Determination of the masses of electrical weak gauge bosons with L3

This thesis presents the measurement of the masses of the carriers of the weak force in the Standard Model of Particle Physics, the gauge bosons W and Z. The masses are determined using the kinematics of the bosons' decay products. The data were collected by the L3 experiment at the Large Electron Positron Collider (LEP) at centre-of-mass energies, sqrt(s), between 183 GeV and 209 GeV in the years 1997 to 2000. The mass of the Z-boson, mZ, is already known very precisely: The L3 collaboration determined it to be mZ = 91.1898 +- 0.0031 GeV from a scan of the Z resonance. Therefore the main aim of this analysis is not the determination of the numerical value of mZ; instead the analysis is used to cross-check the measurement of the W boson mass since the methods are similar. Alternatively, the analysis can be used to measure the mean centre-of-mass energy at the L3 interaction point. The Z-boson mass is determined to be mZ = 91.272 +- 0.046 GeV. If interpreted as measurement of the centre-of-mass energy, this value means a shift of Delta sqrt(s) = -175 MeV compared to the value determined by the LEP Energy Working Group. The second part of this analysis describes the measurement of the mass of the W-boson, mW. This mass is not only a prominent parameter of the Standard Model, it is also of great importance when checking the consistency of the model. The masses mW and mZ are related to the weak mixing angle, theta_W, by the Higgs mechanism: cos(theta_W) = mW/mZ. On the other hand, the weak mixing angle is defined by the weak couplings g and g' of the SU(2)xU(1) gauge symmetry: cos(theta_W) = g/sqrt(g^2+(g')^2. Therefore, there is a direct relation between the masses mW and mZ and the couplings g and g'. This relation can be tested by using the precise measurements of mW and mZ and the mesurements of other parameters of the Standard Model which lead to a measurement of cos(theta_W). By a study of the radiative corrections one can determine from these measurements the value of the mass of Higgs boson, mH. Not only the determination of the numerical value of mW is of great importance, but also the study of systematic uncertainties of the measurement. The main error sources are detector effects and effects from the hadronisation of the W bosons. Examples are uncertainties in the number of kaons or protons and interaction between the decay products of two hadronically decaying W bosons, known as Bose Einstein Correlations and Colour Reconnection. The study of these effects led to a noticeable reduction of the uncertainty compared to preliminary analyses. The W-boson mass is determined to be mW = 80.242 +- 0.057 GeV in this analysis. If combined with the L3 results at lower centre-of-mass energies, the final W boson mass value is mW = 80.270 +- 0.055 GeV. The rho parameter is defined as rho = mW^2/(mZ^2*cos^2(theta_W)), being equal to 1 in the Standard Model. Using the value of mZ obtained in the Z resonance scan, the final value for mW and the value of theta_W, rho is obtained to be rho = 0.9937 +- 0.0024, yielding a 2.6 sigma deviation from 1. Combining the L3 value for mW with the results of the LEP experiments ALEPH, DELPHI, and OPAL and the TEVATRON experiments CDF and D0 yields a W boson mass of mW = 80.392 +- 0.029 GeV. Together with other measurements this determines the best value of the Higgs-boson mass to be mH = 85 +39 -28 GeV.