Decay properties of the Zc(3900) through the Fierz rearrangement

We systematically construct all the tetraquark currents/operators of JPC = 1(+-) with the quark configurations [cq][(c) over bar(q) over bar], [(c) over barq][(q) over barc] and [(c) over barc][(q) over barq] (q = u/d), and derive their relations through the Fierz rearrangement of the Dirac and color indices. Using the transformations of [qc][(q) over bar(c) over bar] -> [(c) over barc][(q) over barq] and [(c) over barq][(q) over barc], we study decay properties of the Z(c)(3900) as a compact tetraquark state; while using the transformation of [(c) over barq][(q) over barc] -> [(c) over barc][(q) over barq], we study its decay properties as a hadronic molecular state.