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