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Decay of a Bound Muon to a Bound Electron

 Author / Creator
 Morozova, Anna

A bound muon in the presence of a nucleus can decay into an electron, which belongs to either continuous or discrete (bound) energy spectrum. The underlying physics of both cases differ a lot, and so does their importance. The Standard Model decay of a bound muon into an outgoing energetic electron provides a background in the experimental searches for the leptonflavorviolating µ → e conversions in the field of nucleus, whereas the decay into a bound electron for large value of Z has its analogy with the QCD due to the strong electromagnetic interaction. The present thesis focuses on the study of the latter case, i.e., the exclusive weak decay (Zµ) → (Ze) νµνe. This decay proceeds through the muon decay µ → e + νµ + νe in the presence of a spinless nucleus. We consider the setup where all the electrons were removed from the atom and there is only a muon in 1S state. The decay rates for Z = 10 and Z = 80 are calculated in two different approaches, namely, an Atomic Alchemy formalism developed by C. Greub et al., Phys. Rev. D52, 4028 (1995) and by modifying the one developed by A. Czarnecki et al., Phys. Rev. D84, 013006 (2011) for the decay of a bound muon into an outgoing energetic electron. We consider the interaction between electron and nucleus to be a Coulomb one and the spin of the nucleus is neglected. Point nucleus wave functions are used for numerical calculations of the decay rate and for the second formalism the case of a finite nucleus with the Fermi charge distribution is considered as well. It is found that the results for these approaches match for the small value of Zα, however, they are different by 41 % in the large Zα limit. In order to see if the two approaches coincide in certain approximations, we have considered two limiting cases: the muon and electron masses being almost equal and the small Zα limit. Again, in these limiting cases a good agreement, both analytical and numerical, is found between the two formalisms.

 Graduation date
 Spring 2019

 Type of Item
 Thesis

 Degree
 Master of Science

 License
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