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This thesis presents a search for dark matter production in association with a Higgs boson decaying to a pair of bottom quarks, using data from 20.3\,fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of 8 TeV collected by the ATLAS detector at the LHC. The dark matter particles are assumed to be Weakly Interacting Massive Particles, and can be produced in pairs at collider experiments. Events with large missing transverse energy are selected when produced in association with high momentum jets, of which at least two are identified as jets containing b-quarks consistent with those from a Higgs boson decay. To maintain good detector acceptance and selection efficiency of the signal across a wide kinematic range, two methods of Higgs boson reconstruction are used. The Higgs boson is reconstructed either as a pair of small-radius jets both containing b-quarks, called the ``resolved'' analysis, or as a single large-radius jet with substructure consistent with a high momentum $b\bar{b}$ system, called the ``boosted'' analysis. The resolved analysis is the focus of this thesis. The observed data are found to be consistent with the expected Standard Model backgrounds. The result from the resolved analysis is interpreted using a simplified model with a Z' gauge boson decaying into different Higgs bosons predicted in a two-Higgs-doublet model, of which the heavy pseudoscalar Higgs decays into a pair of dark matter particles. Exclusion limits are set in regions of parameter space for this model. Model-independent upper limits are also placed on the visible cross-sections for events with a Higgs boson decaying into $b\bar{b}$~and large missing transverse momentum with thresholds ranging from 150 GeV to 400 GeV.


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