Abstract

The renormalization group governs the scale dependence of couplings and operators, providing a systematic improvement to the perturbative expansion of quantum field theory. In this talk, I will present recent progress in deriving the two-loop renormalization group equations for the Standard Model Effective Field Theory (SMEFT) and the Low-Energy Effective Field Theory (LEFT), two central frameworks in modern particle physics. After briefly reviewing the key concepts of effective field theory, I will outline the main computational techniques used in our work: the ’t Hooft–Veltman scheme for \gamma_5, the tadpole method, and the R-operation. I will also discuss the geometric formulation of EFTs, where fields are treated as coordinates on a manifold. These methods are applied to the renormalization of the LEFT , the scalar SMEFT , the O(n) EFT , and chiral perturbation theory at two loops. The results contribute to a broader community effort toward extending the EFT framework to next-to-leading-logarithmic accuracy.