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arXiv 2002.04441hep-ph
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光子-光子散射中的$πη$相互作用和$a_0$共振

The $πη$ interaction and $a_0$ resonances in photon-photon scattering

Junxu Lu, B. Moussallam

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40 pages, 13 figures, revised improved version
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摘要：

我们重新审视了两个最轻的$a_0$共振和$S$波$πη$散射，可以从光子-光子散射实验中提取的信息。为此，我们构造了一个模型的$S$波光子光子振幅满足解析性质，双通道幺正性和遵守软光子以及软π约束。基本的I=1强子$T$ -矩阵涉及六个唯象参数，并能够占两个共振低于1.5 GeV。我们进行了组合拟合的$γγ\to πη$和$γγ\to K_SK_S$高统计实验数据从贝尔合作。最小化的$χ^2$被发现有两个不同的解决方案与近似相等的$χ^2$。其中之一表现出轻而窄的激发$a_0$共振类似于在贝尔分析中发现的。然而，这需要$J=0$和$J=2$共振效应之间的特殊巧合，这可能是非物理的。在这两个解决方案的$a_0(980)$共振出现作为一个极点的第二个黎曼面。这个极点在物理溶液中的位置被确定为$m-iΓ/2=1000.7^{+12.9}_{-0.7} -i\,36.6^{+12.7}_{-2.6}$ MeV。的解决方案也进行了比较，实验数据中的运动学区域的衰变$η\toπ^0γγ$。在这个区域中，与$π^+π^-$再散射相关的同位旋破坏贡献必须被添加，为此我们提供了色散评估。

英文摘要：

We revisit the information on the two lightest $a_0$ resonances and $S$-wave $πη$ scattering that can be extracted from photon-photon scattering experiments. For this purpose we construct a model for the $S$-wave photon-photon amplitudes which satisfies analyticity properties, two-channel unitarity and obeys the soft photon as well as the soft pion constraints. The underlying I=1 hadronic $T$-matrix involves six phenomenological parameters and is able to account for two resonances below 1.5 GeV.We perform a combined fit of the $γγ\to πη$ and $γγ\to K_SK_S$ high statistics experimental data from the Belle collaboration. Minimisation of the $χ^2$ is found to have two distinct solutions with approximately equal $χ^2$. One of these exhibits a light and narrow excited $a_0$ resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the $J=0$ and $J=2$ resonance effects which is likely to be unphysical. In both solutions the $a_0(980)$ resonance appears as a pole on the second Riemann sheet. The location of this pole in the physical solution is determined to be $m-iΓ/2=1000.7^{+12.9}_{-0.7} -i\,36.6^{+12.7}_{-2.6}$ MeV. The solutions are also compared to experimental data in the kinematical region of the decay $η\toπ^0γγ$. In this region an isospin violating contribution associated with $π^+π^-$ rescattering must be added for which we provide a dispersive evaluation.

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