Standard Model Extended by a Heavy Singlet: Linear vs. Nonlinear EFT

TL;DR

This paper compares linear and nonlinear effective field theories derived from an extended Standard Model with a heavy scalar singlet, clarifying their systematic relations and transition criteria.

Contribution

It provides a detailed top-down analysis of the linear and nonlinear EFTs for a Standard Model extension, illustrating their systematic connection and transition.

Findings

Confirmed the power-counting rules for EFTs

Clarified the relation between linear and nonlinear EFTs

Validated bottom-up procedures with a top-down approach

Abstract

We consider the Standard Model extended by a heavy scalar singlet in different regions of parameter space and construct the appropriate low-energy effective field theories up to first nontrivial order. This top-down exercise in effective field theory is meant primarily to illustrate with a simple example the systematics of the linear and nonlinear electroweak effective Lagrangians and to clarify the relation between them. We discuss power-counting aspects and the transition between both effective theories on the basis of the model, confirming in all cases the rules and procedures derived in previous works from a bottom-up approach.