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

TL;DR

This paper presents a comprehensive NNLO QCD analysis of top-quark pair production near threshold in e+e− collisions using NRQCD and potential NRQCD. By solving a momentum-space Schrödinger equation with a momentum-cutoff scheme, it obtains the total cross section and the top-quark momentum distribution, and explains why using the pole mass leads to unstable predictions. The authors introduce the 1S mass, a short-distance definition, which stabilizes the peak position and enables more robust top-mass extraction, while still requiring careful relation to the MSbar mass. They implement the top width consistently within this framework and address theoretical uncertainties, highlighting that normalization corrections remain sizable at NNLO and are not fully removable by mass redefinitions. The work lays the groundwork for precise top-mass determination at future linear or muon colliders and clarifies how to relate threshold observables to MSbar quantities.

Abstract

The complete NNLO QCD corrections to the total cross section $σ(e^+e^- \to Z*,γ*\to t\bar t)$ 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 $dσ/d |\vec k_t|$ 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.

Figures (17)

• Figure 1: Routing convention for loop momenta in ladder diagrams.
• Figure 2: The two-loop NRQCD vector current correlator with the exchange of one Coulomb gluon without relativistic corrections (a) and with the kinetic energy corrections (b).
• Figure 3: The total vector-current-induced cross section $Q_t^2 R^v$ for centre-of-mass energies $344\,\hbox{GeV}< \sqrt{q^2}< 352$ GeV in the pole mass scheme. The dependence on the renormalization scale $\mu$ (a), on the cutoff $\Lambda$ (b) and on $\alpha_s(M_Z)$ (c) is displayed. More details and the choice of parameters are given in the text.
• Figure 4: The total axial-vector-current induced cross section $R^a$ for centre-of-mass energies $344\,\hbox{GeV}< \sqrt{q^2}< 352$ GeV in the pole mass scheme. The dependence on the renormalization scale $\mu$ (a), on the cutoff $\Lambda$ (b) and on $\alpha_s(M_Z)$ (c) is displayed. More details and the choice of parameters are given in the text.
• Figure 5: The three-momentum distribution of the vector-current-induced cross section $Q_t^2 R^v$ for centre-of-mass energies $\sqrt{q^2}=M_{peak}$ and $M_{peak}+5$ GeV in the pole mass scheme. The dependence on the renormalization scale $\mu$ (a), on the cutoff $\Lambda$ (b) and on $\alpha_s(M_Z)$ (c) is displayed. More details and the choice of parameters are given in the text.