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" [(3_bar,3)+(3,3_bar)] 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 [(3_bar,3)+(3,3_bar)] 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 [(3_bar,3)+(3,3_bar)] and having quantum numbers J^{PC}=1^{-+}.