Tetraquark bound states in a Bethe-Salpeter approach

TL;DR

This paper calculates tetraquark masses using a Bethe-Salpeter approach with a coupled two-body system, supporting the meson molecule picture for light states and predicting a narrow all-charm tetraquark.

Contribution

It introduces a novel coupled two-body Bethe-Salpeter framework for tetraquark mass calculations based on quark and gluon substructure.

Findings

Light scalar tetraquark mass around 400 MeV

Wave function dominated by pion-pion constituents

Potential narrow all-charm tetraquark in 5-6 GeV range

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 f_0(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5-6 GeV.