Bose-Einstein Correlations in W pair production and multi-jet $Z^0$ decays at LEP

For more than a decade, LEP has provided particle physicists with a treasure of data. This data allowed a precise measurement of many of the Standard Model parameters, in order to test its consistency and to hunt for the undiscovered Higgs boson. In comparison, little is known about the confinement of quarks inside hadrons. Theoretical calculations in the non-perturbative regime of QCD have proven to be cumbersome and most of the time one has to rely on phenomenological models, which nature is often semi-classical. It is however clear that quantum-mechanics is the proper framework to understand the binding of quarks inside hadrons. The Bose-Einstein effect is a clear and undeniable part of this theory, complicating the statistical description of multi-hadron final states. It states that the wave function, describing a system of identical bosons (particles with integer spin) should be symmetric under permutation of these particles. As a consequence the four-momentum differences between identical bosons in a multi-hadron final state will be smaller than in a world where Bose-Einstein statistics would not apply. The main question, however, is whether bosons obey this principle if they originate from two different sources, even if the distance between these sources is known to be a factor ten smaller than the distance needed to produce a boson. The hadronic decay of two pair-produced $W$ bosons in the reaction $e^+e^- \to W^+W^-$ provides us with a laboratory to study this question. If correlations between identical bosons coming from different $W$'s can be attributed to the Bose-Einstein effect, a physical correct implementation in the current hadronisation models will not be straightforward. In addition, it will add a systematic uncertainty in the precise determination of the mass of the $W$ boson in the fully-hadronic decay channel, since it assumes the two produced $W$'s to decay independently. In this thesis, the two-particle correlations in the hadronic final states of the reaction $e^+e^- \to W^+W^-$ are extensively studied. These processes, recorded by the DELPHI detector, being one of the four LEP experiments, are separated from a range of other reactions. This is done at several centre-of-mass energies, ranging from 189-209 GeV. Nearly 6000 hadronic $WW$ decays were selected from the total data sample, 55\% of which are found to be candidates of the process $e^+e^- \to W^+W^- \to q_1\bar{q_2}q_3\bar{q_4}$, where inter-$W$ Bose-Einstein correlations can take place. The inter-$W$ BEC effect is isolated, using the remaining subset of $WW$ events corresponding to the reaction $e^+e^- \to W^+W^- \to q_1\bar{q_2}l\bar{\nu_l}$. These events are mixed and used as a reference sample where no inter-$W$ BEC can exist. Using this technique, an indication of inter-$W$ BEC was found. So far, none of the other LEP experiments have reported a similar observation. In order to quantify our result, a quantity $\Lambda$, being zero in the absence of inter-$W$ BEC, was extracted from the two particle densities measured from the data. The measured value of this parameter amounts to \begin{equation*} \Lambda=0.241 \pm 0.075 \pm 0.038, \end{equation*} where the first error is statistical and the second systematic. Using our measured result, a systematic shift in the measured $W$ mass in the fully-hadronic decay channel, using the DELPHI mass reconstruction method, is deduced. It was found that at 68\% confidence level a mass shift of 36.1 MeV/c$^2$ can not be excluded. This uncertainty will be further reduced if no other LEP experiment finds an indication for inter-$W$ BEC and if the mass information obtained from semi-leptonic decays is added. In addition to $WW$ decays, three-jet $Z^0$ decays, produced during the LEP1 period at centre-of-mass energies around 91.2 GeV, can be identified as two hadronizing sources. The three-jet topologies correspond to the reaction $e^+e^- \to Z^0 \to q\bar{q}g$, where one of the two quarks radiates a hard gluon. A semi-quantitative study of this system is made of, in particular, the correlations between particles originating from the gluon. It is found that, concerning two-particle BEC, the hadronic decays of a $Z^0$ are very similar to hadronic $WW$ decays, provided that only light quark decays are considered. The correlations inside three-jet $Z^0$ decays are nearly as strong as those measured in two jet decays, confirming the presence of BEC between two hadronizing sources. Moreover, strong correlations are observed inside gluon jets. The nature of these correlations and the shape of the normalised density distribution in this system needs to be further investigated in order to obtain further insights on the true nature of Bose-Einstein correlations in two hadronizing systems.