The Smoking Gun: Search for a $CP$-odd Higgs boson decaying to a heavy $CP$-even Higgs boson and a $Z$ boson in the $\ell\ell t\bar{t}$ and $\nu\bar{\nu}b\bar{b}$ final states with the ATLAS experiment and upgrade of the ATLAS Inner Tracker for the High Luminosity LHC

The Standard Model (SM) of particle physics is considered one of the most outstanding achievements of modern physics. It has successfully explained the existence of elementary particles and their interactions. Numerous experiments have been conducted to confirm the SM's predictions. So far, the experimental observations agree with the SM predictions. One of the most significant confirmations came in 2012 with the discovery of the Higgs Boson at the LHC. However, the SM alone cannot address many outstanding questions in modern physics, such as the existence of baryon-antibaryon asymmetry, dark matter, and dark energy (DE) in our universe. Electroweak Baryogenesis (EWB) is one of the most straightforward mechanisms explaining baryon-antibaryon asymmetry. EWB generates the observed asymmetry via the dynamics of the Electroweak symmetry breaking, hence making it tightly related to the properties of the Higgs boson. Since the Standard Model does not satisfy the conditions for baryogenesis, the simplest extension, "The Two Higgs Doublet Model" (2HDM), which predicts the existence of 5 Higgs-like particles, could potentially explain the matter-antimatter asymmetry when $300 \leq m_A \leq 700$ GeV and $m_A-m_H \geq 250$ GeV where $A$ is the CP-Odd Higgs and $H$ is the heavy neutral Higgs. The analysis presented in the thesis uses the full Run 2 ATLAS dataset of $140\text{ fb}^{-1}$ to search for a CP-odd Higgs boson $A$ that decays to a $Z$ boson and heavy neutral Higgs $H$ with two final states where the $Z$ decays into leptons or neutrinos and $H$ decays into two beauty quark or two top quarks, $A \rightarrow ZH\rightarrow lltt/vvbb$. The ATLAS experiment is preparing to upgrade the inner tracking (ITk) detector for High-luminosity LHC operation starting in 2029. One of the major components of the ITk upgrade is quality assurance and control (QA/QC), which requires testing and characterizing the micro-strip sensors and front-end electronics for noise. Studies and results of the QA/QC of the silicon microstrip sensor and development/ validation of the front-end calibration scans for the ITk microstrip sensors are presented.