Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: Are σ and κ tetraquarks?

We investigate whether the lightest scalar mesons σ and κ have a large tetraquark component q̄q̄qq, as is strongly supported by many phenomenological studies. A search for possible light tetraquark states with JPC=0⁺⁺ and I=0,2,1/2,3/2 on the lattice is presented. We perform the two-flavor dynamical simulation with chirally improved quarks and the quenched simulation with overlap quarks, finding qualitative agreement between both results. The spectrum is determined using the generalized eigenvalue method with a number of tetraquark interpolators at the source and the sink, and we omit the disconnected contractions. The time dependence of the eigenvalues at the finite temporal extent of the lattice is explored also analytically. In all the channels, we unavoidably find the lowest scattering states π(k)π(-k) or K(k)π(-k) with back-to-back momentum k=0,2π/L,.... However, we find an additional light state in the I=0 and I=1/2 channels, which may be interpreted as the observed resonances σ and κ 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.