Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution

TL;DR

This paper presents precise NNLO QCD calculations for top quark pair production near threshold, introduces a new 1S mass definition to improve stability, and discusses implications for top mass measurements at linear colliders.

Contribution

It provides the first complete NNLO QCD corrections for the total cross section and momentum distribution near the top threshold, and proposes a new top mass scheme for better stability.

Findings

NNLO corrections significantly affect the peak position and normalization

The 1S mass definition stabilizes the cross section peak

Potential for 200 MeV top mass measurement accuracy at linear colliders

Abstract

The complete NNLO QCD corrections to the total cross section $\sigma(e^+e^- \to Z*,\gamma*\to t\bar t)$ in the kinematic region close to the top-antitop threshold are calculated by solving the corresponding Schroedinger 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 $d\sigma/d |\vec k_t|$ 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 mass definition, the 1S mass M_1S, 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 1S top mass measurement of 200 MeV from the total cross section at the linear collider seems possible. We discuss how well the 1S mass can be related to the $\bar{MS}$ mass. We propose a consistent way to implement the top quark width at NNLO by including electroweak effects into the NRQCD matching coefficients, which then can become complex.