Abstract
The observed mass pattern of scalar resonances below 1 GeV suggests a tetraquark assignment over the conventional $\overline{q}q$ assignment for these states. We present a search for tetraquarks with isospins 0, $1/2$, 1 in lattice QCD, where the isospin channels $1/2$ and 1 have not been studied before. We determine three energy levels in each isospin channel using the variational method. The scattering states and possible tetraquark states are distinguished by considering the volume dependence of spectral weights and by considering the time dependence of correlators near $t\ensuremath{\simeq}T/2$. We find no indication for light tetraquarks at our range of pion masses, $344--576\text{ }\text{ }\mathrm{MeV}$. However, our simulation does not exclude a possibility of finding tetraquarks in a simulation with smaller pion masses or a different interpolator basis.
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