The $\bar B_s^0 \to J/\psi \pi^0 \eta$ decay and the $a_0(980)-f_0(980)$ mixing

TL;DR

This paper investigates the isospin violation and mixing of scalar mesons $f_0(980)$ and $a_0(980)$ in $ar B_s^0$ decays, highlighting the role of meson-meson interactions and kaon mass differences.

Contribution

It demonstrates that isospin breaking in meson-meson transition matrices and kaon loop effects are key to understanding $f_0(980)$ and $a_0(980)$ mixing in $B_s$ decays.

Findings

Main isospin violation source is meson-meson transition matrix breaking.

Kaon mass differences cause non-cancellation in loops.

Predicted $a_0(980)$ production branching ratio is about $5 imes 10^{-6}$.

Abstract

We study the $\bar B_s^0 \to J/\psi f_0(980)$ and $\bar B_s^0 \to J/\psi a_0(980)$ reactions, and pay attention to the different sources of isospin violation and mixing of $f_0(980)$ and $a_0(980)$ resonances where these resonances are dynamically generated from meson-meson interaction. We find that the main cause of isospin violation is the isospin breaking in the meson-meson transition $T$ matrices, and the other source is that the loops involving kaons in the production mechanism do not cancel due to the different masses of the charged and neutral kaons. We obtain a branching ratio for $a_0(980)$ production of the order of $5 \times 10^{-6}$. Future experiments can address this problem, and the production rate and shape of the $\pi^0 \eta$ mass distribution will definitely help to better understand the nature of scalar resonances.