Lowest-lying Tetra-Quark Hadrons in Anisotropic Lattice QCD

TL;DR

This study uses anisotropic lattice QCD to investigate the lowest-lying tetraquark states, finding a scalar 4-quark state slightly below the f0(980) mass but no evidence of a localized tetraquark resonance.

Contribution

First lattice QCD analysis to identify scalar and other tetraquark states, revealing their nature as scattering states rather than localized resonances.

Findings

Scalar 4q state mass ~927 MeV, slightly below f0(980)

No evidence of tetraquark resonance in I=1 and I=2 channels

4q potential indicates a bound state that unbinds at critical separation

Abstract

We present a detailed study of lowest-lying $q^{2}\bar{q}^{2}$ hadrons in quenched improved anisotropic lattice QCD. Using the $\pi\pi$ and diquark-antidiquark local and smeared operators, we attempt to isolate the signal for $I(J^{P})=0(0^{+}), 2(0^{+})$ and $1(1^{+})$ states in two flavour QCD. In the chiral limit of light-quark mass region, the lowest scalar $4q$ state is found to have a mass, $m^{I=0}_{4q}=927(12)$ MeV, which is slightly lower than the experimentally observed $f_{0}(980)$. The results from our variational analysis do not indicate a signature of a tetraquark resonance in I=1 and I=2 channels. After the chiral extrapolation the lowest $1(1^{+})$ state is found to have a mass, $m^{I=1}_{4q}=1358(28)$ MeV. We analysed the static $4q$ potential extracted form a tetraquark Wilson loop and illustrated the behaviour of the $4q$ state as a bound state, unbinding at some critical diquark separation. From our analysis we conclude that scalar $4q$ system appears as a two-pion scattering state and that there is no spatially-localised $4q$ state in the light-quark mass region.