Since its discovery in cosmic rays in 1937, the muon has played an important role in our understanding of nature. The muon has been extensively studied to determine its own properties and interactions and it has also been used as a probe to reveal the nature of other particles and systems. Indeed, it was the muon which gave us the first indication that nature replicates particles in a similar pattern, now known as generations. The existence of generations, and the muon itself for that matter, persists as a big mystery after over 50 years. With its 2.2 s mean life, one of the longest of all elementary particles unstable under weak decay, it also provides a rich variety of applications in diverse areas of science, including condensed matter physics and chemistry.
From my somewhat biased point of view, currently there is renewed interest in basic muon physics, mainly on two fronts. High energy physicists are seriously considering the design and construction of a muon collider (the First Muon Collider), which if realized, has a potential to become a ``Higgs Factory,'' as well as achieving a much higher collision energy than the existing electron colliders. At low energy, or the precision front as it is sometimes called, muonic processes forbidden (or highly suppressed) by the Standard Model, such as the decays , and , have drawn continuing and perhaps recently more intensified attention as a probe of the physics beyond the Standard Model. In particular, many Supersymmetic and/or Grand-Unified extensions of the Standard Model, the current theoretical favorite, naturally require these processes to occur, which, if observed, would have a considerable impact on the way we see our Universe.
Although its fundamental properties and interactions are of great interest, for the purpose of this thesis, which focuses on atomic and molecular aspects of muon physics, much of the behavior of the negative muon can be described by that of a heavy electron. Nevertheless, because of the muon's heavy mass, comparable to that of light nuclei, the muonic system exhibits many unique characteristics, including the catalysis of nuclear fusion among hydrogen isotopes. As we will see, the nuclear and particle physics aspects of muonic processes become important experimentally in understanding various systematic effects and background processes encountered in our experiment. In addition, because of the use of solid targets, condensed matter physics comes into play. Indeed, this experiment allows me an opportunity to learn about a rich variety of physics at energy scales spanning over more than twelve orders of magnitude, from the hydrogen Debye temperature of 10-2 eV to the electroweak scale of 1011 eV.
In the rest of this chapter, I will give a brief review of CF and describe the concept of our experiment. Chapter 2 focuses on the theoretical aspect, while the experiment apparatus is described in Chapter 3. Chapter 4 gives a summary of our experimental runs. After explaining our simulation codes in Chapter 5, the details of the analysis will be given in Chapters 6-8, which be followed by a discussion and conclusion.