论文标题
Nemerator海鸥和Feynman积分的扩展对称性
Numerator Seagull and Extended Symmetries of Feynman Integrals
论文作者
论文摘要
Feynman积分（SFI）方法的对称性首次扩展，以结合不可还能的分子。这是在所谓的真空和繁殖器海鸥图的背景下完成的，分别具有3和2环，并且都具有一个不可还原的分子。为此，开发了SFI（XSFI）的扩展版本。对于具有一般质量的海鸥图，发现SFI方程系统延伸了两个其他方程。第一个是分子功率中的递归方程，该方程具有替代形式作为生成函数的微分方程。第二个方程仅适用于繁殖器海鸥，不涉及分子。我们在两种情况下解决了方程系统：在单个基因座和特定的3级扇区中，我们获得了新颖的封闭形式评估和Epsilon扩展，从而扩展了无分子情况的先前结果。
The Symmetries of Feynman Integrals (SFI) method is extended for the first time to incorporate an irreducible numerator. This is done in the context of the so-called vacuum and propagator seagull diagrams, which have 3 and 2 loops, respectively, and both have a single irreducible numerator. For this purpose, an extended version of SFI (xSFI) is developed. For the seagull diagrams with general masses, the SFI equation system is found to extend by two additional equations. The first is a recursion equation in the numerator power, which has an alternative form as a differential equation for the generating function. The second equation applies only to the propagator seagull and does not involve the numerator. We solve the equation system in two cases: over the singular locus and in a certain 3 scale sector where we obtain novel closed-form evaluations and epsilon expansions, thereby extending previous results for the numerator-free case.
