Lowest-lying tetra-quark hadrons in anisotropic lattice QCD

Abstract

We present a detailed study of the lowest-lying \(q^{2}\bar{q}^{2}\) 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 I=04q =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=14q =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.