Z Boson Resonance

This report discusses the calculation and results of electron-positron annihilation cross sections that produce muon-anitmuon pairs, including intermediate effects such as Z boson resonance. This investigation is conducted for a range of energies using computational trapezium rule and Monte Carlo simulations and possible extensions to the investigation are suggested. The computational methods are reviewed as well as the numerical evaluation and error analysis. Introduction Electron-positron annihilation is a focus in the area of high energy particle physics. During the collision process the effects of photon exchange and the z-boson, which was discovered in 1983 at the super proton synchrotron1, can be seen as well as the interference effects that they produce. The coannihilation of electrons and positrons can produce almost any lepton-antilepton pair but this report shall specifically focus on the centre of mass energies (?s=91GeV) that produce muon-antimuon pairs. The intermediate process in this collision is the exchange of a virtual or real Z boson, which is 100 times heavier than each of the muons produced, and a photon. This exchange is mediated by the weak force which is responsible for beta decay (see fig 1) among many other types of decay, the details of which can be described by quantum electrodynamics. Quantum electrodynamics (QED) is known in the physics community as the quantum field theory (QFT) of the electromagnetic force. The aim of using QFT in this way is to help with the theoretical descri ption of high energy interactions. Dirac originally postulated this theoretical descri ption and which was then transformed into QED and used to determine weak interactions by Fermi. The purpose of this report is to investigate some of these weak interactions, namely the decay of the Z boson. QED implies that the photon is the result of the electromagnetic force with infinite range between the electron and positron. QFT leads to the conclusion that the force is infinite since it is inversely proportional to mass of the quantum exchanged. The quanta of the fields come in two varieties: fermions and bosons. The weak force is represented by the appearance of the Z boson, which is massive compared to the photon, and only exists over a miniscule range about 0.01% of the size of a proton. Z boson resonance within the electron-positron annihilation cross section is of specific interest because it's decay occurs so quickly due to it's instability that the actual particle cannot be observed. This intermediate stage lasts a billionth of a billionth of a billionth of a second2. This means that the Z-boson is virtual and only exists quantum mechanically, therefore the only place it can be observed is within the details of the cross-section.. It is also important to study this process since the discovery of the Z boson quickly lead to the discovery of weak neutral current reactions in the scattering of neutrinos on electrons and neutrons3. It was also greatly studied on the path to the discovery of the Higgs boson. Electron-positron annihilation are invaluable in everyday uses such as in medical applications, especially positron-electron tomography, more commonly known as PET, and in observations in astronomy. The mathematical formulation behind this problem can be found in section two, followed by the computational method in section three. Section four is a summary of the results found which are then discussed in section five. For extensions to this project, such as different types of particle annihilations and products, see section six.