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 (3 c , 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 = |000 , 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 (6 c ,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 = |011 . The two configurations, |000 and |011 , 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 and |211 , and we discuss possible candidates in the physical spectrum.

Possible signatures for tetraquarks from the decays of $$a_0(980)$$ a 0 ( 980 )

“…[20]. Our tetraquark wave functions are based on a diquark-antidiquark picture schematically of the form, q 1 q 2q 3q4 , where q 1 q 2 denotes the diquark, andq 3q4 denotes the antidiquark.…”

“…The other component is the configuration where q 1q 3 and q 2q 4 are separately combined into a color octet. Thus, our tetraquarks contain the component of the open decay channels in their wave function which affect the masses through the expectation value of the color-spin interaction [20], and the decay couplings through the mixing. This role driven by the open decay channels is in some sense consistent with the findings from the coupled-channel analysis where the resonances are dynamically generated from the meson-meson decay channels coupled to the quark-antiquark channels or others [31,32,[34][35][36].…”

“…Specifically, the spin-0 tetraquarks, in a diquark-antidiquark form, can be constructed also from the spin and color configurations |011 , |1 c , 6 c ,6 c . The tetraquarks of this type are found to mix strongly with the ones above, |000 , |1 c ,3 c , 3 c , through the color-spin interaction [20]. The physical states can be realized by the mixtures of |000 and |011 , which diagonalize the hyperfine mass matrix coming from the color-spin interaction.…”

“…Along this line, we have recently proposed [20] that the spin-1 diquark with the flavor and color structure of3 f , 6 c , which is the second most compact object among all the possible diquarks [16], could be an important ingredient in the formation of tetraquarks. Specifically, the spin-0 tetraquarks, in a diquark-antidiquark form, can be constructed also from the spin and color configurations |011 , |1 c , 6 c ,6 c .…”

“…This paper is organized as follows. After a brief introduction of the tetraquark wave functions for a 0 (980), a 0 (1450) [20], we examine possible modes of their fall-apart decays. We then demonstrate the suppression or enhancement of the couplings related to the fall-apart decays.…”