Top-quark pair production near threshold.

We present a novel formalism to calculate the total and the differential cross sections for heavy unstable top-quark pair production near threshold. Within the context of the nonrelativistic quark model, we introduce the running toponium width Γ Θ (E, p) in the Schrodinger equation for the three-point Green's function that governs the tt contribution to the e + e − annihilation process. The effect of the running of the width is found to be significant in two aspects: (i) it takes account of the phase-space volume for the decay process tt → bW + bW − and provides a consistent framework for calculating the differential cross sections; and (ii) it reduces the widths of the low-lying resonances to considerably less than 2Γ t (m t 2 )