Joint Theory Seminar: Daniele Artico

Title: Integration by parts identities for parametrized Feynman integrals

Abstract: Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. In my talk, I will provide a different viewpoint on these tools by working in Feynman-parameter space. I will derive a general expression for sets of IBP identities in parameter space, valid to any loop order and relying on the properties of the integrand in its projective domain. I will validate this method by deriving systems of differential equations for diagrams up to 4 loops, providing a unified perspective on the existing results and describing how non-linear algebra could further simplify the reduction problem.