论文标题
使用辅助载体减少一般的单环积分
Reduction of General One-loop Integrals Using Auxiliary Vector
论文作者
论文摘要
作为处理循环积分的关键方法，可以使用逐个组的集成（IBP）方法来减少并建立主积分的微分方程。但是，在谈论张量减少时，Passarino-Veltman（PV）还原方法也被广泛用于单环积分。最近，我们提出了一种改进的PV降低方法，即使用辅助矢量$ r $的PV减少方法，可以轻松地为任何张量级提供分析降低结果。但是，我们的结果仅适用于具有功率一的传播器的积分。在本文中，我们将我们的方法推广到具有一般张量结构和具有一般力量的传播器的一环积分。我们的想法很简单。我们通过将质量分化和适当的降低限制与供电的传播器结合在一起来解决广义还原问题。最后，我们用几个示例演示了我们的方法。在本文中，我们已经证明，使用辅助载体改进的PV还原方法是一种单环积分的自组还原方法。
As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the Passarino-Veltman (PV) reduction method is also widely used for one-loop integrals. Recently, we have proposed an improved PV reduction method, i.e., the PV reduction method with auxiliary vector $R$, which can easily give analytical reduction results for any tensor rank. However, our results are only for integrals with propagators with power one. In this paper, we generalize our method to one-loop integrals with general tensor structures and propagators with general powers. Our ideas are simple. We solve the generalised reduction problem by combining differentiation over masses and proper limit of reduction with power-one propagators. Finally, we demonstrate our method with several examples. With the result in this paper, we have shown that our improved PV-reduction method with auxiliary vector is a self-completed reduction method for one-loop integrals.
