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

Abstract

We systematically construct all the tetraquark currents of $J^{PC}=1^{++}$ with the quark configurations $[cq][\bar{c}\bar{q}]$, $[\bar{c}q][\bar{q}c]$, and $[\bar{c}c][\bar{q}q]$ ($q=u/d$). 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 $X(3872)\to {\chi }_{c0}\pi$, ${\eta }_c\pi \pi$, and ${\chi }_{c1}\pi \pi$ decay processes in particle experiments.

Comments: 18 pages, 4 figures, 2 tables, revised version to be published in Commun. Theor. Phys. arXiv admin note: text overlap with arXiv:1910.03269, arXiv:2103.08586