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We apply a mixing framework to the light meson systems and examine tetraquarkpossibility in the scalar channel. In the diquark-antidiquark model, a scalardiquark is a compact object when its color and flavor structures are in($\bar{\bm{3}}_c$, $\bar{\bm{3}}_f$). Assuming that all the quarks are in an$S$-wave, the spin-0 tetraquark formed out of this scalar diquark has only onespin configuration, $|J,J_{12},J_{34}\rangle=|000\rangle$, where $J$ is thespin of the tetraquark, $J_{12}$ the diquark spin, $J_{34}$ the antidiquarkspin. In this construction of the scalar tetraquark, we notice that anothercompact diquark with spin-1 in ($\bm{6}_c$, $\bar{\bm{3}}_f$) can be usedalthough it is less compact than the scalar diquark. The spin-0 tetraquarkconstructed from this vector diquark leads to the spin configuration$|J,J_{12},J_{34}\rangle=|011\rangle$. The two configurations, $|000\rangle$and $|011\rangle$, are found to mix strongly through the color-spininteraction. The physical states can be identified with certain mixtures of thetwo configurations which diagonalize the hyperfine masses of the color-spininteraction. Matching these states to two scalar resonances $a_0(980),a_0(1450)$ or to $K^*_0(800), K^*_0(1430)$ depending on the isospin channel, wefind that their mass splittings are qualitatively consistent with the hyperfinemass splittings which can support their tetraquark structure. To test ourmixing scheme further, we also construct the tetraquarks for $J=1,J=2$ with thespin configurations, $|111\rangle$ and $|211\rangle$, and discuss possiblecandidates in the physical spectrum.

Spin-1 diquark contributing to the formation of tetraquarks in light mesons