We present a data-driven analysis of the resonant $S$-wave $\pi \pi \to \pi \pi$ and $\pi K\to \pi K$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion in a suitably constructed conformal variable. The fits are performed to experimental and lattice data as well as Roy analyses. For the $\pi \pi$ scattering we present both a single- and a coupled-channel analysis by including additionally the $K\overline{K}$ channel. For the latter the central result is the Omnès matrix, which is consistent with the most recent Roy and Roy-Steiner results on $\pi \pi \to \pi \pi$ and $\pi \pi \to K\overline{K}$, respectively. By the analytic continuation to the complex plane, we found poles associated with the lightest scalar resonances $\sigma /f_0(500)$, $f_0(980)$, and $\kappa /K_0^{*}(700)$ for the physical pion mass value and in the case of $\sigma /f_0(500)$, $\kappa /K_0^{*}(700)$ also for unphysical pion mass values.

中文翻译：

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ππ和πK散射的数据驱动色散分析

我们提出了谐振的数据驱动分析 $秒$-海浪 $\pi \pi \to \pi \pi$ 和 $\pi 钾\to \pi 钾$使用分波色散关系的反应。在适当构造的共形变量中使用泰勒展开来解释左手切割的贡献。对实验和晶格数据以及 Roy 分析进行拟合。为了$\pi \pi$ 散射我们通过额外包括单通道和耦合通道分析 $钾\overline{钾}$渠道。对于后者，中心结果是 Omnès 矩阵，这与最近的 Roy 和 Roy-Steiner 结果一致$\pi \pi \to \pi \pi$ 和 $\pi \pi \to 钾\overline{钾}$， 分别。通过对复平面的解析延展，我们发现了与最轻的标量共振相关的极点$\sigma /F_0(500)$, $F_0(980)$， 和 $\kappa /{钾}_0^{*}(700)$ 对于物理 pion 质量值和 $\sigma /F_0(500)$, $\kappa /{钾}_0^{*}(700)$ 也适用于非物理 pion 质量值。