- The paper introduces a three-step procedure that connects UV theories and weak scale phenomena through SM EFT.
- It details the covariant derivative expansion technique to compute effective actions while preserving gauge invariance.
- Renormalization group evolution and mapping to precision observables enable robust predictions for new physics across electroweak measurements.
The paper "How to use the Standard Model effective field theory" by Henning, Lu, and Murayama presents a comprehensive methodology for employing the Standard Model Effective Field Theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. This work encapsulates a systematic three-step procedure: matching, running, and mapping, which simplifies the process of deriving experimental implications of new physics models from their theoretical formulations.
Purpose and Motivation
The primary aim of the paper is to provide a practical pathway that bridges the gap between UV models, which often represent potential Beyond the Standard Model (BSM) physics, and observable quantities at scales accessible to experiments. The authors underscore the importance of SM EFT as a tool that respects electroweak gauge invariance and hence provides a robust framework for extending the Standard Model (SM) consistently.
Key Contributions
Covariant Derivative Expansion (CDE)
A significant contribution of the paper is the detailed exposition of the Covariant Derivative Expansion, a technique that allows the calculation of the effective action from a given UV model while maintaining gauge invariance at every step. This method simplifies the matching step by expressing the effective action as a series of commutators involving the covariant derivatives and fields, making the connection between the UV theory and low-energy effective operators more transparent and systematized. The authors provide universal results that apply to a wide variety of scenarios involving scalars, fermions, and gauge fields.
Renormalization Group (RG) Running
The authors address the importance of RG evolution in going from the high-energy matching scale to the weak scale, where measurements are made. The running of the Wilson coefficients due to the SM interactions is crucial for making precise predictions. The paper discusses when RG running becomes practically significant, particularly emphasizing its relevance when the Wilson coefficients are generated at tree level in the UV model. The authors also elaborate on the choice of operator basis, which is essential for using published anomalous dimension matrices effectively.
Mapping to Precision Observables
The mapping of Wilson coefficients onto weak scale observables forms the last segment of the proposed procedure. The paper systematically calculates the effects of dimension-six operators on electroweak precision observables, triple gauge couplings, Higgs decay widths, and production cross sections. The results are presented for purely bosonic operators, assuming no direct coupling to fermions, which often characterize new physics scenarios focusing on the Higgs and gauge sector.
Implications and Speculations
The methodology outlined in this paper has profound implications for theoretical and experimental physics. It provides a robust framework for interpreting precision measurements and offers a universal formalism that can be applied across various UV models of new physics. The use of SM EFT allows for the retention of gauge invariance and unitarity, avoiding the pitfalls of alternative parametrization schemes that violate these principles.
In terms of future developments, the approach detailed by the authors could be instrumental in the exploration of Higgs physics and electroweak symmetry breaking, offering a path to integrate new experimental data with theoretical models. As experimental capabilities advance, particularly with potential future colliders, the framework will help bridge theoretical predictions and experimental data, potentially illuminating physics beyond the Standard Model.
This paper provides not just a theoretical toolset but also pragmatic guidance for researchers aiming to navigate the complex landscape of BSM physics. By detailing the covariant derivative expansion, discussing RG evolution, and providing comprehensive mapping results, Henning, Lu, and Murayama have laid down an invaluable framework for future explorations in particle physics. The paper serves as both a reference and a practical guide for employing the SM EFT in assessing the implications of new physics models, contributing to our understanding of the fundamental interactions in the universe.