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

Abstract

We study the $J/\psi \to \varphi \eta {\pi }^0$ 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 $\varphi {\pi }^0$ mass distributions that were branded as ``non $\varphi$" contribution in the experimental analysis; 3) The existence of two triangle mechanisms developing a triangle sigularity at the same energy where the ``non $\varphi$" 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 $\varphi$ looking at $K^{+}{K}^{-}$ in a narrow window of invariant mass around the $\varphi$ mass. We suggest that these triangle singularities could be observed with other methods to identify the $\varphi$.

Comments: 11 pages, 7 figures; v2: discussions added, references added, version to appear in Phys. Rev. D