Scalar Mesons a 0 ( 1450 ) and σ ( 600 ) from Lattice QCD

We study the a0 and σ mesons with the overlap fermion in the chiral regime with the pion mass as low as 182MeV in the quenched approximation. After the ηN ghost states are separated, we find that the a0 mass with qq̄ 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 a0(1450) being the ud̄ meson and K 0 (1430) being the us̄ meson. We also calculate the scalar mesonium with a tetraquark interpolation field. In addition to the two pion scattering states, we found a state at ∼ 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 σ(600) meson. Unlike pseudoscalar, vector, and tensor mesons, the scalar mesons are not well known in terms of their SU(3) classification, nor are the particle content of their composition and their spectroscopy. Part of the problem is that there are too many experimental candidates for the qq̄ nonet. Fig. 1 shows the current experimentally known scalar mesons whose number more than doubles that of a nonet. One viable solution is that low-lying scalars, such as the σ(600), a0(980) and f0(980) are tetraquark mesoniums whose classification and spectroscopy have been studied in the MIT bag model [1] and the potential model [2]. Another suggestion is that a0(980) and f0(980) are the KK̄ molecular states [3]. Other candidates for tetraquark mesoniums include those vector mesons pairs produced in γγ reactions [4] and hadronic productions [5] and the recently discovered charmed narrow resonances [6].