Massive elementary particles in the Standard Model and its supersymmetric triplet Higgs extension

In this dissertation, we focus on massive elementary particles in the Standard Model and its supersymmetric triplet Higgs extension. In the first part, we start with a review of electroweak (EW) sector in the Standard Model. Motivated by nonzero neutrino masses, we consider triplet scalars in addition to the Standard Model. The vacuum expectation values of scalar triplets are strongly constrained by the $\rho$ parameter, extracted from electroweak precision measurements. Therefore, we introduce a custodial symmetry to weaken this constraint and obtain the well-known Georgi-Machacek (GM) Model. The GM model still requires fine-tuning to satisfy the $\rho$ parameter constraint. It is because the custodial symmetry is broken by the hypercharge gauge interaction, which leads to quadratic divergences in the quantum corrections to the $\rho$ parameter, starting at the 1-loop level. By adopting supersymmetry (SUSY), which solves the quadratic divergence problem in quantum corrections both to the $\rho$ parameter and to the squared mass of Higgs simultaneously, we obtain the Supersymmetric Custodial Triplet Model (SCTM). It doubles the GM scalar fields with the \emph{mirror}-GM sector. In the limit of large dimensionful parameters, $B$-terms, the \emph{mirror}-GM particles are decoupled, and the spectrum of the GM-like particles looks the same as that in the GM model at the electroweak scale. We dub this limit as the ``supersymmetric GM (SGM) model\u27\u27, which serves as a weakly coupled origin for the GM model. Incorporating the gauge-mediated supersymmetry breaking (GMSB) mechanism, we perform a phenomenological study for a pair of benchmark scenarios to illustrate when the SGM model can behave in the same way as the GM model, and when the GM and SGM models are distinguishable. When confronting the experimental diphoton data, we take the GM and SGM models as explicit examples to show how a light exotic Higgs boson can escape the current experimental constraints through cancellations between different loop contributions to the effective couplings, or via decaying into the invisible sector. In the second part, we focus on massive particle production, both in DIS experiments and at hadron-hadron colliders. By applying the QCD factorization theorem, hadronic cross sections can be factorized as convolutions of long-distance parton distribution functions (PDFs) and short-distance partonic cross sections. The partonic cross section can be obtained through perturbative calculations, thanks to the asymptotic freedom of the strong interaction. The universal PDFs have to be extracted from experimental data and are gradually becoming the largest uncertainty source that obscures the discovery of the new physics, especially at hadron colliders. Precise determinations of the PDFs require us to treat the massive quarks correctly. We discuss various factorization schemes to deal with the massive quarks in DIS, and we perform the calculations of the DIS structure functions in the intermediate-mass scheme at N3LO. We develop a new method called the SACOT-MPS (Simplified-ACOT with massive phase space) scheme to deal with heavy-quark production at hadron colliders, and we apply it to the $B^{\pm}$ production at the LHCb experiment