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

Understand

We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't~Hooft's one-loop result.

• The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field.
• We show that diagrams with factorizable topologies do not contribute to the renormalization group equations.
• The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.