Building Bases of Loop Integrands

Understand

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories.

• We provide a graph-theoretic definition of `power-counting' for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior.
• This allows amplitude integrands to be constructed iteratively.
• We illustrate these ideas with concrete applications.