13:00
Mellin transforms for recursive sums of Feynman integrals
Abstract
In recent meetings of the journal club, two constructions that have been
discussed are Mellin transforms and chord diagrams. In my talk, I will
continue that thread and review how a Mellin transform describes the
insertion of subgraphs into Feynman integrals. This operation comes up
in various contexts, as a concrete example, I will show how to compute
the infinite sum of rainbow diagrams in phi^3 theory in 6 dimensions. On
a combinatorial level, the procedure can be encoded by chord diagrams,
or by tubings of rooted trees, which I will mention in passing.
The talk is loosely based on doi 10.1112/jlms.70006 .