Transverse Polarization of Top Quarks Produced in ee-Annihilation at O(αs)

We present the results of an O(αs) calculation of the transverse polarization of top quarks produced in e+e−-annihilation. In a first step we determine the transverse polarization of the top with regard to the hadron plane spanned by the (q, q, g) system. We then rotate the transverse components of the polarization to the lepton plane spanned by the (q, e, e−) system. After azimuthal averaging we determine the three remaining inclusive transversely polarized structure functions. Together with the one-loop and Born term contributions they determine the sin θ and sin 2θ beam-quark polar angle dependence of the transverse polarization. We present analytic and numerical results for the polarized structure functions and the polar angle dependence of the transverse polarization. We briefly comment on the transverse polarization of bottom quarks produced in e+e−-annihilation. ∗Supported in part by the BMFT, FRG, under contract 06MZ566, and by HUCAM, EU, under contract CHRX-CT94-0579 The recent discovery of the top quark at Fermilab in pp̄-collisions provides the challenge and motivation to further investigate its production and decay characteristics in other processes. A very convenient tool in this regard is the proposed linear e+e−-collider that has sufficient energy to produce top quark pairs. The produced top quarks in e+e−annihilations will be highly polarized. Furthermore they are so heavy that they decay before hadronizing. Thus the measurement of the polarization components of the produced top quarks is feasible through the study of spin-momentum correlations in top quark decay [1]. In this note we will be concerned with the transverse components of the top quark’s polarization. The Born term contributions to the top quark’s transverse polarization have been computed some time ago [2,3]. We shall present one-loop O(αs) corrections to these results. We mention that in particular the transverse normal polarization has been widely discussed in the last few years because it is a T -odd observable and thus has implications for the possible observation of CP -violation in this process. For the three-body process (γV , Z) → q(p1) + q(p2) + g(p3) we define a polarized hadron tensor according to (q = p1 + p2 + p3) Hμν(q, p1, p2, s) = ∑ q,g spins 〈q q g|jμ|0〉〈0|j ν|q q g〉 (1) Note that the spin sum does not include the quark’s spin which one wants to observe. The hadronic tensor Hμν(q, p1, p2, s) can be decomposed into a number of spin dependent and spin independent structure functions which depend on q and on the two energy variables y = 1− 2p1·q/q and z = 1− 2p2·q/q. For our purposes it is convenient to work in terms of helicity structure functions which we shall sometimes refer to as rate functions. In Table 1 we have listed a complete set of three-body helicity structure functions both in terms of the helicity and the Cartesian components of the hadron tensor. We have also listed the angular coefficients that multiply the rate functions after contraction of the hadron and the lepton tensor. The relative hadron-lepton orientation angles θ (polar) and χ (azimuthal) are defined in Fig. 1. In the following we shall refer to the plane spanned by (q, q, g) as the hadron plane and the plane spanned by (q, l, l−) as the lepton plane. In this paper we restrict our analysis to the case of unpolarized e and e− beams. Longitudinal beam polarization effects can easily be incorporated into the analysis since