Traces of the new $a_0(1780)$ resonance in the $J/\psi\to \phi K^+K^-(K^0\bar{K}^0)$ reaction

TL;DR

This paper investigates the decay of J/psi into phi and kaon pairs, revealing a potential new resonance near 1780 MeV and analyzing isospin violations and threshold effects in the mass distribution.

Contribution

It identifies a possible new $a_0(1780)$ resonance and clarifies the role of threshold effects and isospin violation in the decay process.

Findings

Small isospin violation (~5%) in kaon production rates.

A shape in the $K ar K$ mass distribution mimics $a_0$ production.

Threshold effects can produce features similar to resonances.

Abstract

We study the $J/\psi \to \phi K \bar K$ decay, looking for differences in the production rates of $K^+ K^-$ or $K^0 \bar K^0$ in the region of 1700-1800 MeV, where two resonances appear dynamically generated from the vector-vector interaction. Two resonances are known experimentally in that region, the $f_0(1710)$ and a new resonance reported by the BABAR and BESIII collaborations. The $K \bar K$ should be produced with $I=0$ in that reaction, but due to the different $K^{*0}$ and $K^{*+}$ masses some isospin violation appears. Yet, due to the large width of the $K^*$, the violation obtained is very small and the rates of $K^+ K^-$ or $K^0 \bar K^0$ production are equal within $5\%$. However, we also find that due to the step needed to convert two vectors into $K \bar K$, a shape can appear in the $K \bar K$ mass distribution that can mimic the $a_0$ production around the $K^* \bar K^*$ threshold, and is simply a threshold effect.