The A Experiment (APEX), which is approved to run at the Thomas Jefferson Accelerator Facility (JLab) Hall A, will search for a new vector boson that is hypothesized to be a possible force carrier that couples to dark matter. APEX results should be sensitive to the mass range of 65 MeV to 550 MeV, and high sensitivity will be achieved by means of a high intensity ∼ 100 µA beam on a ∼ 0.3 g/cm 2 Tungsten target resulting in very high luminosity. The experiment should be able to observe an A with a coupling constant α ∼ 1×10 7 times smaller than the electromagnetic First and foremost I want to thank my advisor Prof. Gordon Cates. It has been an honor to work with him all these years and learn from one of the best in the field. I am very fascinated by his excitement and enthusiasm when he talks about physics and it always kept me motivated, even during tough times in the Ph.D. pursuit. Apart from physics, I really enjoyed our discussions on politics, religion, culture, music and his life experiences. Prof. Cates supported me not only by providing a research assistantship for over five years, but also academically and emotionally through the rough road to finish this thesis. Above all, I am thankful for being such a nice person, which made my life as a graduate student joyful. The members of my research and thesis committee, Prof. Dinko Počanić, Prof. Don Crabb and Prof. Wilson Miller provided feedback through out these years to steer my project and thesis to a success .