This thesis explores two dominant frontiers of theoretical physics, high energy
colliders and hidden sectors. The Large Hadron Collider (LHC) is just starting
to reach its maximum operational capabilities. However, already with the current
data, large classes of models are being put under significant pressure. It is crucial
to understand whether the (thus far) null results are a consequence of a lack of
solution to the hierarchy problem around the weak scale or requires expanding
the search strategy employed at the LHC. It is the duty of the current generation
of physicists to design new searches to ensure that no stone is left unturned. To
this end, we study the sensitivity of the LHC to the couplings in the Standard
Model top sector. We find it can significantly improve the measurements on Zt R t R
coupling by a novel search strategy, making use of an implied unitarity violation
in such models. Analogously, we show that other couplings in the top sector can
also be measured with the same technique. Furthermore, we critically analyze a
set of anomalies in the LHC data and how they may appear from consistent UV
completions. We also propose a technique to measure lifetimes of new colored
particles with non-trivial spin.
While the high energy frontier will continue to take data, it is likely the only
collider of its kind for the next couple decades. On the other hand, low-energy
experiments have a promising future with many new proposed experiments to
probe the existence of particles well below the weak scale but with small couplings
to the Standard Model. In this work we survey the different possibilities, focusingon the constraints as well as possible new hidden sector dynamics. In particular,
we show that vector portals which couple to an anomalous current, e.g., baryon
number, are significantly constrained from flavor changing meson decays and rare Z
decays. Furthermore, we present a new mechanism for dark matter freezeout which
depletes the dark sector through an out-of-equilibrium decay into the Standard
Model
