The separation of scales in quantum field theories is an essential step when studying the low energy phenomenology of a given model. To this end it is convenient to construct an effective field theory (EFT) containing only the light degrees of freedom and matching it to the full theory ensuring that both describe the same low energy physics. It is important to perform this matching beyond the leading order, as a great amount of observables, like FCNC, only appear at the loop level in the SM and in many new physics scenarios. One possibility of obtaining the low energy EFT from the full theory is by integrating out the heavy particles using path integral techniques and the background field method. We will present this functional matching procedure at the one-loop level, compare it to the conventional diagrammatic approach, and discuss common challenges involved in determining the matching conditions for EFTs. Due to the great diversity of models to match and the complexity of the computations involved an automation of this procedure is desirable. On this matter, we will also present the ongoing effort to develop the Mathematica package “Matchete” facilitating the fully automatic matching for a broad range of theories. When completed, this will significantly simplify the analysis of the low energy phenomenology of BSM theories.
