Abstract

Our article is devoted to the computation of two three-loop diagrams that contribute to the decay \(b \to s\gamma \) at \(\alpha _{s}^{2}\) order. We use differential equations for master integrals (MI) to compute these diagrams for an arbitrary c-quark mass. The program CANONICA is used to obtain differential equations on a canonical basis. Using them, it is possible to solve the differential equations and obtain expressions for MI-s in terms of GPL functions. We hope that the same method can be used for other three-loop diagrams which contribute to the decay \(b \to s\gamma \) at order \(\alpha _{s}^{2}\).

中文翻译：

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高阶量子色动力学校正的计算

摘要

我们的文章是专门用于两个三回路图的有助于衰减的计算\（B \为s \伽马\）在\（\阿尔法_ {S} ^ {2} \）的顺序。我们使用主积分 (MI) 的微分方程来计算任意 c 夸克质量的这些图。程序 CANONICA 用于在规范基础上获得微分方程。使用它们，可以求解微分方程并根据 GPL 函数获得 MI-s 的表达式。我们希望同样的方法可以用于其他有助于衰减\(b \to s\gamma \)在顺序\(\alpha _{s}^{2}\) 的其他三环图。