# 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.

## Key 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.