Executive Summary : | The discovery of the Higgs boson has expanded the particle spectrum of the Standard Model (SM), suggesting the need for particles beyond the structure of the SM. Observations of lepton flavour universality violation in B mesons and the anomalous magnetic moment of the muon have led to the need to develop and understand the synergy between different probes of particle physics, particularly the physics of Kaons and direct searches relevant for the Large Hadron collider and future colliders. The analysis will explore signatures complementary to those in B decays and the muon g-2 experiment, as well as new possibilities unexplored or out of reach of these experiments. A futuristic approach will be used to demonstrate possible physics goals in the event the experiment reaches the proposed sensitivity. A similar methodology will be adapted for analyses for LHC and future $pp$ colliders. The analysis will begin by studying the effects of varying momentum reconstruction resolution of muons on eventual results, then include tau leptons using state-of-the-art techniques to improve resolution. Machine learning algorithms will be explored to achieve the best efficiencies. The final goal is to explore Axion like particles (ALPs) at both hadron and electron-positron colliders, which are a well-motivated solution to explain the difference between experimental and SM expectations of the muon g-2. The production of long-lived ALPs in association with a monochromatic photon will be probed at the pp colliders, with a systematic understanding of their backgrounds and origins. |