Electroweak Tests

In the years 1989-1995 LEP was operated at centre-of-mass energies around 91 GeV in order to investigate the vector boson Z⁰, the neutral field quantum of electroweak interactions. According to the Standard Model the Z⁰ boson always decays into two fermions: either into a quark-antiquark pair which immediately fragment into jets of hadrons, or into two leptons, i.e. a pair of electrons, muons, tauons or invisible neutrinos. Fig. 2.1 shows typical Z⁰ events as reconstructed by the computer.

**Figure 2.1:** Typical Z⁰ decays seen in the ALEPH Detector a) in e⁺e^-, b) in $\mu^{+}_{}$ $\mu^{-}_{}$ , c) in two hadron jets, d) in three hadron jets.
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With 5 million hadronic Z⁰ decays registered in the ALEPH detector the electroweak parameters are precisely measured. The most famous example is the Z⁰ resonance curve ( Fig. 2.2 ) which shows clearly that only three generations of light neutrinos couple to the Z⁰. Dozens of electroweak observables like cross sections, asymmetries and polarizations have been studied in ALEPH, all in agreement with the Standard Model.

**Figure 2.2:** The Z⁰ resonance curve as measured in the ALEPH detector with predictions for 2,3 and 4 neutrino generations.
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In the years 1996-2000 the storage ring LEP was operated at centre of mass energies up to 209 GeV. Here the vector bosons W^±, the charged field quanta of electroweak interactions, are produced in pairs. Fig. 2.3 shows the measured cross section as a function of energy, which agrees nicely with the Standard Model prediction for a W mass of 80.45 GeV. The reconstructed W⁺W^- events are also used to measure the W mass which is found to be (80.45±0.04) GeV. This is presently the most precise measurement of this important quantity.

**Figure 2.3:** Measured W pair cross section in comparison to electroweak calculations.
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Both electroweak and strong interactions are described by non-abelian gauge theories which, contrary to QED, imply selfcouplings of the gauge bosons. The non-abelian nature of QCD has been proven at LEP in the analysis of four-jet events in hadronic Z decays. With the increased LEP energy also the couplings of the electroweak gauge bosons ( $\gamma$ WW and ZWW ) which are precisely predicted by the Standard Model are measured directly from the angular distributions of e⁺e^- $\to$ W⁺W^- events. Up to now no differences to the theory have been found. From hadronic W decays into charm the CKM matrix element V_cs, which was only poorly known from indirect measurements before, is now determined with high accuracy.

2003-11-11