Well, thanks to Marco for this nice mention, made even more significant by the company of several quite esteemed theorists! I believe he mentioned me because we discussed the current and future expectations for measuring the higgs boson self-coupling at the LHC, when I could give him some information on the matter.
The article discusses two models that produce mass terms for fermions and bosons. These models do not require spontaneous symmetry breaking and have interesting experimental consequences in the absence of trilinear and quartic self-couplings of the Higgs boson. They write:
"We note that the absence of the cubic and quartic Higgs self-interactions can be tested experimentally. In particular, it is reasonable that, in a near future, LHC will give some evidence about the possible absence of the eta^3 term in the lagrangian density. This can be checked in the production of two Higgs, with a virtual Higgs decaying in two real Higgs. The process to be investigated at LHC is of course p + p → H + H. Their absence would be a fundamental check of the present model for the Higgs mechanism. We also note that possible precision tests may be suggested by the present model."
Since I am working on the search for HH pair production with CMS, I wish I could jump up and say "I will disprove your model, don't worry!" But I fear it may take a while, as the observation of Higgs pair production will require high-luminosity LHC running, which will not happen for at least one more decade. But theoretical ideas have been seen to have a long lifetime, so this is of course okay...