  We study the decay of a heavy Higgs boson into a light Higgs pair at one loop
in the singlet extension of the Standard Model. To this purpose, we construct
several renormalization schemes for the extended Higgs sector of the model. We
apply these schemes to calculate the heavy-to-light Higgs decay width at
next-to-leading order electroweak accuracy, and demonstrate that certain
prescriptions lead to gauge-dependent results. We comprehensively examine how
the NLO predictions depend on the relevant singlet model parameters, with
emphasis on the trademark behavior of the quantum effects, and how these change
under different renormalization schemes and a variable renormalization scale.
Once all present constraints on the model are included, we find mild NLO
corrections, typically of few percent, and with small theoretical
uncertainties.
