  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.

High Energy Physics - Lattice