论文标题
轮廓变形的三点函数的分析结构
The analytic structure of three-point functions from contour deformations
论文作者
论文摘要
我们使用轮廓变形探索三点函数的分析结构。该方法允许分析从间距类型到及时式制度进行持续计算。我们首先阐明了两点函数的情况，并具有明确的解释，如何变形集成轮廓和集成中的切割以获得积分的已知切割结构。然后将其应用于一环三分积分。我们根据轮廓变形阐明了相应的Landau分析的个体条件。特别是，奇异点在复杂整合平面中的出现和位置与确定物理阈值有关。作为该方法的数值实现的探索性演示，我们将其应用于传播器的功能方程组和$ ϕ^3 $理论的三点顶点的耦合系统。我们证明，在通用情况下，三点顶点函数显示剪切，可以根据修改后的Landau条件确定。
We explore the analytic structure of three-point functions using contour deformations. This method allows continuing calculations analytically from the spacelike to the timelike regime. We first elucidate the case of two-point functions with explicit explanations how to deform the integration contour and the cuts in the integrand to obtain the known cut structure of the integral. This is then applied to one-loop three-point integrals. We explicate individual conditions of the corresponding Landau analysis in terms of contour deformations. In particular, the emergence and position of singular points in the complex integration plane are relevant to determine the physical thresholds. As an exploratory demonstration of this method's numerical implementation we apply it to a coupled system of functional equations for the propagator and the three-point vertex of $ϕ^3$ theory. We demonstrate that under generic circumstances the three-point vertex function displays cuts which can be determined from modified Landau conditions.
