A very interesting paper
appeared one week ago in the Arxiv. It is titled "Higgs Self-Coupling Measurements at the LHC
", and it is authored by M.Dolan, C.Englert, and M.Spannovsky. The idea is that once and if a Higgs boson is found at the LHC, the next natural step of the research would be its characterization as a pure standard model object or a more complex, or just different, beast.
Of course, once a signal were established, the LHC experiments would certainly want to measure all its properties as precisely as possible: mass, angular distributions, cross section in all the production mechanisms, and decay modes.