$.