  The scalar singlet model extends the Standard Model with the addition of a
new gauge singlet scalar. We re-examine the limits on the new scalar from
oblique parameter fits and from a global fit to precision electroweak
observables and present analytic expressions for our results. For the case when
the new scalar is much heavier than the weak scale, we map the model onto the
dimension-six Standard Model effective field theory (SMEFT) and review the
allowed parameter space from unitarity considerations and from the requirement
that the electroweak minimum be stable. A global fit to precision electroweak
data, along with LHC observables, is used to constrain the parameters of the
high scale singlet model and we determine the numerical effects of performing
the matching at both tree level and 1-loop.
