论文标题
驯服Calabi-yau Feynman积分：四环相等的香蕉积分
Taming Calabi-Yau Feynman integrals: The four-loop equal-mass banana integral
论文作者
论文摘要
某些Feynman积分与Calabi-yau几何形状有关。我们演示了如何使用微分方程方法计算这些积分。四环相等的香蕉积分是最简单的Feynman积分，其几何形状是非平凡的calabi-yau歧管。我们表明，它的微分方程可以施加到$ \ varepsilon $ fartorized表单中。这使我们能够在维数正则化参数$ \ varepsilon $中获得任何所需订单的解决方案。该方法通用到其他Calabi-Yau Feynman积分。我们的计算还表明，四环香蕉积分仅比在两个或三个循环下的相应的Feynman积分更为复杂。
Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how these integrals can be computed with the method of differential equations. The four-loop equal-mass banana integral is the simplest Feynman integral whose geometry is a non-trivial Calabi-Yau manifold. We show that its differential equation can be cast into an $\varepsilon$-factorised form. This allows us to obtain the solution to any desired order in the dimensional regularisation parameter $\varepsilon$. The method generalises to other Calabi-Yau Feynman integrals. Our calculation also shows that the four-loop banana integral is only minimally more complicated than the corresponding Feynman integrals at two or three loops.
