The discovery of the Higgs boson in 2012 provided confirmation of the
proposed mechanism for preserving the electroweak $SU(2) imes U(1)$
gauge symmetry of the Standard Model of particle physics. It also
heralded in a new era of precision Higgs physics. This thesis presents a
measurement of the rate at which the Higgs boson is produced by vector
boson fusion in the $WW^{(ast)}ightarrow,elluellu$ decay channel. With gauge boson couplings
in both the production and decay vertices, a VBF measurement in this
channel is a powerful probe of the $VVH$ vertex strength. Using
$4.5$~fb$^{-1}$ and $20.3$~fb$^{-1}$ of $pp$ collision data collected
at respective center-of-mass energies of 7 and $8 ev$ in the ATLAS
detector, measurements of the statistical significance and the signal
strength are carried out in the Higgs mass range $100 leq m_H leq
200 gev$. These measurements are enhanced with a boosted decision
tree that exploits the correlations between eight kinematic inputs in
order to separate signal and background processes. At the benchmark
Higgs mass of $125.36 gev$, the significance of the data assuming the
background-only hypothesis to be true has been observed to be
$3.2sigma$ ($2.7sigma$ expected), constituting evidence of VBF Higgs boson
production. The measured signal strength (ratio of observed cross section times
branching ratio to that predicted by the SM) is
$1.27^{+0.53}_{-0.45}$. The inclusive cross section times
branching ratio is found to be $0.51^{+0.22}_{-0.17}$~pb at $sqrts =
8 ev$, consistent with the SM prediction of $0.34$~pb. No
significant deviations from the SM predictions for VBF Higgs boson
production are observed.
