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arXiv 2201.00492hep-phhep-exnucl-th
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轻标量介子$f_{0}(980)$和$a_0(980)$的复合性质分析

Analysis on the composite nature of the light scalar mesons $f_{0}(980)$ and $a_0(980)$

Ze-Qiang Wang, Xian-Wei Kang, J. A. Oller, Lu Zhang

摘要:

我们研究了$ππ$ - $K\bar{K}$和$πη$ - $K\bar{K}$分别在$f_0(980)$和$a_0(980)$共振组成中的权重或组成。要么我们使用总宽度和复合性的饱和度,要么我们使用Flatté参数化,同时考虑近阈值共振的谱函数。我们将这两种方法联系起来并进行比较。我们从文献中的几个测定中获取极点质量和宽度的输入值。此外,我们采取的第三个输入的总的复合性或衰减宽度分支比的轻通道的每个共振。结果表明,对于所考虑的极点,$f_0(980)$共振的介子-介子分量占优势,而$a_0(980)$共振的介子-介子分量占次优势.我们还提供了部分衰减宽度和部分复合系数,使$K\bar{K}$组件是最重要的一个$f_0(980)$。此外,这项研究强调,需要区分裸和穿着耦合和宽度在Flatté参数化。我们详细说明的部分衰变宽度计算的穿着耦合和实际测量的连接。由于耦合通道动力学,当极点位于第二黎曼单中较重的阈值附近时,需要对标准关系进行一些修改。

英文摘要:

We study the weight or compositeness of the $ππ$-$K\bar{K}$ and $πη$-$K\bar{K}$ in the composition of the $f_0(980)$ and $a_0(980)$ resonances, respectively. Either we use the saturation of the total width and compositeness, or we use a Flatté parameterization taking also into account the spectral function of a near-threshold resonance. We make connections and compare between these two methods. We take input values for the pole mass and width from several determinations in the literature. In addition, we take as third input either the total compositeness or the decay-width branching ratio to the lighter channel for each resonance. It turns out that for the poles considered the meson-meson components are dominant for the $f_0(980)$, while for the $a_0(980)$ resonance they are subdominant. We also provide partial decay widths and partial compositeness coefficients, so that the $K\bar{K}$ component is the most important one for the $f_0(980)$. Additionally, this study stresses the need to distinguish between the bare and dressed couplings and widths in a Flatté parameterization. We elaborate on the connection between the partial-decay widths calculated in terms of the dressed couplings and the actual measured ones. Due to the coupled-channel dynamics when the pole lies near the heavier threshold in the second Riemann sheet some changes are needed with respect to standard relations.

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