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The observed mass pattern of scalar resonances below 1 GeV gives preferenceto the tetraquark assignment over the conventional $\bar qq$ assignment forthese states. We present a search for tetraquarks with isospins 0,1/2,1 inlattice QCD, where isospin channels 1/2 and 1 have not been studied before. Oursimulation uses Chirally Improved fermions on quenched gauge configurations. Wedetermine three energy levels for each isospin using the variational method.The ground state is consistent with the scattering state, while the two excitedstates have energy above 2 GeV. Therefore we find no indication for lighttetraquarks at our range of pion masses 344-576 MeV.

A lattice study of light scalar tetraquarks with isopins 0, 1/2 and 1