  Perhaps the most important question in particle physics today is whether the
boson with mass near 125 GeV discovered at the Large Hadron Collider (LHC) is
the Higgs Boson of the Standard Model. Since a particularly important property
of the Standard Model Higgs is its role in unitarizing longitudinal WW
scattering, we study the ability of the LHC to probe this process in the case
of same-sign W pair production. We find that the use of the Matrix Element
Method increases the significance with which the Higgs sector can be probed in
this channel. In particular, it allows one to distinguish between a light and
heavy SM Higgs in this channel alone with a high degree of significance, as
well as to set important limits in the parameter space of the Two Higgs Doublet
Model and the Strongly-Interacting Light Higgs Model with less than 200/fb at
the 14-TeV LHC, thus providing crucial information about the putative Higgs
boson's role in electroweak symmetry breaking.
