Modified perturbation theory approach for tt̄ production and decay

The modified perturbation theory (MPT), based on direct expansion of probabilities instead of amplitudes, allows one to avoid divergences in the phase–space integrals resulting from production and decay of unstable particles. In the present Letter the range of applicability of MPT is determined numerically in the case of the process e+e−→(γ,Z)→tt̄→W+bW−b̄. It is shown that with the complete expansion in powers of the coupling constant (without Dyson resummation) MPT operates best at the energies located near the maximum of the cross-section and slightly above the maximum. In this region the MPT expansion within the next-to-leading order considerably exceeds in accuracy well-known DPA approach.