The Standard Model as an Effective Field Theory (1706.08945v3)

Abstract: Projecting measurements of the interactions of the known Standard Model (SM) states into an effective field theory (EFT) framework is an important goal of the LHC physics program. The interpretation of measurements of the properties of the Higgs-like boson in an EFT allows one to consistently study the properties of this state, while the SM is allowed to eventually break down at higher energies. In this review, basic concepts relevant to the construction of such EFTs are reviewed pedagogically. Electroweak precision data is discussed as a historical example of some importance to illustrate critical consistency issues in interpreting experimental data in EFTs. A future precision Higgs phenomenology program can benefit from the projection of raw experimental results into consistent field theories such as the SM, the SM supplemented with higher dimensional operators (the SMEFT) or an Electroweak chiral Lagrangian with a dominantly $J^P = 0^+$ scalar (the HEFT). We discuss the developing SMEFT and HEFT approaches, that are consistent versions of such EFTs, systematically improvable with higher order corrections, and comment on the pseudo-observable approach. We review the challenges that have been overcome in developing EFT methods for LHC studies, and the challenges that remain.

• The paper demonstrates that treating the Standard Model as an effective field theory allows inclusion of higher-dimensional operators to capture subtle effects beyond traditional predictions.
• It details how the SMEFT and HEFT frameworks systematically extend the Standard Model to interpret precision data from high-energy experiments.
• The study highlights challenges such as theoretical consistency and complex higher-order corrections, underscoring the need for refined EFT methods in future research.

The Standard Model as an Effective Field Theory: A Summary

The paper "The Standard Model as an Effective Field Theory" by Ilaria Brivio and Michael Trott provides an in-depth exploration of the application of effective field theory (EFT) to the Standard Model (SM), particularly in the context of high-energy physics research conducted at the Large Hadron Collider (LHC). The overarching goal is to accommodate potential deviations from the Standard Model at higher energies, which are crucial due to the absence of new state discoveries beyond the Higgs boson at the LHC.

Key Concepts and Insights

1. Effective Field Theory (EFT) Framework:
   • EFT is presented as a powerful tool for interpreting measurements at the LHC, where the SM is treated as an EFT that could break down at higher energies.
   • This framework allows theorists to analyze data and predict new physics by considering the SM supplemented with higher dimensional operators (SMEFT) or electroweak chiral Lagrangians like HEFT.
2. SMEFT and HEFT:
   • The Standard Model Effective Field Theory (SMEFT) involves extending the SM by including higher-dimensional operators that encapsulate possible new physics effects without assuming specific heavy particles or dynamics.
   • The Higgs Effective Field Theory (HEFT) generally considers modifications to Higgs coupling without committing to a specific model, contrasting the SMEFT by not embedding the Higgs in a full SU(2) doublet context.
3. Interpretation and Measurements:
   • The EFT approach provides a systematic method to interpret experimental data, projecting raw results into consistent field theories.
   • The paper emphasizes integrating electroweak precision data with EFT, illustrating how historical examples and precision Higgs phenomenology contribute to understanding possible SM anomalies.
4. Challenges and Developments:
   • The authors discuss the challenges in adopting EFT methods for interpreting LHC data, particularly in dealing with the complexities of higher order corrections and pseudo-observable approaches.
   • A compelling aspect is the focus on existing challenges such as ensuring theoretical consistency, studying the IR effects of potential UV completions, and managing ambiguities in indirect knowledge of BSM physics.
5. Future Prospects and Theoretical Implications:
   • The review considers the role of indirect evidence in leading new physic discoveries, historically gathering momentum from precise SM predictions.
   • Theoretical ambiguities associated with indirect discovery suggest a potential richness in future data exploration that could distinguish between competing EFT formulations.

Practical and Theoretical Implications

The paper articulates that through systematic improvement and theoretical precision, effective field theories like SMEFT and HEFT can offer deeper insights into our current understanding of particle physics. Practically, this means that even in the absence of direct discoveries, research efforts must focus on refining our comprehension of SM physics to sharpen predictions and highlight possible deviations that would indicate new physics. The theoretical landscape, additionally, is expanded by proposing methods for systematically improving and encoding data into formats suitable for future explorations where the SM might falter.

Conclusion

"The Standard Model as an Effective Field Theory" stands as a comprehensive review and a roadmap for utilizing EFT to interpret high-energy physics data. The paper's insightful discussion on the development, applications, and complications of SMEFT and HEFT highlights the continuing dialogue in particle physics research: setting the stage for potential breakthroughs in our understanding of fundamental interactions through indirect evidence and the precision paper of known particles, particularly the Higgs boson. As physicists advance in analyzing LHC results and other experimental data, the meticulous application of EFT principles becomes crucial in the exploration for physics beyond the current paradigm of the Standard Model.