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

TL;DR

This paper explores the decay properties of the $X(3872)$ meson by constructing tetraquark currents and analyzing their relations via Fierz rearrangement, aiming to distinguish between compact tetraquark and molecular interpretations.

Contribution

It systematically constructs all relevant tetraquark currents and derives their relations, providing a framework to study $X(3872)$ decays under different structural hypotheses.

Findings

Proposes specific decay channels for experimental search.

Provides a theoretical basis for distinguishing tetraquark vs. molecular nature.

Analyzes relations among tetraquark currents using 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 $X(3872) \rightarrow \chi_{c0} \pi$, $\eta_c \pi \pi$, and $\chi_{c1} \pi \pi$ decay processes in particle experiments.