How to use the Standard Model effective field theory

TL;DR

<3-5 sentences>We present a practical SMEFT framework to connect UV models to weak-scale observables via a three-step workflow: matching at a high scale to obtain Wilson coefficients, RG running down to the weak scale using the one-loop anomalous dimension matrix, and mapping these coefficients onto electroweak and Higgs observables. The covariant derivative expansion (CDE) provides a gauge-covariant, largely universal method for tree- and one-loop matching, yielding explicit dimension-six operators and their coefficients for a variety of UV scenarios. The paper consolidates these results with complete mappings to electroweak precision observables, triple gauge couplings, Higgs decay widths, and Higgs production cross sections, emphasizing bosonic operators and providing extensive appendices with Feynman rules and detailed derivations. This framework enables model builders and experimental analyses to translate precision data into robust constraints on UV physics in a gauge-invariant, systematically improvable way.

Abstract

We present a practical three-step procedure of using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. With this procedure, one can interpret precision measurements as constraints on a given UV model. We give a detailed explanation for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. This covariant derivative expansion method dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy to use for a variety of UV models. A few general aspects of RG running effects and choosing operator bases are discussed. Finally, we provide mapping results between the bosonic sector of the SM EFT and a complete set of precision electroweak and Higgs observables to which present and near future experiments are sensitive. Many results and tools which should prove useful to those wishing to use the SM EFT are detailed in several appendices.

Figures (11)

• Figure 1: SM EFT as a bridge to connect UV models and weak scale precision observables.
• Figure 2: Example diagrams that arise in the one-loop effective action.
• Figure 3: Feynman diagrams for $\vec{\Phi}_c \ne 0$ effects at one-loop.
• Figure 4: Numerical results of auxiliary functions $f_a(s)$, $f_b(s)$, and $f_c(s)$ in $\epsilon_{WWh,I}^{}(s)$. Mathematica code for these auxiliary functions can be found at http://hitoshi.berkeley.edu/HiggsEFT/auxiliary.html.
• Figure 5: Feynman rules for vacuum polarization functions.