Bose-Einstein Correlations in multi-hadronic Z$^{0}$ Decays

In a head on collision of an accelerator experiment two particles collide with a certain center of mass energy E$_{cm}$. For this study the particles are leptons (e$^{+}$,e$^{-}$ and the energy is set to 91.2 GeV, which is roughly the rest mass of the Z$^{0}$ boson. When the leptons collide, three possible processes can occur. Two of them are elastic e+e− scattering (Bhabha scattering) and inelastic e+e− scattering where both virtual photons interact and produce hadrons. The third is the annihilation of e+e− into an intermediate particle: a photon, Z$^{0}$ boson or even a mixture of both. If e+e− annihilates into an intermediate particle, at Ecm = MZ, the one into a Z$^{0}$ is preferred (see section 2.2.3). With a probability of about 30% the Z$^{0}$ decays into two leptons, either a νν¯, µ+µ−, τ+τ− or again a e+e− pair, and with about 70% probability the Z$^{0}$ decays into a qq¯ (quark-antiquark) pair which further on evolves into a final hadronic state[1]. This hadronic channel is subject of this study. During the evolution of e+e− to hadrons many different physical processes take place. Un- fortunately, the only things that can be measured, or about which the experimentalists can be quite sure, is the very initial state (electron-positron pair) and the very final state (lots of neutral and charged particles). With this information at hand it is the aim of particle physics to reveal the processes which take place during the transition from initial to final state. The theory which attempts to describe all this is the so called standard model of particle physics. Due to the complexity of the seemingly basic process e+e− → hadrons it takes the whole power of the standard model to describe all stages from initial to final state and to reproduce the measured event topologies and other quantities by means of Monte Carlo simulations. A consequence of this probabilistic treatment is that some properties or processes which take place and are measured elude themselves from being described or reproduced. The Bose-Einstein effect, which is a purely quantum mechanical effect, is an example. Even though the BE effect may play a minor role for most studies of multihadronic Z$^{0}$ decays, it is a good place to test suitable algorithms to describe it. Event topologies at the Z$^{0}$ peak are complex but not as complex as for fully hadronic W +W − decays or even events which result from proton antiproton collisions (at Fermilab for example). For those studies, BE effects are more important. For the first (W +W − decays), because the BE effect may introduce an unknown shift on the calculation of the W mass, for the second (pp¯ collisions) because way more identical bosons, which underly the BE effect, are produced. Algorithms which describe BE effects in multihadronic Z0 decays are also thought of being capable to describe the effect when it comes to W +W − decays or even pp¯ events. Chapter 2 gives an overview of the process of interest (e+e− → hadrons) and of the theories behind the different stages. In chapter 3 the experimental setup is presented and relevant aspects of the detector are discussed. A brief introduction to the theory of the BE effect and a sensitive quantity to measure it (→ Q-distribution) is given in chapter 4. Analysis related things, i.e. event selection and the measured Q-distribution, are presented in chapter 5. Chapter 6 gives a theoretical overview of the two basic methods, namely PYBOEI (BE routine of PYTHIA) and a model by V.Kartvelishvili and R.Kvatadze, used to implement BE effects into MC simulations. How the algorithms are applied and results for all used variations of the basic methods can be read in chapter 7 and chapter 8 presents an application of the BE algorithm PYBOEI on 2, 3 and 4 jet topologies. Finally chapter 9 gives a summary of what has been done.