  The electroweak sector of the Standard Model can be formulated in a way
similar to Chiral Perturbation Theory (ChPT), but extended by a singlet scalar.
The resulting effective field theory (EFT) is called Higgs-Electroweak Chiral
Lagrangian (EWCh$\mathcal{L}$) and is the most general approach to new physics
in the Higgs sector. It solely assumes the pattern of symmetry breaking leading
to the three electroweak Goldstone bosons (i.e. massive $W$ and $Z$) and the
existence of a Higgs-like scalar particle. The power counting of the
EWCh$\mathcal{L}$ is given by a generalization of the momentum expansion of
ChPT. It is connected to a loop expansion, making the theory renormalizable
order by order in the EFT.
  I will briefly review the construction of the EWCh$\mathcal{L}$ and its power
counting. Then, I will discuss the complete one-loop renormalization of the
EWCh$\mathcal{L}$ employing the background-field method and the
super-heat-kernel expansion. This computation confirms the power counting
assumptions, is consistent with the completeness of the operator basis, and
reproduces known results of subsectors in the appropriate limits.
