Lattice QCD study of the scalar mesons a0(1450) and σ(600)

We study the a(0) and sigma mesons with the overlap fermion in the chiral regime with the pion mass as low as 182 MeV in the quenched approximation. After the eta(')pi ghost states are separated, we find the a(0) mass with the q (q) over bar interpolation field to be almost independent of the quark mass in the region below the strange quark mass. The chirally extrapolated results are consistent with a(0)(1450) being the u (d) over bar meson and K-0(*)(1430) being the u (s) over bar meson with calculated masses at 1.42 +/- 0.13 GeV and 1.41 +/- 0.12 GeV, respectively. We also calculate the scalar mesonium with a tetraquark interpolation field. In addition to the two-pion scattering states, we find a state at similar to 550 MeV. Through the study of volume dependence, we confirm that this state is a one-particle state, in contrast to the two-pion scattering states. This suggests that the observed state is a tetraquark mesonium which is quite possibly the sigma(600) meson.