论文标题
$ππ$和$πk$散射数据的分散分析
Dispersive analysis of the $ππ$ and $πK$ scattering data
论文作者
论文摘要
我们提出了S-Wave $ππ\至ππ\的数据驱动分析，（i = 0,2）$和$πk\toπk\toπk\，（i = 1/2，3/2）$使用部分波分散性关系。使用适当构建的保形变量中的扩展来对左手切割的贡献进行参数化，这说明了其分析结构。使用$ n/d $方法对部分波分散关系进行数值求解。拟合在阈值和Adler Zero处的手性扰动理论的约束的实验数据中，结果与Roy样（Roy-Steiner）分析一致。对于$ππ$散射，我们通过包括$ k \ bar {k} $ channel来介绍耦合通道分析。通过分析延续到复杂平面，我们发现了与最轻的标量共鸣$σ/f_0（500）$，$ f_0（980）$和$κ/k_0^*（700）$相关的极。对于所有通道，我们还直接执行了物理区域中类似Roy的（Roy-Steiner）溶液的拟合，以最大程度地减少复杂平面中的$ N/D $不确定性，并提取最约束的Omnès函数。
We present a data-driven analysis of the S-wave $ππ\to ππ\,(I=0,2)$ and $πK \to πK\,(I=1/2, 3/2)$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are parametrized using the expansion in a suitably constructed conformal variable, which accounts for its analytical structure. The partial-wave dispersion relation is solved numerically using the $N/D$ method. The fits to the experimental data supplemented with the constraints from chiral perturbation theory at threshold and Adler zero give the results consistent with Roy-like (Roy-Steiner) analyses. For the $ππ$ scattering we present the coupled-channel analysis by including additionally the $K\bar{K}$ channel. By the analytic continuation to the complex plane, we found poles associated with the lightest scalar resonances $σ/f_0(500)$, $f_0(980)$, and $κ/K_0^*(700)$. For all the channels we also performed the fits directly to the Roy-like (Roy-Steiner) solutions in the physical region, in order to minimize the $N/D$ uncertainties in the complex plane and to extract the most constrained Omnès functions.
