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.
Categories: hep-lat