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Forward-Backward Asymmetry

Another observable that can be measured experimentally is the forward-backward asymmetry of the top quark [10]. Generally in a fermion pair production process, a forward-backward asymmetric distribution originates from an interference of the vector and axial-vector ${f}\bar{{f}}$ production vertices at tree level of electroweak interaction. One can show from the spin-parity argument that in the threshold region the $t\bar{t}$ vector vertex creates S-wave resonance states, while the $t\bar{t}Z$ axial-vector vertex creates P-wave states. Therefore, by observing the forward-backward asymmetry of the top quark, we observe an interference of the S-wave and P-wave states.

In general, S-wave resonance states and P-wave 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 S-wave and P-wave states. Fig. 4.3 shows the pole position $E_n \! - \! i\Gamma_t$ of these states on the complex energy plane.

  
Figure 4.3: The positions of poles of the S-wave and P-wave states on the complex energy plane, together with the forward-backward asymmetry as a function of the energy, taking $\alpha _s(M_Z) = 0.118$ and mt = 175 GeV. The right-axis is for the forward-backward asymmetry.
\epsfxsize=7cm\epsffile{phystop/fbasym.eps}

One sees that the widths of the resonances are comparable to the mass difference between the lowest lying S-wave and P-wave states, and exceeds by far the level spacings between higher S-wave and P-wave states. This gives rise to a forward-backward 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 forward-backward asymmetry as a function of the energy. It is seen that the asymmetry takes its minimum value at around the lowest lying S-wave state, where the interference is smallest, and increases up to $\sim 10$% with energy as the resonance spectra appear closer to each other. One may also confirm that essentially the forward-backward asymmetry measures the degree of overlap of the S-wave and P-wave states by varying the coupling constant $\alpha _s$ or the top quark decay width $\Gamma_t$.


next up previous contents
Next: B) Decay of Top Up: 4.2.3 Observables Previous: Top Momentum Distribution
ACFA Linear Collider Working Group
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