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 ΓFTHETA(E,p) in the Schr\"odinger 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⁺b{}W^- 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 2Γₜ(mₜ²). Furthermore, the running of the width causes the total cross section to decrease significantly at c.m. energies below the first ``resonance'' enhancement, whereas it makes the ``peak'' cross section more distinct than is obtained in the fixed toponium width approximation. We use the two-loop-improved QCD potential in our calculation, and the αₛ(mZ{)}_{MS{{}}}$ dependences of the total and differential cross sections are studied quantitatively, where MS{} denotes the modified minimal subtraction scheme. We find that the correlations in the αₛ and mₜ measurements are opposite in the total and differential cross sections, and the simultaneous measurements would lead to an accurate determination of both parameters.