Electroweak corrections in fermionic decays of heavy Higgs bosons

Extensions of the Standard Model often come with additional, possibly  
electroweakly charged Higgs states, the prototypal example being the  
Two-Higgs-Doublet Model. While collider phenomenology does not exclude  
the possibility for some of these new scalar fields to be light, it is  
relatively natural to consider masses in the multi-TeV range, in which  
case the only remaining light Higgs boson automatically receives  
SM-like properties. The appearance of a hierarchy between the  
new-physics states and the electroweak scale then leads to sizable  
electroweak corrections, e.g. in the decays of the heavy Higgs bosons,  
which are dominated by effects of infrared type, namely Sudakov  
logarithms. Such radiative contributions obviously affect the two-body  
decays, but should also be paired with the radiation of electroweak  
gauge bosons (or lighter Higgs bosons) for a consistent picture at the  
one-loop order. Resummation of the leading terms is also relatively  
easy to achieve. We re-visit these questions in the specific case of  
the fermionic decays of heavy Higgs particles in the Next-to-Minimal  
Supersymmetric Standard Model, in particular pointing out the  
consequences of the three-body final states for the branching ratios  
of the heavy scalars.