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We investigate whether the lightest scalar mesons sigma and kappa have alarge tetraquark component, as is strongly supported by many phenomenologicalstudies. A search for possible light tetraquark states with J^PC=0^++ and I=0,2, 1/2, 3/2 on the lattice is presented. We perform the two-flavor dynamicalsimulation with Chirally Improved quarks and the quenched simulation withoverlap quarks, finding qualitative agreement between both results. Thespectrum is determined using the generalized eigenvalue method with a number oftetraquark interpolators at the source and the sink, and we omit thedisconnected contractions. The time-dependence of the eigenvalues at finitetemporal extent of the lattice is explored also analytically. In all thechannels, we unavoidably find lowest scattering states pi(k)pi(-k) orK(k)pi(-k) with back-to-back momentum k=0, 2*pi/L,... However, we find anadditional light state in the I=0 and I=1/2 channels, which may be interpretedas the observed resonances sigma and kappa with a sizable tetraquark component.In the exotic repulsive channels I=2 and I=3/2, where no resonance is observed,we find no light state in addition to the scattering states.

Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: are sigma and kappa tetraquarks?