An Algebraic Formula for Two Loop Renormalization of Scalar Quantum Field Theory

Elizabeth E. Jenkins, Aneesh V. Manohar, Luca Naterop, Julie Pagès

Published 2023-08-11Version 1

We give a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, which extends 't Hooft's one-loop result. We show that factorizable topologies do not contribute to the renormalization group equations. The results will be combined with the geometric method in a subsequent paper to obtain the renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.