Much Ado About Nothing: Searches for Higgs Boson Decays to Invisible Particles

The Standard Model (SM) predicts a branching ratio of the Higgs boson decaying to invisible particles of O(0.001), though current measurements have only set weak upper limits on this value. The small SM-allowed rate can be enhanced if the Higgs boson decays into new particles such as dark matter. This dissertation considers three searches for this signature. Two efforts involve 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV proton--proton collision data collected at the LHC with the ATLAS detector. Special attention is paid to the Vector Boson Fusion production channel - the most sensitive LHC channel to this measurement. The lack of statistically significant tension with the SM allowed an upper limit on the observed (expected) branching ratio BR(Hinv) to be placed at BR(Hinv) < 0.13 (0.13) at 95% confidence level. This result also informed a statistical combination of three independent ATLAS searches for this signature through different Higgs production mechanisms, refining the upper limit to BR(Hinv) < 0.11 (0.11) obs (exp) - the strictest limit set to date. As ATLAS collects more data, this value will continue to improve. The proposed International Linear Collider `Higgs factory' will provide unprecedented precision of this electroweak measurement. Preliminary studies presented in this dissertation use 1800 fb$^{-1}$ of $\sqrt{s}=250$ GeV polarized electron--positron data modeled with the SiD detector and predict an upper limit of BR(Hinv) < 0.003. This could provide the first evidence of non-SM Higgs boson decays.