Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO

TL;DR

This work presents the most general electroweak effective field theory incorporating a light Higgs as a singlet, organized nonlinearly to capture possible strong dynamics of electroweak symmetry breaking. It establishes a consistent power-counting scheme and derives the complete set of next-to-leading order operators, classified into six classes, each dressed with Higgs-dependent functions. The authors explain how this chiral framework encompasses linear EFTs (e.g., dimension-6 SILH) in the small-ξ limit and illustrate UV realizations, such as MCHM5 and Higgs portal, showing concrete mappings to the EFT coefficients. The formalism enables model-independent analyses of TeV-scale new physics and provides a structured path to include loop corrections and UV completions.

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 $Λ$ 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, ${\cal O}(v^2/Λ^2)$. 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.