SMEFT ATLAS: The Landscape Beyond the Standard Model

TL;DR

This work provides a comprehensive, operator-centric atlas for the SMEFT, connecting a high-scale ultraviolet theory to low-energy observables through a structured chain of effective theories (SMEFT → WET). It details the Warsaw dim-6 basis and extended bases, explains how RG evolution mixes operators across classes, and highlights the role of flavour symmetries in reducing parameter space for global fits. The atlas presents systematic charts, tables, and coefficients (ρki, ηkm) that quantify how UV operators propagate to IR observables, enabling efficient UV-model discrimination and exploration of correlations across ΔF=0,1,2 processes. By integrating top-down and bottom-up approaches with advanced computational tools and comprehensive observable mappings, the paper provides a practical framework for identifying viable ultraviolet completions behind potential flavour anomalies and for guiding future experimental tests across Higgs, EWPO, and flavour sectors.

Abstract

The Standard Model Effective Field Theory (SMEFT) based on the unbroken gauge group $\text{SU(3)}_C\otimes\text{SU(2)}_L\otimes\text{U(1)}_Y$ and containing only particles of the Standard Model (SM) has developed in the last decade to a mature field. It is the framework to be used in the energy gap from scales sufficiently higher than the electroweak scale up to the lowest energy scale at which new particles show up. We summarize the present status of this theory with a particular emphasize on its role in the indirect search for new physics (NP). While flavour physics of both quarks and leptons is the main topic of our review, we also discuss electric dipole moments, anomalous magnetic moments $(g-2)_{μ,e}$, $Z$-pole observables, Higgs observables and high-$p_T$ scattering processes within the SMEFT. We group the observables into ten classes and list for each class the most relevant operators and the corresponding renormalization group equations (RGEs). We exhibit the correlations between different classes implied both by the operator mixing and the $\text{SU(2)}_L$ gauge symmetry. Our main goal is to provide an insight into the complicated operator structure of this framework which hopefully will facilitate the identification of valid ultraviolet completions behind possible anomalies observed in future data. Numerous colourful charts, and 85 tables, while representing rather complicated RG evolution from the NP scale down to the electroweak scale, beautify the involved SMEFT landscape. Over 950 references to the literature underline the importance and the popularity of this field. We discuss both top-down and bottom-up approaches as well as their interplay. This allows us eventually to present an atlas of different landscapes beyond the SM that includes heavy gauge bosons and scalars, vector-like quarks and leptons and leptoquarks.

Figures (23)

• Figure 1: Here we show the non-zero entries of the ADM.
• Figure 2: The RG running of the down-basis SMEFT Wilson coefficients from the new physics scale $\Lambda$ to the EW scale ${\mu_\text{ew}}$ is shown. Down-type Yukawa running generates a tilde-basis ($\widetilde{\cal{C}}_a$), which has to be rotated back to the down-basis ($\mathcal{C}_a$) at the EW scale. Subsequently, the Wilson coefficients are matched onto the WET and further evolved down to lower scales (${\mu_\text{had}}$) to estimate flavour observables.
• Figure 3: Cartoon of the operator mixing between the operator sets collected in Tab. \ref{['tab:grandpattern']}. See text for explanations.
• Figure 4: Class 1: Operator mixing as per criteria-I relevant for $\Delta\,F=2$ observables for the $K^0-\bar{K}^0$ and $B_{s,d}-\bar{B}_{s,d}$ mixing in the Warsaw down-basis. The solid red, dashed green and solid black lines indicate the mixing due to strong, electroweak and third generation-Yukawa couplings, respectively. Self-mixing is not depicted. The top panel is also valid for $D^0-\bar{D}^0$ mixing in the up-basis by replacing the RH down-quark $d$ with a RH up-quark $u$ in the corresponding operators. In contrast, all lines in the bottom panel are absent in the up-basis. The indices in round and curly brackets correspond to the non-conjugate and conjugate operators, respectively.
• Figure 5: Class 1: Operator mixing relevant for $D^0-\bar{D}^0$-mixing in the Warsaw up-basis. The solid black lines indicate the mixing due to bottom-Yukawa couplings. The self-mixing is not shown here.