ACFA report

Precision measurement of top mass (from threshold):
For example, suppose that the Higgs boson is discovered in the future, and suppose that we want to test predictions of its mass by the Minimal Supersymmetric Model within 50 MeV accuracy. Then we need to know the top quark mass with a similar accuracy due to the large dependence of the radiative correction on the top quark mass:
Method: mass can be extracted from the shape of the total tt cross section as a function of beam energy.

The peak is the 1S resonance; the maximum sensitivity to the top mass comes from its peak position. The simple rise is not a good estimator (while it is for WW) since QCD smears the mass dependence in a way that is difficult to deconvolute.

Bound tt states:
They will exist very briefly, providing a unique interplay between QCD and EW interactions.
We will be able to make detailed tests of the dynamics of the boundstate formation and decays. This aspect is important since predictability of the theory on the quarkonium physics has improved dramatically recently. For example, so far the quarkonium wave functions calculated in perturbative QCD have never been tested experimentally, and this will be possible for the tt resonances.
By measuring the Pt distribution, we can disentangle the superposition of toponium states:

By observing forward-backward asymmetries we can disentagle the mixing between S and P states. S states come from the vector vertex, P states from axial vertex.
The spectrum of the would-be toponium resonances is such that the lowest-lying S-wave resonance (1S state) stands alone, while the higher S-wave resonances are accompanied by nearly degenerate P-wave resonances. The level spacings are determined by α_s while the resonance widths are determined mainly by the top quark width. The relative size of the two determines the size of the interference. Therefore, we expect that the forward-backward asymmetry provides additional information on the top quark width.

Polarization studies:
The top quark can be polarized maximally by polarizing the electron beam; we are guaranteed to be (almost) in the rest frame of the top quark without need to reconstruct its momentum; we do not gain resolving power by raising the c.m. energy.

CP violating couplings:
Within the SM, CP-violation in the top quark sector is extremely small. If any CP-violating effect is detected in the top quark sector in a near-future experiment, it immediately signals new physics.
There can be many sources of CP-violation in models that extend the SM. Besides, the observed baryon asymmetry in the Universe suggests existence of CP violating mechanisms beyond the SM.
In a relatively wide class of models beyond the SM, CP violation emerges especially sizably in the top quark sector.
Method:
one uses the lepton, whose same angular distribution is

If we consider the average of the lepton direction, for instance, we may extract the top quark polarization vector (S) efficiently:

(and all asymmetries will be calculated with respect to the S direction.)
The average is to be taken at the top quark rest frame, but in the threshold region, we may take the average in the laboratory frame barely without loss of sensitivities to the anomalous couplings.

Top mass from dileptonic decays:
In contrast to the hadron colliders, the beam energy at the Linear Collider provides constraints in the kinematic reconstruction.
So, at the end the dileptonic channel has much less systematic (from JES) than single-leptonic.

Yukawa coupling:
Observing ttH probes the yukawa coupling of the top, since the contribution from diagrams with H radiated from the Z is negligible:

Main bkg: tt + jets from FSR. This bkg can be reduced by cutting on the thrust:

Another bkg is ttZ, whose cross section times BR is comparable with ttH.

Other beams:
Instead of e+e-, the ILC could be run as a photon-photon or a photon-electron collider:

The photon beam is generated by inverse-Compton scattering.
Advantages for top physics: the polarization of initial state photons are controllable.