标题： 在闵可夫斯基区域中评估参数积分而无需进行围道变形 显示英文标题

标题： Evaluating Parametric Integrals in the Minkowski Regime without Contour Deformation

摘要： 我们提出了一些示例，展示了在闵可夫斯基区域中数值计算环路积分的一种替代方法。 该方法专注于识别奇异超曲面（$\mathscr{F}$多项式的流形），并将其映射到已知点，然后通过使用爆破/扇形分解技术来解决，从而避免了轮廓变形的需要。 使用此技术，我们实现了改进的收敛性，而无需轮廓变形，众所周知，轮廓变形会通过引入例如$\mathscr{F}$多项式的导数和复杂的雅可比行列式显著增加被积函数的复杂性。 我们指出，尽管我们仅在选定的一环、两环和三环无质量以及一环有质量的例子上测试了该方法，但它在实际应用中显示出前景，相较于传统方法可能具有潜在优势。 与现有的轮廓变形实现进行比较，评估时间以说明这种替代方法的性能。 显示英文摘要

摘要： We present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the $\mathscr{F}$ polynomial) and mapping them to known points which can then be resolved by employing blow-ups/sector decomposition techniques, thereby avoiding the need for contour deformation. Using this technique, we achieve improved convergence properties without the need for contour deformation, which is known to significantly increase the complexity of the integrand by introducing, for example, derivatives of the $\mathscr{F}$ polynomial and complicated Jacobians. We highlight that while we have only tested the approach on selected one-, two- and three-loop massless and one-loop massive examples, it shows promise for practical applications, offering potential benefits over the traditional approach. Evaluation times are compared with existing contour deformation implementations to illustrate the performance of this alternative method.