The $J/ψ\to φηπ^0$ reaction: $a_0(980)$ production, triangle singularity and non $φ$ background

TL;DR

This work analyzes the isospin-violating channel $J/\psi \to \phi \eta \pi^0$ to understand the production of $a_0(980)$ and to clarify the origin of TS-related features and the BESIII-identified non-$\phi$ background. Using a SU(3)-based hadronization framework and final-state interaction in a chiral unitary approach, it links the narrow $a_0(980)$ signal to $K\bar{K} \to \pi^0 \eta$ transitions, with isospin breaking driven by charged-neutral kaon mass differences. It also analyzes a triangle mechanism that yields a TS near $M_{\phi\pi^0} \approx 1385$ MeV, finding the TS peak to be far weaker than the observed non-$\phi$ peak, which itself arises mainly from tree-level $K^+K^-$ production within the BESIII $\phi$-tagging window. The study demonstrates that the prominent features in the data can be attributed to a combination of $a_0(980)$ production, tree-level backgrounds, and limited TS effects, and it suggests alternative methods for observing the TS to better probe isospin-violating dynamics in this system.

Abstract

We study the $J/ψ\toφηπ^{0}$ 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 $π^0η$ mass distributions, with the typical narrow width observed in isospin violating processes; 2) The origin of two peaks in the $φπ^{0}$ mass distributions that were branded as ``non $φ$" contribution in the experimental analysis; 3) The existence of two triangle mechanisms developing a triangle sigularity at the same energy where the ``non $φ$" 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 $φ$ looking at $K^+K^-$ in a narrow window of invariant mass around the $φ$ mass. We suggest that these triangle singularities could be observed with other methods to identify the $φ$.

Figures (7)

• Figure 1: Loop mechanism involving FSI of $K\bar{K}$ for $J/\psi \to \phi \pi^0 \eta$.
• Figure 2: Triangle diagrams for $J/\psi \to \phi \pi^0 \eta$ decay. The momenta of the particles are written in parentheses. $P$ is the sum of the $\pi^0$ and $\phi$ momenta. $K^* \equiv K^*(890)$.
• Figure 3: Tree level contribution for $J/\psi \to \pi^0 \eta K^+ K^-$ decay (non $\phi$ contribution), with $K^* \equiv K^*(890)$.
• Figure 4: Results for the $\phi\pi^{0}$ invariant mass distribution. The red error bars represent experimental data from Ref. BESIII:2023zwx. The black solid line corresponds to the total result; the green dashed line shows the tree level contribution; the blue dotted line represents the $t_{a_{0}}$ contribution, the brown solid line corresponds to the triangle singularity, and the purple and orange dash-dotted line denote the contributions from the $\phi(1680)$ and $h_{1}(1900)$, repectively. Note that we write $M_{\rm inv}(\phi\pi^0)$ to keep the same nomenclature as in Ref. BESIII:2023zwx, but it is actually $M_{\rm inv}(K^+K^-\pi^0)$ with the cut of Eq. \ref{['eq:BEScut']}. In the large tree contribution, the $K^+, K^-$ do not correspond to the $\phi$ since they are in $I=1$. This corresponds to the "non $\phi$" contribution of Ref. BESIII:2023zwx.
• Figure 5: Only triangle singularity result for the $\phi\pi^{0}$ invariant mass distribution.