Lowest-lying tetra-quark hadrons in anisotropic lattice QCD

We present a detailed study of the lowest-lying hadrons in quenched improved anisotropic lattice QCD. Using the π π 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 the light-quark mass region, the lowest scalar 4q state is found to have a mass, m _4q ^I=0=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 _4q ^I=1=1358(28) MeV. We analysed the static 4q potential extracted from 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 the 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.