The Decay Rates of Ps Species and Bound Muon to Bound Electron Decay Behaviour
Md Samiur Rahman Mir
2021
This study of bound states composed of short-lived particles (i.e., positron and muon) serves a common purpose to describe their bound properties precisely. The calculation of a scattering amplitude can be lengthy and cumbersome when we have a specific spin preference and many Feynman diagrams. We introduce a simple technique of constructing matrices from the spinor product in the amplitudes that can reduce the number of terms saving a significant amount of time. The decay rates of positronium
more »
... tom and positronium ion have been reproduced to verify this method. The decay rate of the two-photon annihilation of di-positronium molecule is also calculated for the first time including all contributions from the tree level Feynman diagrams. On the other hand, neutrino oscillation has motivated physicists to look for charged lepton flavor violation (CLFV). The Standard Model prediction for CLFV is too small to detect in an experiment; thus any trace of this violation will require new physics. One of the important backgrounds of muon-electron conversion is the weak decay in a muonic atom. The bound muon decay rate has been analytically evaluated with approximations when the decay electron is bound in the atom. The decay rate has vanishing features at two extreme points which have been explained. ii Preface Chapter 2 and 3 are the result of close collaboration with Muhammad Mubasher. Prof. Andrzej Czarnecki and Prof. M. Jamil Aslam showed the tree level diagrams for Ps − → e − γ and Ps 2 → γγ. The symmetry factor in Appendix B was derived based on Dr. Wen Chen's note on positronium ion decay and communication with Prof. Andrzej Czarnecki and Prof. M. Jamil Aslam. Chapter 4 is a review of the search experiments and provides the motivation for bound muon study based on [1, 2, 3] . The asymptotic decay rate ratio for γ → 1 (shown in Section 5.3) was derived by Prof. Andrzej Czarnecki first; later I found the ratio for γ near 0 and 1 confirming his result. The procedure of integration in Chapter 5 was devised by me; Prof. Andrzej Czarnecki simplified the final expression with a common factor. The interpretations for vanishing decay ratio developed from the discussions with Prof. Andrzej Czarnecki and Prof. M. Jamil Aslam; my contribution was to find that neutrino wave function suppresses the radial integral in M when γ → 1. iii
doi:10.7939/r3-nkx3-0t11
fatcat:2czib45kqnczrmqv6ak24qhyeq