  The Standard Model of particle physics (SM) is presently the best description
of nature at small distances and high energies. However, with tiny but nonzero
neutrino masses, a Higgs boson mass unstable under radiative corrections, and
little guidance on understanding the hierarchy of fermion masses, the SM
remains an unsatisfactory description of nature. Well-motivated scenarios that
resolve these issues exist but also predict extended gauge (e.g., Left-Right
Symmetric Models), scalar (e.g., Supersymmetry), and/or fermion sectors (e.g.,
Seesaw Models). Hence, discovering such new states would have far-reaching
implications.
  After reviewing basic tenets of the SM and collider physics, several beyond
the SM (BSM) scenarios that alleviate these shortcomings are investigated.
Emphasis is placed on the production of a heavy Majorana neutrinos at hadron
colliders in the context of low-energy, effective theories that simultaneously
explain the origin of neutrino masses and their smallness compared to other
elementary fermions, the so-called Seesaw Mechanisms. As probes of new physics,
rare top quark decays to Higgs bosons in the context of the SM, the Types I and
II Two Higgs Doublet Model (2HDM), and the semi-model independent framework of
Effective Field Theory (EFT) have also been investigated. Observation prospects
and discovery potentials of these models at current and future collider
experiments are quantified.
