Scalar and Vector 4Q Systems in Anisotropic Lattice QCD

TL;DR

This study investigates scalar and vector four-quark states in anisotropic lattice QCD, finding evidence for a scalar 4q state near 980 MeV and no indication of localized tetraquark resonances in other channels.

Contribution

It provides the first detailed lattice QCD analysis of four-quark states using improved anisotropic lattices and variational methods, clarifying their nature as scattering states or bound states.

Findings

Scalar 4q state mass around 927 MeV, close to f0(980)

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

4q potential analysis shows unbinding at critical separation

Abstract

We present a detailed study of some $4q$ 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.