The striking success of the standard model in explaining precision data and, at the same time, its lack of explanations for various fundamental phenomena, such as dark matter and the baryon asymmetry of the Universe, suggest new physics at an energy scale that greatly exceeds the electroweak scale. In the absence of a short-range–long-range conspiracy, the standard model can be viewed as the leading term of an effective “remnant” theory (referred to as the SMEFT) of a more fundamental structure. In recent years, many aspects of the SMEFT have been investigated, and it has become a standard tool for analyzing experimental results in an integral way. In this review, after a presentation of the salient features of the standard model, the construction of the SMEFT is reviewed. The range of its applicability and bounds on its coefficients imposed by general theoretical considerations are discussed. Since new-physics models are likely to exhibit exact or approximate accidental global symmetries, especially in the flavor sector, their implications for the SMEFT are also discussed. The main focus of the review is the phenomenological analysis of experimental results. How to use various effective field theories to study the phenomenology of theories beyond the standard model is explicitly shown. Descriptions of the matching procedure and the use of the renormalization group equations are given, allowing one to connect multiple effective theories that are valid at different energy scales. Explicit examples from low-energy experiments and from high-$p_T$ physics illustrate the workflow. Also commented upon are the nonlinear realization of electroweak symmetry breaking and its phenomenological implications.

• Received 27 March 2023

DOI:https://doi.org/10.1103/RevModPhys.96.015006