Abstract
We consider the Standard Model, including a light scalar boson h, as an effective theory at the weak scale v=246 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 Λ is taken to be at 4πv 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, O(v2/Λ2). 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.
Highlights
The recent discovery of a scalar sector in the Standard Model has been one of the most important breakthroughs of the last decades in particle physics
This paper is organized as follows: in Section 2 we review the Standard Model chiral Lagrangian at leading order as the most general description of electroweak symmetry breaking
The framework allows for the possibility of dynamical electroweak symmetry breaking and a composite nature of h
Summary
The recent discovery of a scalar sector in the Standard Model has been one of the most important breakthroughs of the last decades in particle physics. More natural solutions typically call for new physics states at the TeV scale, for which there is no evidence so far Their eventual existence would typically induce deviations from the Standard Model Higgs parameters, which, even if only slight, would be of profound significance for the renormalizability and unitarization of the theory and, more generally, for our understanding of the dynamics of electroweak symmetry breaking. Given the large energy gap between the electroweak scale v = 246 GeV and the expected new physics scale Λ ∼ few TeV, this broader framework can be most cast in an effective field theory (EFT) language This EFT should provide, by construction, the most general description of the electroweak interactions in the presence of a light scalar h, and provide the right framework to test its dynamical nature.
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