A Systematic Approach to the SILH Lagrangian

Abstract

We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small $\xi =v^2/f^2$. Here $v$ is the electroweak scale and $f$ is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SILH) to first order in $\xi$, can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in $\xi$ has to be performed. We point out that terms of order ${\xi }^2$, which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order $\xi /16{\pi }^2$ that are retained, as long as $\xi >1/16{\pi }^2$. Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset $SO(5)/SO(4)$ is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on $SU(2{)}_L\otimes SU(2{)}_R/SU(2{)}_V$.

22 pages, 1 figure; improved presentation of the results in section 4

References in corpus (8)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Light custodians in natural composite Higgs models
• A Higgs-Higgs bound state due to New Physics at a TeV
• Tasi 2009 lectures: The Higgs as a Composite Nambu-Goldstone Boson
• Pseudo-Goldstone Higgs Production via Gluon Fusion
• Minimal Composite Higgs Models at the LHC
• Sigma Decomposition

Cited by in corpus (4)

• Higgs boson couplings: measurements and theoretical interpretation
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• Tracks of resonances in electroweak effective Lagrangians
• The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector