, 72:2204,
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The “closed” chiral symmetry and its application to tetraquark


We investigate the chiral (flavor) structure of tetraquarks, and study chiral transformation properties of the “non-exotic” $[(\bar{\mathbf{3}}, \mathbf{3})\oplus(\mathbf{3}, \bar{\mathbf{3}})]$ and [(8,1)⊕(1,8)] tetraquark chiral multiplets. We find that as long as this kind of tetraquark states contains one quark and one antiquark having the same chirality, such as $q_{L} q_{L} \bar{q}_{L} \bar{q}_{R} + q_{R} q_{R} \bar{q}_{R} \bar{q}_{L}$ , they transform in the same way as the lowest level $\bar{q} q$ chiral multiplets under chiral transformations. There is only one $[(\bar{\mathbf{3}}, \mathbf{3})\oplus (\mathbf{3}, \bar{\mathbf{3}})]$ chiral multiplet whose quark-antiquark pairs all have the opposite chirality ( $q_{L} q_{L} \bar{q}_{R} \bar{q}_{R} + q_{R} q_{R} \bar{q}_{L} \bar{q}_{L}$ ), and it transforms differently from others. Based on these studies, we construct local tetraquark currents belonging to the “non-exotic” chiral multiplet $[(\bar{\mathbf{3}}, \mathbf{3})\oplus(\mathbf{3}, \bar{\mathbf{3}})]$ and having quantum numbers J PC =1−+.