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

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.

arXiv comment12 pages, 4 figures; v2: version published in Chin. Phys. C

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