Phenomenology of New Physics Beyond the Standard Model at the LHC and Future Colliders

The Standard Model (SM) of particle physics has been the accepted theory of elementary particle physics for the past half century, though many of the unsolved puzzles indicate that the SM is incomplete and many promising beyond the Standard Model (BSM) theories are proposed, which would be discoverable at the Large Hadron Collider (LHC) if realized in nature. However, after the Higgs boson discovery, no direct search for new particles has yielded positive signals at the LHC. If new physics exists, it is either heavy (above the reach of current searches) or hidden (currently indistinguishable from standard model backgrounds in conventional searches). In this dissertation, we cover several aspects of new physics discovery, focusing on non-standard signal signatures at the LHC and direct or indirect searches at the future colliders. First, we consider a prototype model in which multiple dark-sector particles with similar quantum numbers couple to the fields of the visible sector via a massive mediator, which can serve as a candidate model to explain the observed dark matter (DM). We point out that such model gives rise to long dark decay chains with producing visible matter in each step, resulting in multi-jet collider signatures. We find that existing mono-jet and multi-jet searches can only exclude a tiny fraction of parameter space of this model. Such decay cascades provide a potential discovery route for multi-component dark sectors at current and future colliders. We next turn to the subject of direct searches for new particles (e.g. non-SM scalars) at future 100 TeV $pp$ colliders. The Type II Two-Higgs-Doublet Model (2HDM) is a particularly well motivated scenario, which predicts two CP-even Higgses $h$ and $H$, one CP-odd Higgs $A$, and a pair of charged Higgses $H^\pm$. If the mass splitting between the non-SM Higgs states is large enough, exotic Higgs decay channels into either a Higgs plus a Standard Model gauge boson or two lighter Higgses open up, which can weaken the reach of the conventional Higgs decay channels into SM particles. We systematically study the discover and exclusion reach via this type of decays at the LHC and future 100 TeV $pp$ colliders. We show that a future collider can significantly improve the reach compared to the LHC and cover the entire regions of parameter space allowed for such exotic decays. Finally, taking neutral naturalness models and the Minimal Supersymmetric Standard Model (MSSM) as examples, we discuss how the Higgs precision measurements at future Higgs factories can constrain the parameter space of these models, which is complementary to direct searches for new particles at high energy colliders