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arXiv 2007.15210hep-ph
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从$a_0(1450) \to a_0^0(980) f_0(500) \to π^+ π^- f_0(500)$混合$f_0(980)$的研究

Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450) \to a_0^0(980) f_0(500) \to π^+ π^- f_0(500)$

Xiao-Dong Cheng, Ru-Min Wang, Yuan-Guo Xu

摘要:

$a_0^0(980)-f_0(980)$混合是了解$a_0^0(980)$和$f_0(980)$性质的最有潜力的工具之一。利用最近在北京谱仪上测得的$f_0(980)$ - $a_0^0(980)$混合强度$ξ_{af}$,计算了同位旋破坏衰变$J/ψ\rightarrowγη_c \rightarrow γπ^0 a_0^0(1450)\rightarrow γπ^0 a_0^0(980)f_0(500)\rightarrow γπ^0 f_0(980) f_0(500) \rightarrow γπ^0 π^+π^- π^+π^-$的分支比.发现分支比的值为$O(10^{-6})$,这可以用在BESIII收集的$10^{10}$ $J/ψ$事件观察到。还可以观察到$π^+π^-$质量平方谱中$f_0(980)$ - $a_0^0(980)$混合的窄峰。此外,我们还研究了$a_0^0(1450)\rightarrow f_0(980) π^+π^-(\text{non-resonant})$的非共振衰变,它主要是由$a_0^0(980)$ - $f_{0}(980)$的混合所决定的。我们发现,在实验中可以将非共振衰变$a_0^0(1450)\rightarrow f_0(980) π^+π^-$和衰变$a_0^0(1450)\rightarrow f_0(980) f_0(500)$结合起来测量混合强度$ξ_{af}$。这些衰变是对BESIII观测到的衰变$χ_{c1}\rightarrow f_{0}(980)π^{0}\toπ^{+}π^{-}π^{0}$的完美补充,它们的观测将使混合强度$ξ_{af}$的测量更加精确。

英文摘要:

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 $ξ_{af}$ measured recently at BESIII, we calculate the the branching ratio of the the isospin violation decay $J/ψ\rightarrowγη_c \rightarrow γπ^0 a_0^0(1450)\rightarrow γπ^0 a_0^0(980)f_0(500)\rightarrow γπ^0 f_0(980) f_0(500) \rightarrow γπ^0 π^+π^- π^+π^-$. The value of the branching ratio is found to be $O(10^{-6})$, which can be observed with $10^{10}$ $J/ψ$ events collected at BESIII. The narrow peak from the $f_0(980)$-$a_0^0(980)$ mixing in the $π^+π^-$ mass square spectrum can also be observed. In addition, we study the non-resonant decay $a_0^0(1450)\rightarrow f_0(980) π^+π^-(\text{non-resonant})$, which is dominated by the $a_0^0(980)$-$f_{0}(980)$ mixing. We find that the non-resonant decay $a_0^0(1450)\rightarrow f_0(980) π^+π^-$ and the decay $a_0^0(1450)\rightarrow f_0(980) f_0(500)$ can be combined to measure the mixing intensity $ξ_{af}$ in experiment. These decays are the perfect complement to the decay $χ_{c1}\rightarrow f_{0}(980)π^{0}\toπ^{+}π^{-}π^{0}$ which had been observed at BESIII, the observations of them will make the measurement of the mixing intensity $ξ_{af}$ more precisely.

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