Abstract
The $a_0^0(980)-f_0(980)$ mixing is one of the most potential tools to learn about the nature of $a_0^0(980)$ and $f_0(980)$. Using the $f_0(980)$-$a_0^0(980)$ mixing intensity $\xi_{af}$ measured recently at BESIII, we calculate the the branching ratio of the the isospin violation decay $J/\psi \rightarrow\gamma\eta_c \rightarrow \gamma \pi^0 a_0^0(1450)\rightarrow \gamma \pi^0 a_0^0(980)f_0(500)\rightarrow \gamma \pi^0 f_0(980) f_0(500) \rightarrow \gamma \pi^0 \pi^+\pi^- \pi^+\pi^-$. The value of the branching ratio is found to be $O(10^{-6})$, which can be observed with $10^{10}$ $J/\psi$ events collected at BESIII. The narrow peak from the $f_0(980)$-$a_0^0(980)$ mixing in the $\pi^+\pi^-$ mass square spectrum can also be observed. In addition, we study the non-resonant decay $a_0^0(1450)\rightarrow f_0(980) \pi^+\pi^-(\text{non-resonant})$, which is dominated by the $a_0^0(980)$-$f_{0}(980)$ mixing. We find that the non-resonant decay $a_0^0(1450)\rightarrow f_0(980) \pi^+\pi^-$ and the decay $a_0^0(1450)\rightarrow f_0(980) f_0(500)$ can be combined to measure the mixing intensity $\xi_{af}$ in experiment. These decays are the perfect complement to the decay $\chi_{c1}\rightarrow f_{0}(980)\pi^{0}\to\pi^{+}\pi^{-}\pi^{0}$ which had been observed at BESIII, the observations of them will make the measurement of the mixing intensity $\xi_{af}$ more precisely.
Highlights
The inner structure of the light scalar mesons such as a00ð980Þ and f0ð980Þ has been studied for over 30 years, and it is still a hot topic in particle physics
These decays are the perfect complement to the decay χc1 → f0ð980Þπ0 → πþπ−π0, which had been observed at the BESIII experiment, the observations of which will make the measurement of the mixing intensity ξaf more precisely
Based on the data samples of 1010 J=ψ events collected in the BESIII experiment [60,61,62,63], about 107 a0ð1450Þ mesons can be produced through decays J=ψ → γηc → γa0ð1450Þπ0; this large a0ð1450Þ sample at the BESIII experiment will make it possible to investigate the properties of a0ð1450Þ meson and study the related physics
Summary
The inner structure of the light scalar mesons such as a00ð980Þ and f0ð980Þ has been studied for over 30 years, and it is still a hot topic in particle physics. Based on the data samples of 1010 J=ψ events collected in the BESIII experiment [60,61,62,63], about 107 a0ð1450Þ mesons can be produced through decays J=ψ → γηc → γa0ð1450Þπ0; this large a0ð1450Þ sample at the BESIII experiment will make it possible to investigate the properties of a0ð1450Þ meson and study the related physics. We predict the branching ratio of this reaction by using the recent measurements at the BESIII experiment and calculate the distribution of the πþπ− mass square spectrum near the KKthresholds. We discuss the a0ð1450Þ→f0ð980Þπþπ−ðnonresonantÞ→ πþπ−πþπ− decay process, which is realized mainly via the a00ð980Þ − f0ð980Þ mixing
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