Decay properties of the $Z_c(3900)$ through the Fierz rearrangement

Abstract

We systematically construct all the tetraquark currents/operators of $J^{PC}=1^{+-}$ with the quark configurations $[cq][\bar{c}\bar{q}]$, $[\bar{c}q][\bar{q}c]$, and $[\bar{c}c][\bar{q}q]$ ($q=u/d$), and derive their relations through the Fierz rearrangement of the Dirac and color indices. Using the transformations of $[qc][\bar{q}\bar{c}]\to [\bar{c}c][\bar{q}q]$ and $[\bar{c}q][\bar{q}c]$, we study decay properties of the $Z_c(3900)$ as a compact tetraquark state; while using the transformation of $[\bar{c}q][\bar{q}c]\to [\bar{c}c][\bar{q}q]$, we study its decay properties as a hadronic molecular state.

Comments: 20 pages, 5 figures, 4 tables, to be published in CPC