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arXiv 1708.02764hep-ph
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在$χ_{c1} \to π^0 f_0(980) \to π^0 π^+ π^-$和$χ_{c1} \to π^0 a_0(980) \to π^0 π^0 η$中混合$a_0(980) - f_0(980)$

$a_0(980) - f_0(980)$ mixing in $χ_{c1} \to π^0 f_0(980) \to π^0 π^+ π^-$ and $χ_{c1} \to π^0 a_0(980) \to π^0 π^0 η$

M. Bayar, V. R. Debastiani

备注：
revised manuscript, new figures, new references; 8 pages, 6 figures
发表信息：
Phys. Lett. B 775, 94 (2017)
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摘要：

我们研究了反应$χ_{c1} \to π^0 π^+ π^-$和$χ_{c1} \to π^0 π^0 η$中的同位旋破缺及其与$a_0(980) - f_0(980)$混合的关系。我们表明，相同的理论模型，以前开发的研究$χ_{c1} \to ηπ^+ π^-$反应（也测量BESIII），并进一步探讨预测的$η_{c} \to ηπ^+ π^-$，可以成功地采用在本研究中。我们假设的$χ_{c1}$表现为$SU(3)$单线找到的重量，其中创建的三个pseudoscalars，其次是介子对的最终状态相互作用来描述如何动态生成的$a_0(980)$和$f_0(980)$，在耦合通道中使用手征酉方法。同位旋破坏是通过使用不同的质量的带电和中性的K介子，无论是在传播的介子对中创建的$χ_{c1}$衰变，或在传播的$T$矩阵内，通过对赝标介子的散射和跃迁振幅的么正化构造。我们发现$T$矩阵中的同位旋破坏使得$π^0η\to π^+π^-$振幅不为零，这是一个重要的贡献，同时也增强了$K\bar{K}$项的作用.此外，我们发现，在总振幅的最重要的影响是同位旋打破内的$T$矩阵，由于$π^0η\to π^+π^-$和$K\bar{K} \to π^+ π^-$的建设性和，这是必不可少的得到一个很好的协议与实验测量的混合。

英文摘要：

We study the isospin breaking in the reactions $χ_{c1} \to π^0 π^+ π^-$ and $χ_{c1} \to π^0 π^0 η$ and its relation to the $a_0(980) - f_0(980)$ mixing, which was measured by the BESIII Collaboration. We show that the same theoretical model previously developed to study the $χ_{c1} \to ηπ^+ π^-$ reaction (also measured by BESIII), and further explored in the predictions to the $η_{c} \to ηπ^+ π^-$, can be successfully employed in the present study. We assume that the $χ_{c1}$ behaves as an $SU(3)$ singlet to find the weight in which trios of pseudoscalars are created, followed by the final state interaction of pairs of mesons to describe how the $a_0(980)$ and $f_0(980)$ are dynamically generated, using the chiral unitary approach in coupled channels. The isospin violation is introduced through the use of different masses for the charged and neutral kaons, either in the propagators of the pairs of mesons created in the $χ_{c1}$ decay, or in the propagators inside the $T$ matrix, constructed through the unitarization of the scattering and transition amplitudes of pairs of pseudoscalar mesons. We find that violating isospin inside the $T$ matrix makes the $π^0η\to π^+π^-$ amplitude nonzero, which gives an important contribution and also enhances the effect of the $K\bar{K}$ term. Also, we find that in the total amplitude the most important effect is the isospin breaking inside the $T$ matrix, due to the constructive sum of $π^0η\to π^+π^-$ and $K\bar{K} \to π^+ π^-$, which is essential to get a good agreement with the experimental measurement of the mixing.

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