Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO (1307.5017v3)

Abstract: We consider the Standard Model, including a light scalar boson $h$, as an effective theory at the weak scale $v=246\,{\rm GeV}$ of some unknown dynamics of electroweak symmetry breaking. This dynamics may be strong, with $h$ emerging as a pseudo-Goldstone boson. The symmetry breaking scale $\Lambda$ is taken to be at $4\pi v$ or above. We review the leading-order Lagrangian within this framework, which is nonrenormalizable in general. A chiral Lagrangian can then be constructed based on a loop expansion. A systematic power counting is derived and used to identify the classes of counterterms that appear at one loop order. With this result the complete Lagrangian is constructed at next-to-leading order, ${\cal O}(v^2/\Lambda^2)$. This Lagrangian is the most general effective description of the Standard Model containing a light scalar boson, in general with strong dynamics of electroweak symmetry breaking. Scenarios such as the SILH ansatz or the dimension-6 Lagrangian of a linearly realized Higgs sector can be recovered as special cases.

• The paper develops a comprehensive EFT by extending the electroweak chiral Lagrangian to NLO, incorporating a light Higgs as a dynamic degree of freedom.
• It introduces a systematic power-counting method for operator classification, streamlining the identification of counterterms in loop calculations.
• The framework bridges traditional and contemporary approaches, aligning with models like composite Higgs to enhance tests for new physics.

Overview of Electroweak Chiral Lagrangian with a Light Higgs at NLO

The paper by Buchalla, Cata, and Krause addresses a nuanced aspect of the Standard Model (SM) of particle physics, particularly in the context of electroweak symmetry breaking. The focus is on formulating an effective field theory (EFT) that incorporates a light scalar boson, often identified with the Higgs particle, within the framework of a chiral Lagrangian. This treatment allows for an exploration of potential deviations from the SM due to unknown dynamics at higher energy scales. The paper systematically extends the electroweak chiral Lagrangian to next-to-leading order (NLO) by incorporating a Higgs-like scalar and applying a loop expansion to identify the requisite counterterms.

Key Contributions

1. Effective Field Theory Framework: The authors present a comprehensive EFT at the electroweak scale $v = 246$ GeV, considering system dynamics that include a Higgs boson as a low-energy degree of freedom. The symmetry breaking scale $\Lambda$ is assumed to be $\sim 4\pi v$ or greater, allowing the SM to be treated as an effective theory by itself with potential strong dynamics influencing electroweak symmetry breaking.
2. Chiral Lagrangian Formulation: The leading-order chiral Lagrangian is revised to include the Higgs boson, extending beyond previous approaches that focused merely on the Goldstone bosons. This formulation respects the nonlinear realization of the symmetry and introduces complex operators that represent all possible interactions up to NLO.
3. Power Counting and Operator Classification: A systematic power-counting approach is developed to classify the operators by their order in $v/\Lambda$, which facilitates the identification and organization of counterterms in the loop expansion. This distinguishes the EFT developed from merely a dimension-based expansion, aligning it closer to a realistic mapping of the SM’s limitations.
4. Comparison with Traditional Approaches: The paper delineates how this formulation surpasses traditional EFTs that use a linearly transforming Higgs by discussing its relation with the SILH framework and the dimension-6 Lagrangian. It emphasizes that the presented chiral approach encompasses these as special cases but offers broader applicability.
5. Implications and Model Linkages: The paper also examines specific UV completions like the composite Higgs model and the Higgs portal mechanism, illustrating how these models integrate into the chiral framework. Such approaches demonstrate how higher-dimensional operators contribute to the EFT and offer practical venues for probing beyond-standard-model physics at the TeV scale.

Theoretical and Practical Implications

Theoretically, this work provides a robust framework for exploring electroweak symmetry breaking with a light Higgs boson and offers a systematic approach to examining potential deviations from SM predictions. The structured elaboration on chiral dynamics enriches our understanding of theoretical constructs like partial compositeness, where both strongly and weakly coupled dynamics are considered.

Practically, this EFT serves as a pivotal tool for testing new physics signatures in collider experiments. It equips researchers with a comprehensive set of operators at NLO, which are essential for precision tests of the Higgs sector and potential discoveries that may signal the presence of physics beyond the SM.

Future Directions

Looking forward, advancements in both theoretical and experimental fronts could sharpen the predictions made by such EFTs. Refinements in loop computations and numerical techniques may provide more precise characterizations of potential deviations from the SM. Moreover, as experimental capabilities expand with next-generation colliders, this EFT framework could significantly contribute to detecting subtle effects that hint at new physics realms.

In summary, the paper's adoption of a chiral Lagrangian incorporating a light Higgs stands as a detailed and mathematically rigorous advancement for the physics community, stimulating further inquiry into the fundamental interactions that govern particle physics.