Differential equations for loop integrals without squared propagators
Kasper Larsen (University of Southampton)

A powerful approach to compute multi-loop Feynman integrals is to reduce the integrals to a basis of integrals and set up a first-order linear system of partial differential equations for the basis integrals. In this talk I will discuss the differential equations that arise when the loop integrals are parametrized in Baikov representation. In particular, I give a proof that dimension shifts (which are undesirable) can always be avoided.
I will moreover show that in a large class of two- and three-loop diagrams it is possible to avoid integrals with squared propagators in the intermediate stages of setting up the differential equations. This is interesting because it implies that the differential equations can be set up using a smaller set of reductions.