In t-channel diagrams the helicities of the incoming beams are directly coupled to the chirality of the (new) particles produced. If both beams are polarized, it is possible to adjust independently the polarizations of both beams. This ability provides unique possibilities for probing directly the properties of the produced particles.

Polarized e+ with P(e+)=60% in addition to P(e-)=90% rise the effective polarization up to 97% compared with only P(e-)=90%. The precision in the left--right asymmetry is given by the polarimeter resolution; it is improved by more than a factor 3 if polarized e+ are provided. Similarly, the number of interacting particles can only be enhanced with the polarization of both beams, with (P(e-),P(e+))=(80%,60%) by about a factor 1.5. These pure statistical factors are, for instance, important for top and Higgs studies.

Polarization effects have been studied at the top threshold and in the continuum. The measurement of the left-right asymmetry is crucial. Using both beam polarized (P(e-),P(e+))=(80%,60%) compared with (80%,0) leads to an improvement factor of about 3, for pure statistical reasons as explained before.

The top-Yukawa coupling plays a keyrole in understanding the mechanism of electroweak symmetry breaking. At the LHC a precision of about 20% is expected. At the ILC with 500 GeV, the measurement is particularly challenging due to kinematical limitations. A precision of 24% for mH=120 GeV for unpolarized beams is expected at the ILC. The improvement factor is about 2.5 when using (P(e-),P(e+))=(80%,60%) compared with (80%,0%) and will be rather substantial for the achievable precision.

For instance, the chiral quantum numbers of the scalar partners of the electron/positron have to be verified. This association can only be directly tested in the production of the pairs sel+L sel-R. Even a highly polarized electron beam may not be sufficient to separate this process from sel+R sel-R, since both can be produced with almost identical cross sections and have the same decay. Applying simultaneously polarized positrons, the pairs get different cross sections, can be isolated and the properties of the particles can be tested separately.

Conversely, in the case of a spin-1 resonance, e.g. the Z' particle in the SSM model (right plot), the corresponding resonance peak would be strongest for the LR configuration, with a similar polarization dependence as the SM background.

The crucial point is the fact that the systematic errors can be significantly reduced when both beams are polarized.

In order to derive model-independent bounds it is necessary to have both beams polarized.

Representative examples are the models of Randall-Sundrum (RS) and Arkani-Hamed, Dimopoulos, Dvali (ADD). The new asymmetry vanishes for both the SM and the RS scenario, so that a non-zero value unambiguously signals the ADD graviton exchange. Study was done at sqrt(s)=500 GeV.

The ultimate precision cannot be reached with Compton polarimetry, but by using a modified Blondel scheme, which requires the polarization of both beams. One gains about 1 order of magnitude in the accuracy of sin^2 theta_eff, when using (P(e-),P(e+))=(80%,60%) instead of (80%,0%).

Comparing the indirect constraints on the Higgs-boson mass with a direct measurement of m_h provides a sensitive test of the electroweak theory at the quantum level. Such a highly sensitive consistency test of the model may also possibly point towards large new-physics scales.

Such stringent bounds in Supersymmetry due to the large increase in the precision of sin^2 theta_eff will constitute, in analogy to the SM case, a powerful consistency test of SUSY at the quantum level and may be crucial to constrain SUSY parameters that are not directly experimentally accessible and to outline the required high-energy stage of the ILC.

Longitudinally-polarized e- and e+ beams are sufficient for most TGCs: for determining the TGCs, one gains about a factor 1.8 with both beams longitudinally polarized, compared with having only polarized electrons. However, transversely-polarized beams provide the unique access to one specific TGC. Both beams polarized are therefore needed to fully exploit the TGCs as sensitive test of the electroweak gauge group.