Top-quark pair production close to threshold: Top-quark mass, width, and momentum distribution

Abstract

The complete next-to-next-to-leading order (NNLO) QCD corrections to the total cross section (Formula presented) in the kinematic region close to the top-quark–top-antiquark threshold, are calculated by solving the corresponding Schrödinger equations exactly in momentum space in a consistent momentum cutoff regularization scheme. The corrections coming from the same NNLO QCD effects to the top-quark three-momentum distribution (Formula presented) are determined. We discuss the origin of the large NNLO corrections to the peak position and the normalization of the total cross section observed in previous works and propose a new top-quark mass definition, the (Formula presented) mass (Formula presented) which stabilizes the peak in the total cross section. If the influence of beamstrahlung and initial state radiation on the mass determination is small, a theoretical uncertainty on the (Formula presented) top-quark mass measurement of 200 MeV from the total cross section at the linear collider seems possible. We discuss how well the (Formula presented) mass can be related to the (Formula presented) mass. We propose a consistent way to implement the top-quark width at NNLO by including electroweak effects into the NRQCD matching coefficients, which can then become complex. © 1999 The American Physical Society.