The light scalar mesons as tetraquarks

TL;DR

This paper numerically solves the four-quark Bethe-Salpeter equation to explore the nature of light scalar mesons, suggesting they are predominantly tetraquark states with meson-meson correlations.

Contribution

It provides a dynamical calculation showing that light scalar mesons can be understood as tetraquarks dominated by pseudoscalar meson-meson interactions.

Findings

The sigma/f0(500) mass is around 350 MeV.

Tetraquarks are dominated by meson-meson correlations.

Supports a tetraquark or meson-molecule interpretation of light scalar mesons.

Abstract

We present a numerical solution of the four-quark Bethe-Salpeter equation for ground-state scalar tetraquarks with J^PC = 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_sigma ~ 350 MeV which is comparable to that of the sigma/f0(500). The masses of its multiplet partners kappa and a0/f0 follow a similar pattern. This provides support for a tetraquark interpretation of the light scalar meson nonet in terms of 'meson molecules'.