Heavy to light Higgs boson decays at NLO in the singlet extension of the Standard Model

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.