Scalar and Vector 4Q Systems in Anisotropic Lattice QCD

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, $m_{4q}^{I=0}=927(12)$ 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 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.

9 pages, 10 figures, typos corrected

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