Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics

Abstract: We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman integrals, Fourier transform of Feynman integrals, and spin-resummed dynamics in post-Minkowskian gravity. First, we construct a mathematical framework that manifests the geometric interpretation of twisted Feynman integrals. Next, we generalise the standard mathematical tools for studying Feynman integrals for application to their twisted cousins, and explore their mathematical properties. In particular, it is found that (i) twisted Feynman integrals fall under the class of exponential periods, and (ii) the leading singularity approach using the (generalised) Baikov parametrisation applied to twisted Feynman integrals fail to detect the geometry underlying their function space.