Towards matching effective theories efficiently

Separation of scales in quantum field theories is essential when studying the low-energy phenomenology of a given UV model. To this end, it is necessary to construct an effective field theory containing only the light degrees of freedom and matching it to the full theory, ensuring that both describe the same low-energy dynamics. Performing this matching beyond the leading order is crucial, as a great number of observables, like FCNC, only appear at the loop level in the Standard Model and in many new physics scenarios. One possibility to obtain the low-energy theory is by integrating out the heavy particles from the full theory using path integral techniques. We review this functional matching procedure at the one-loop level and discuss common challenges involved in determining the matching conditions for effective theories. Due to the great diversity of beyond the Standard Model theories and the complexity of the matching computations, an automation of this procedure is desirable. On this matter, we 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 beyond the Standard Model physics. These proceedings are based on arXiv:2012.08506 and work in progress.Comment: Contribution to the proceedings of "La Thuile 2022, Les Rencontres de Physique de la Vall\'ee d'Aoste", 6-12 March 202