Running couplings in high-temperature effective field theory

In this work, we study the renormalization-group evolution of parameters in the three-dimensional effective field theory (3D EFT) that describes the thermally driven electroweak phase transition of the Higgs field. We consider tree-level and radiatively generated barriers induced by beyond the Standard Model physics, enabling a first-order phase transition at and below the soft scale, respectively. For each case, we compute the two-loop running of the 3D EFT couplings, including the effects of the leading nonrenormalizable terms. We then analyze how the new contributions to the beta functions compare with those in the super-renormalizable case, highlighting their impact on perturbative computations of the scalar potential, which describes the vacuum structure of the theory. By incorporating higher-order corrections in the mass parameter evolution, as well as the running of other effective operators, we set the stage for testing their impact on phase transition dynamics in lattice simulations.