Pattern of Light Scalar Mesons

TL;DR

This paper proposes a pattern for light scalar mesons based on lattice calculations and phenomenological studies, suggesting a tetraquark nonet below 1 GeV and a $q\bar{q}$ nonet above 1 GeV, with $f_0(1710)$ as a scalar glueball.

Contribution

It combines recent lattice results and phenomenological analysis to propose a unified pattern for light scalar mesons, including their quark and glueball compositions.

Findings

Scalar mesons below 1 GeV form a tetraquark nonet.

Above 1 GeV, scalar mesons are mainly $q\bar{q}$ states with SU(3) symmetry.

$f_0(1710)$ is identified as an almost pure scalar glueball.

Abstract

Combining the recent lattice calculation of $a_0(1450)$ and $\sigma(600)$ mesons with the overlap fermion in the chiral regime with the pion mass less than $300 {\rm MeV}$, the quenched lattice calculation of the scalar glueball, and the phenomenological study of the mixing of isoscalar scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$ through their decays, a simple pattern for the light scalar mesons begins to emerge. Below 1 GeV, the scalar mesons form a nonet of tetraquark mesoniums. Above 1 GeV, the nonent $q\bar{q}$ mesons are made of an octet with largely unbroken SU(3) symmetry and a fairly good singlet which is $f_0(1370)$. $f_0(1710)$ is identified as an almost pure scalar glueball with a $\sim 10%$ mixture of $q\bar{q}$.