In 1995 the top quark was discovered at the Tevatron proton-antiproton collider at Fermilab by the CDF and DO collaborations. It is the most massive known elementary particle and its mass is currently measured with a precision of about 1.3%. However, the measurements of several other top quark properties are still statistically limited, so the question remains whether the Standard Model of elementary particle physics successfully predicts these properties. This thesis addresses one interesting aspect of top quark decay, the helicity of the produced W boson. Until the start of the Large Hadron Collider (LHC) at CERN, the Tevatron with a center-of-mass energy of ps = 1.96 TeV is the only collider, where top quarks can be produced. In the Standard Model the top quark decays predominantly into a W boson and a b quark, with a branching ratio close to 100%. The V-A structure of the weak interaction of the Standard Model predicts that the W+ bosons from the top quark decay --> W+b are dominantly either longitudinally polarized or left handed, while right handed W bosons are heavily suppressed and even forbidden in the limit of a massless b quark. Under the assumption of a massless b quark, for a top quark mass of 173 GeV/c2 the Standard Model predicts the fraction F0 of longitudinally polarized W bosons to be 0.7 and 0.3 for the fraction F- of left handed W bosons, while the fraction F+ of right handed W bosons is predicted to be zero. Since next-to-leading order corrections change these fractions only slightly, a significant deviation from the predicted value for F0 or a nonzero value for F+ could indicate new physics. Left-right symmetric models, for example, lead to a significant right handed fraction of W bosons in top decays. Such a right handed component (V+A coupling) would lead to a smaller left handed fraction, while F0 would remain unchanged. Since the decay rate to longitudinal W bosons depends on the Yukawa coupling of the top quarks, the measurement of F0 is sensitive to the mechanism of electroweak symmetry breaking. Alternative models can lead to an altered F0 fraction. In this analysis the W helicity fractions are measured in a selected sample rich in tt events where one lepton, at least four jets, and missing transverse energy are required. All kinematic quantities describing the tt decay are determined. As a sensitive observable, we use the cosine of the decay angle .*, which is defined as the angle between the momentum of the charged lepton in the W boson rest frame and the W boson momentum in the top quark rest frame. The data used in this analysis were taken with the Collider Detector at Fermilab (CDF II) in the years 2002 - 2006 and correspond to an integrated luminosity of about 955 pb-1.
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