We calculate the full O(α s ) radiative corrections to the three spin independent and five spin dependent structure functions that describe the angular decay distribution in the decay of a polarized top quark into a W -boson (followed by the decay W + → l + + ν l or by W + →q + q) and a bottom quark. The angular decay distribution is described in cascade fashion, i.e. the decay t(↑) → W + + X b is analyzed in the top rest system while the subsequent decay W + → l + + ν l (or W + →q + q) is analyzed in the W rest frame. Since the structure function ratios depend on the ratio m W /m t we advocate the use of such angular decay measurements for the determination of the top quark's mass. Our results for the eight O(α s ) integrated structure functions are presented in analytical form keeping the mass of the bottom quark finite. In the limit m b → 0 the structure function expressions reduce to rather compact forms. We also present results on the m b = 0 unpolarized and polarized O(α s ) scalar structure functions relevant to the semiinclusive decay of a polarized top quark into a charged Higgs boson t(↑) → H + + X b in the Two Higgs Doublet Model when m b = 0 .1 From this point on we shall drop explicit reference to the W + →q + q decay channel since it has the same angular decay distribution as W + → l + + ν l . In fact the branching fraction into the two hadronic channels (d + u) and (s + c) exceeds that of the sum of the three leptonic channels by a factor of approximately two because of the colour enhancement factor. Although not explicitly mentioned further on, the existence of the hadronic decay mode of the W + is always implicitly assumed in the following.
We consider the decay of a polarized top quark into a polarized W -boson plus a bottom quark, followed by the decay of the W -boson into a pair of leptons or quarks. The polar angle distribution of the top spin relative to the W -momentum and the polar angle distribution of the lepton (or quark) in the W -rest frame is governed by three polarized and three unpolarized rate functions which are related to the double density matrix elements of the decay t → W + + b. We obtain analytical expressions for the O(α s ) radiative corrections to the three polarized and three unpolarized rate functions. We also provide a comprehensive discussion of the dependence of the longitudinal, transverse and normal polarization of the top quarks produced at e + e − -colliders on beam polarization parameters.
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases of their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology with an irreducible loop addition.
We calculate one-loop radiative QCD corrections to the three polarized and unpolarized structure functions that determine the beam-quark polar angle dependence of the longitudinal polarization of light and heavy quarks produced in e>e\-annihilations. We present analytical and numerical results for the longitudinal polarization and its polar angle dependence. We discuss in some detail the zero-mass limit of our results and the role of the anomalous spin-flip contributions to the polarization observables in the zero-mass limit. Our discussion includes transverse and longitudinal beam polarization effects.
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