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) over bar, 3) circle plus (3, (3) over bar)] and [(8, 1) circle plus (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)(q) over barq(L)(q) over bar (R) + q(R)q(R)(q) over bar (R)(q) over barq(L), they transform in the same way as the lowest level (q) over barq chiral multiplets under chiral transformations. There is only one [((3) over bar, 3) circle plus (3, (3) over bar)] chiral multiplet whose quark-antiquark pairs all have the opposite chirality (q(L)q(L)(q) over bar (R)(q) over bar (R) + q(R)q(R)(q) over bar (L)(q) over bar (L)), and it transforms differently from others. Based on these studies, we construct local tetraquark currents belonging to the non-exotic chiral multiplet [((3) over bar, 3) circle plus (3, (3) over bar)] and having quantum numbers J(PC) = 1(-+).