Top quark polarization in polarized $e^+e^-$ annihilation near threshold

Abstract

Top quark polarization in e + e − annihilation into tt is calculated for linearly polarized beams. The Green function formalism is applied to this reaction near threshold. The Lippmann-Schwinger equations for the S-wave and P -wave Green functions are solved numerically for the QCD chromostatic potential given by the two-loop formula for large momentum transfer and Richardson's ansatz for intermediate and small momenta. S-P -wave interference contributes to all components of the top quark polarization vector. Rescattering of the decay products is considered. The mean values nℓ of the charged lepton fourmomentum projections on appropriately chosen directions n in semileptonic top decays are proposed as experimentally observable quantities sensitive to top quark polarization. The results for nℓ are obtained including S-P -wave interference and rescattering of the decay products. It is demonstrated that for the longitudinally polarized electron beam a highly polarized sample of top quarks can be produced.

Axial contributions at the top threshold

“…Similarly, an angular dependent polarization of top quarks is induced by the S − P wave interference which adds to the dominant polarization parallel to the e + e − beams [10]. Rescattering corrections [11,12], although important for the detailed quantitative analysis, do not alter this qualitative picture.…”

“…Similarly, an angular dependent polarization of top quarks is induced by the S − P wave interference which adds to the dominant polarization parallel to the e + e − beams [10]. Rescattering corrections [11,12], although important for the detailed quantitative analysis, do not alter this qualitative picture.Clearly, the next step in this sequence of improvements are corrections of order β 2 which, for interacting quarks close to threshold, translate into corrections of order α 2 s and βα s . For the vector current this has been recently persued by different groups, which have demonstrated the importance of these next-to-next-to leading order corrections [13, 14,15].…”

“…Let us also stress that the axial 2 rate, although closely related to the S − P wave interference piece, is an independent observable. Rescattering corrections, which are present in the angular distribution and in the top polarization, are calculated to O(α s ) [11,12] but shown to be unimportant as long as the total cross section is concerned [17,18]. In addition, rescattering corrections do not affect the separation between axial and vector contributions.…”

Probe ofCPviolation ine+e−→tt¯

“…• Since top quarks are produced almost at rest, one can reconstruct the spin information of top quarks from distributions of their decay products without solving detailed kinematics [31].…”

“…On the other hand, it is known that studying various top quark properties in the tt threshold region at future e + e − colliders is promising and interesting; particularly the top quark mass will be determined to unmatched precision. A number of analyses elucidated physics potential of experiments in the tt threshold region [23][24][25][26][27][28][29][30][31][32][33][34][35]. Most of them, however, dealt only with the SM interactions.…”