Maximal cuts and differential equations for Feynman integrals. What lies beyond multiple polylogarithms?
by
Lorenzo Tancredi(KIT Karlsruhe)
→
Europe/Berlin
Main-2-313 (MPI Meeting rooms)
Main-2-313
MPI Meeting rooms
Description
The differential equations method has provided an invaluable tool for the computation of Feynman integrals. In particular, whenever Feynman integrals evaluate to multiple polylogarithms, differential equations can be put in a so called canonical form, which substantially simplifies their calculation. This simplicity can be in part traced back to the fact that canonical Feynman integrals fulfill differential equations with trivial (i.e. constant) homogeneous solutions. Unfortunately, it is well known this is not always the case. An increasing number of physically relevant Feynman integrals has been discovered, which fulfill differential equations with very non-trivial homogeneous solutions (for example, elliptic integrals). In these cases, the standard approach to the solution of their differential equations does not work, as no general method is known for determining the homogeneous solution of an arbitrarily coupled system of differential equations. In this talk I will show how by studying the maximal cut of the Feynman integrals this problem can be solved and an integral representation for the homogeneous solution of the differential equations can always be found. While, in the general case, the integrals so obtained might not be expressible in terms of known special functions, they constitute the fundamental building blocks to construct an analytic solution for the integrals under consideration.
