Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO

TL;DR

This paper develops a comprehensive effective field theory framework for the Standard Model with a light Higgs, incorporating next-to-leading order corrections to account for potential strong electroweak symmetry breaking dynamics.

Contribution

It constructs the complete NLO electroweak chiral Lagrangian with a light Higgs, generalizing previous models and including strong dynamics scenarios.

Findings

Derived systematic power counting for loop expansion.

Identified classes of counterterms at one loop order.

Unified description encompassing SILH and dimension-6 linear Higgs models.

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.