Bound State Phenomena: Positronium Molecule and Muon Decays, and the Electron Magnetic Moment

  • Author / Creator
    Mubasher, Muhammad
  • Particle physics is the study of the fundamental constituents of matter and their interactions. The study of bound states of elementary particles such as positronium and dipositronium, whose lifetime is short, is important for understanding properties of bound leptons with precision. The fundamental measurable quantities are the cross section and the decay rate. Theoretically, both of these quantities require the calculation of transition amplitudes, which is complicated and time consuming. We present a simple technique to compute the amplitudes and write the products of spinors in terms of gamma matrices, which reduces the computational time and provides more insights into the physics of a reaction. After testing the method with the well known problem of positronium, we apply it to $Ps_2 \\to e^- e^+$ and find that the previously published result in [Physical Review A 51, 4514 (1995)] is incorrect. Muons are playing central role for the new physics searches. Experiments, such as Mu2e and COMET, are designed to observe the charged lepton flavor violation (CLFV) for neutrinoless muon to electron conversion. For these experiments, it is important to know all the possible backgrounds, one of which is the bound muon decay that we study in this thesis. We consider the muon bound to a nucleus in 1S state decaying to a bound electron in 1S. Two important limits of the decay rate, namely extreme relativistic and extreme non-relativistic are found. In the non relativistic limit $Z \\to 0$, the resulting expression is valid up to Z = 43 with an error less than 1%.

  • Subjects / Keywords
  • Graduation date
    Fall 2021
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.