$a_0(980)$ production, triangle singularity, and non-$\phi$ background in the $J/\psi \to \phi \eta \pi^0$ reaction

Abstract

We study the $J/\psi\to\phi\eta\pi^{0}$ reaction measured recently by the BESIII collaboration with high precision, paying attention to three important aspects: 1) The production of the $a_0(980)$ in the $\pi^0\eta$ mass distributions, with the typical narrow width observed in isospin violating processes; 2) The origin of two peaks in the $\phi\pi^{0}$ mass distributions that were branded as ``non $\phi$" contribution in the experimental analysis; 3) The existence of two triangle mechanisms developing a triangle sigularity at the same energy where the ``non $\phi$" contribution peaks in the experiment. However, we also show that the strength of these peaks is very small relative to the observed ones, a feature which is tied to the experimental technique used to identify the $\phi$ looking at $K^+K^-$ in a narrow window of invariant mass around the $\phi$ mass. We suggest that these triangle singularities could be observed with other methods to identify the $\phi$.