论文标题
一种提取近阈值共振信息的新方法：格林功能和T-Matrix的均匀的杆位表示
A New Method to Extract Information of Near-Threshold Resonances: Uniformized Pole-Sum Representation of Green's Function and T-matrix
论文作者
论文摘要
我们提出了一种新的，简单的独立于模型的方法，以提取近阈值共振的信息，例如复杂的能量和残基。该方法基于以下观察结果：在变量的复杂平面中，绿色的函数和t-matrix可以表示为所有束缚和谐振线的总和，其中绿色函数和t-matrix是单值函数。杆子的对称性是由S-Matrix的单位性产生的，自然会施加总和来遵守适当的阈值行为。 Green功能和T-Matrix的假想部分与可观察到的物品直接相关，例如散射横截面或强子共振的不变或缺失的质量分布。因此，我们可以通过将其假想部分拟合到可观察到的物体来确定其极点和残基。我们还通过关于$ t $ -matrix的虚构部分来测试新方法，该部分按模型理论准确地计算为虚拟实验数据。作为模型理论，我们在带有频道的手性统一模型中采用双通道梅森 - 巴里昂散射，$ \ overline {k} n（i = 0）$和$πς（i = 0）$。通过拟合通过模型理论计算出的$ t $ -matrix的假想部分，我们获得了极点和残基。将所获得的结果与模型理论中确切计算的结果进行比较，我们得出结论，我们的新方法效果很好。
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.
