The Decay Rates of Ps Species and Bound Muon to Bound Electron Decay Behaviour

Abstract

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 atom 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.