Two Loop Renormalization of Scalar Theories using a Geometric Approach

Understand

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach.

• This formula allows the two-loop results of our previous paper to be applied to a wide range of theories.
• The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives.
• We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field.