While these CP-violating couplings may be studied using CP-violating correlations among momenta and spins which include the t and momenta and spins , it may be much more useful to study asymmetries and correlations constructed out of the initial e+/e- momenta and the momenta of the decay products, which are more directly observable. In addition, the observables using top spin depend on the basis chosen [43,42], and would require reconstruction of the basis which has the maximum sensitivity. In studying decay distributions, this problem is avoided.
Correlations of optimal CP-violating observables have been studied by Zhou . Using purely hadronic or hadronic-leptonic variables, limits on the dipole moment of the order of 10-18 e cm are shown to be possible with GeV and integrated luminosity of 50 fb-1.
Examples of CP-violating asymmetries using single-lepton angular distributions and the lepton energy correlations have been discussed in Sec. 1.6.3. In addition, we have studied, in , additional CP-violating asymmetries which are functions of lepton energy. Using suitable ranges for the lepton energy, it is possible to enhance the relative contributions of CP violation in production and CP violation in decay.
One-loop QCD corrections can contribute as much as 30% to production cross section at GeV . It is therefore important to include these in estimates of sensitivities of CP-violating observables. The effect of QCD corrections in the soft-gluon approximation in decay lepton distributions in were discussed in . These were incorporated in CP-violating leptonic angular asymmetries and corresponding limits possible at JLC with longitudinal beam polarization were presented in . These are in the laboratory frame, do not need accurate detailed top energy-momentum reconstruction, and are insensitive to CP violation (or other CP-conserving anomalous effects) in the tbW vertex.
Four different asymmetries have been studied in . In addition to two
asymmetries where the azimuthal angles are integrated over, and which are exactly
the ones defined in , there are two others which depend on azimuthal
distributions of the lepton. A cut-off
in the forward and
backward directions is assumed in the polar angle of the lepton.
The up-down asymmetry is defined by
The left-right asymmetry is defined by
The simultaneous independent 90% CL limits on the couplings which can be obtained at a linear collider with GeV with integrated luminosity 200 fb-1, and for GeV with integrated luminosity 1000 fb-1and using only e- longitudinal beam polarization are given in Table 4.2.
As can be seen from the table, the limits on the dipole couplings are of the order of a few times 10-17 e cm for GeV.