论文标题
多个带有笔直轮廓的Mellin-Barnes积分
Multiple Mellin-Barnes integrals with straight contours
论文作者
论文摘要
我们展示了最近用于用于多胎Mellin-barnes（MB）积分的分析和非著作评估的圆锥船体方法，可以扩展到这些积分具有与集成变量复杂平面中的想象轴平行的直接集成轮廓的情况。例如，当一个人计算$ε$ - 二维正规化Feynman积分的$ε$扩展时，出现了该类别的MB积分，这是由于应用了两种主要策略之一（在文献中称为A和B），用于解决MB表示的$ε$ $ε$。我们升级了Mathematica软件包MBConichulls.wl，该软件包现在可用于获得具有任意直轮廓的多率MB积分的多变量串联表示形式，为自动计算此类积分提供了有效的工具。提供了包装的这一新功能，并通过计算一般运动学中的尺寸正则无质量的一环五角大楼积分和$ d =4-2ε$的$ε$扩展来提供了应用程序的示例。
We show how the conic hull method, recently developed for the analytic and non-iterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the $ε$-expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in $ε$ of MB representations. We upgrade the Mathematica package MBConicHulls.wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals. This new feature of the package is presented, along with an example of application by calculating the $ε$-expansion of the dimensionally regularized massless one-loop pentagon integral in general kinematics and $D=4-2ε$.
