Top-quark pair production near threshold

Abstract

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 ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{F}\mathit{T}\mathit{H}\mathit{E}\mathit{T}\mathit{A}}$(E,p) in the Schr\odinger equation for the three-point Green's function that governs the tt\ifmmode\bar\else\textasciimacron\fi{} contribution to the ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ annihilation process. The effect of the running of the width is found to be significant in two aspects: (i) it takes account of the phase-space volume for the decay process tt\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}${\mathit{bW}}^{+}$b\ifmmode\bar\else\textasciimacron\fi{}${\mathit{W}}^{\mathrm{\ensuremath{-}}}$ and provides a consistent framework for calculating the differential cross sections; and (ii) it reduces the widths of the low-lying resonances to considerably less than 2${\mathrm{\ensuremath{\Gamma}}}_{\mathit{t}}$(${\mathit{m}}_{\mathit{t}}^{2}$). Furthermore, the running of the width causes the total cross section to decrease significantly at c.m. energies below the first ``resonance'' enhancement, whereas it makes the ``peak'' cross section more distinct than is obtained in the fixed toponium width approximation. We use the two-loop-improved QCD potential in our calculation, and the ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(${\mathit{m}}_{\mathit{Z}}$${)}_{\mathrm{MS}\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}$ dependences of the total and differential cross sections are studied quantitatively, where MS\ifmmode\bar\else\textasciimacron\fi{} denotes the modified minimal subtraction scheme. We find that the correlations in the ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$ and ${\mathit{m}}_{\mathit{t}}$ measurements are opposite in the total and differential cross sections, and the simultaneous measurements would lead to an accurate determination of both parameters.