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

Abstract

We apply a mixing framework to the light meson systems and examine tetraquark possibility in the scalar channel. In the diquark-antidiquark model, a scalar diquark 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 one spin configuration, $|J,J_{12},J_{34}\rangle=|000\rangle$, where $J$ is the spin of the tetraquark, $J_{12}$ the diquark spin, $J_{34}$ the antidiquark spin. In this construction of the scalar tetraquark, we notice that another compact diquark with spin-1 in ($\bm{6}_c$, $\bar{\bm{3}}_f$) can be used although it is less compact than the scalar diquark. The spin-0 tetraquark constructed 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-spin interaction. The physical states can be identified with certain mixtures of the two configurations which diagonalize the hyperfine masses of the color-spin interaction. 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, we find that their mass splittings are qualitatively consistent with the hyperfine mass splittings which can support their tetraquark structure. To test our mixing scheme further, we also construct the tetraquarks for $J=1,J=2$ with the spin configurations, $|111\rangle$ and $|211\rangle$, and discuss possible candidates in the physical spectrum.