Decay properties of the $X(3872)$ through the Fierz rearrangement

Abstract

Abstract We systematically construct all the tetraquark currents of J(PC)=1(++) with the quark configurations [c q][cbar qbar], [cbar q][qbar c], and [cbar c][qbar q] (q=u/d). Their relations are derived using the Fierz rearrangement of the Dirac and color indices, through which we study decay properties of the X(3872) under both the compact tetraquark and hadronic molecule interpretations. We propose to search for the X(3872) -> χc0-π, ηc-π-π, and χc1-π-π decay processes in particle experiments.