Standard model extended by a heavy singlet: Linear vs. nonlinear EFT

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.