一种提取近阈值共振信息的新方法：格林函数与T矩阵的统一化极和表示
A New Method to Extract Information of Near-Threshold Resonances: Uniformized Pole-Sum Representation of Green's Function and T-matrix
摘要：
我们提出了一种新的，简单的模型无关的方法来提取信息的近阈值共振，如复杂的能量和残留物。该方法是基于格林函数和T矩阵可以表示为所有极点的总和，约束和共振极点，在一个变量的复平面中，其中格林函数和T矩阵是单值函数。由S-矩阵的酉性引起的极点的对称性自然地使和服从适当的阈值行为。格林函数的虚部和T矩阵与可观测量直接相关，如散射截面或不变或丢失的强子共振质量分布。因此，我们可以通过拟合它们的虚部来确定它们的极点位置和留数。我们还测试了新的方法作为虚拟实验数据的模型理论计算的$T$ -矩阵的虚部。作为模型理论，我们在带通道的手征幺正模型中考虑双通道介子-重子散射，$\overline{K}N (I=0)$和$πΣ(I=0)$。通过将模型理论中计算的$T$ -矩阵的虚部与均匀化极和的虚部进行拟合，得到了极点位置和留数。将所得结果与模型理论中的精确计算结果进行比较，我们得出结论，我们的新方法工作得很好。
英文摘要：
We propose a new, simple model-independent method to extract information of near-threshold resonances, such as complex energies and residues. The method is based on the observation that the Green's function and the T-matrix can be represented as the sum of all poles, both bound and resonant poles, in the complex plane of a variable in which the Green's function and the T-matrix are single-valued functions. The symmetries of poles, which arise from the unitarity of the S-matrix, naturally impose the sum to obey the proper threshold behaviors. The imaginary part of Green's function and the T-matrix are directly related to observables such as scattering cross sections or invariant or missing mass distributions of hadron resonances. Thus we can determine their pole positions and residues by fitting their imaginary part to observables. We also test the new method by regarding the imaginary part of the $T$-matrix calculated exactly in a model theory as virtual experimental data. As a model theory, we take double-channel meson-baryon scatterings in the chiral unitary model with channels, $\overline{K}N (I=0)$, and $πΣ(I=0)$. By fitting the imaginary part of the $T$-matrix calculated in the model theory by that of the uniformized pole-sum, we obtain the pole positions and residues. Comparing the obtained results with those of the exact calculation in the model theory, we conclude that our new method works very well.
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