Abstract: With no direct observation of physics beyond the Standard Model at the Large Hadron Collier, bottom-up effective field theories (EFTs), especially in the newly established Higgs sector, have become popular in the past years. Depending on the assumptions on the Higgs-like scalar, two different EFTs can be constructed: The Standard Model EFT (SMEFT), which assumes the Higgs is part of an SU(2) doublet, and the Electroweak Chiral Lagrangian (EWChL), which treats the Higgs scalar as independent singlet.

In the first part of my talk, I will discuss the assumptions underlying these two EFTs and the different power counting schemes that arise within them. In the second part, I will derive a master formula for the complete one-loop renormalization of a generic Lagrangian employing background-field method and super-heat-kernel expansion. Then, I will apply the formula to the two Higgs EFTs and discuss the results.