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Another observable that can be measured experimentally
is the forwardbackward asymmetry of the top quark [10].
Generally in a fermion pair production process, a forwardbackward asymmetric
distribution originates from an interference of
the vector and axialvector
production vertices at tree level
of electroweak interaction.
One can show from the spinparity
argument that in the threshold region the
vector vertex
creates Swave resonance states, while the
axialvector vertex creates Pwave states.
Therefore, by observing the forwardbackward asymmetry of the top quark,
we observe an interference of the Swave and Pwave states.
In general, Swave resonance states and Pwave resonance states have
different energy spectra.
So if the c.m. energy is fixed at some resonance in
either one of the spectra, there would be no
contribution from the other.
However, the widths of resonances are large for the toponium
in comparison to their level splittings,
which permit sizable interferences of the Swave and Pwave
states.
Fig. 4.3
shows the pole position
of these states
on the complex energy plane.
Figure 4.3:
The positions of poles of the Swave and Pwave
states on the complex energy plane, together with the forwardbackward
asymmetry as a function of the energy, taking
and m_{t} = 175 GeV.
The rightaxis is for the forwardbackward asymmetry.

One sees that the widths of the resonances are comparable to the
mass difference between the lowest lying Swave and Pwave states, and
exceeds by far the level spacings between higher Swave and Pwave states.
This gives rise to a forwardbackward
asymmetry even below threshold, and provides
information on the resonance level structure which is concealed in the total
cross section.
Shown on the same figure is the forwardbackward asymmetry as a function
of the energy.
It is seen that the asymmetry takes its minimum value
at around the lowest lying Swave state, where the interference is
smallest, and
increases up to % with energy as the resonance spectra appear
closer to each other.
One may also confirm that essentially the forwardbackward asymmetry
measures the degree of overlap of the Swave and Pwave states
by varying the coupling constant
or the top quark
decay width .
Next: B) Decay of Top
Up: 4.2.3 Observables
Previous: Top Momentum Distribution
ACFA Linear Collider Working Group
EMail:acfareport@acfahep.kek.jp