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

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 (anti 3_c, anti 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, vertical stroke J,J₁₂,J₃₄ right angle = vertical stroke 000 right angle, where J is the spin of the tetraquark, J₁₂ the diquark spin, J₃₄ the antidiquark spin. In this construction of the scalar tetraquark, we notice that another compact diquark with spin-1 in (6_c, anti 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 vertical stroke J,J₁₂,J₃₄ right angle = vertical stroke 011 right angle. The two configurations, vertical stroke 000 right angle and vertical stroke 011 right angle, 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 a₀(980), a₀(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 vertical stroke 111 right angle and vertical stroke 2011 right angle, and we discuss possible candidates in the physical spectrum. (orig.)