Higgs constraints from vector boson fusion and scattering

We present results on 4-lepton + 2-jet production, the partonic processes most commonly described as vector boson pair production in the Vector Boson Fusion (VBF) mode. This final state contains diagrams that are mediated by Higgs boson exchange. We focus particularly on the high-mass behaviour of the Higgs boson mediated diagrams, which unlike on-shell production, gives information about the Higgs couplings without assumptions on the Higgs boson total width. We assess the sensitivity of the high-mass region to Higgs coupling strengths, considering all vector boson pair channels, $W^-W^+$, $W^\pm W^\pm$, $W^\pm Z$ and $ZZ$. Because of the small background, the most promising mode is $W^+ W^+$ which has sensitivity to Higgs couplings because of Higgs boson exchange in the $t$-channel. Using the Caola-Melnikov (CM) method, the off-shell couplings can be interpreted as bounds on the Higgs boson total width. We estimate the bound that can be obtained with current data, as well as the bounds that could be obtained at $\sqrt{s}=13$~TeV in the VBF channel for data samples of 100 and 300 fb$^{-1}$. The CM method has already been successfully applied in the gluon fusion (GGF) production channel. The VBF production channel gives important complementary information, because both production and decay of the Higgs boson occur already at tree graph level.