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Top-Antitop Pair Production close to Threshold: Synopsis of recent NNLO Results

A. H. Hoang, M. Beneke, K. Melnikov, T. Nagano, A. Ota, A. A. Penin, A. A. Pivovarov, A. Signer, V. A. Smirnov, Y. Sumino, T. Teubner, O. Yakovlev, A. Yelkhovsky

TL;DR

This work assesses NNLO QCD corrections to near-threshold t t̄ production at the Linear Collider using non-relativistic EFT (PNRQCD), comparing multiple NNLO calculations and diagnosing large corrections in the pole-mass scheme. It demonstrates that the pole mass induces significant renormalon-driven instabilities and normalization uncertainties, while threshold-mass definitions (PS, 1S, kinetic) offer more stable mass extractions with about 100 MeV precision. The study emphasizes that to fully exploit threshold measurements, NNNLO QCD (and a consistent electroweak treatment) as well as differential observable computations are required. Overall, threshold masses emerge as essential for precise top-quark mass determination, whereas normalisation uncertainties limit coupling-width extractions unless higher-order corrections are incorporated. The findings outline concrete technical milestones (three-loop static potential, C coefficient, RG improvements) toward more reliable predictions for top-quark physics at future colliders.

Abstract

Using non-relativistic effective theories, new next-to-next-to-leading order (NNLO) QCD corrections to the total $t\bar t$ production cross section at the Linear Collider have been calculated recently. In this article the NNLO calculations of several groups are compared and the remaining uncertainties are discussed. The theoretical prospects for an accurate determination of top quark mass parameters are discussed in detail. An outlook on possible future improvements is given.

Top-Antitop Pair Production close to Threshold: Synopsis of recent NNLO Results

TL;DR

This work assesses NNLO QCD corrections to near-threshold t t̄ production at the Linear Collider using non-relativistic EFT (PNRQCD), comparing multiple NNLO calculations and diagnosing large corrections in the pole-mass scheme. It demonstrates that the pole mass induces significant renormalon-driven instabilities and normalization uncertainties, while threshold-mass definitions (PS, 1S, kinetic) offer more stable mass extractions with about 100 MeV precision. The study emphasizes that to fully exploit threshold measurements, NNNLO QCD (and a consistent electroweak treatment) as well as differential observable computations are required. Overall, threshold masses emerge as essential for precise top-quark mass determination, whereas normalisation uncertainties limit coupling-width extractions unless higher-order corrections are incorporated. The findings outline concrete technical milestones (three-loop static potential, C coefficient, RG improvements) toward more reliable predictions for top-quark physics at future colliders.

Abstract

Using non-relativistic effective theories, new next-to-next-to-leading order (NNLO) QCD corrections to the total production cross section at the Linear Collider have been calculated recently. In this article the NNLO calculations of several groups are compared and the remaining uncertainties are discussed. The theoretical prospects for an accurate determination of top quark mass parameters are discussed in detail. An outlook on possible future improvements is given.

Paper Structure

This paper contains 5 sections, 9 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Total Cross Section at NNLO and Effective Theory Approach
  3. NNLO Results for the Total Cross Section in the Pole Mass Scheme
  4. Threshold Masses
  5. Summary and Open Issues

Figures (2)

  • Figure 1: The total normalised photon-induced $t\bar{t}$ cross section $R$ at the LC versus the c.m. energy in the threshold regime at LO (dotted curves), NLO (dashed) and NNLO (solid) in the pole mass scheme for $M_t^{\rm pole}=175.05$ GeV, $\alpha_s(M_Z)=0.119$ , $\Gamma_t=1.43$ GeV and $\mu_{\rm soft}=15$, $30$, $60$ GeV. The plots have been generated from results provided by the groups Hoang-Teubner (HT), Melnikov-Yelkhovsky-Yakovlev-Nagano-Ota-Sumino (MYYNOS), Penin-Pivovarov (PP) and Beneke-Signer-Smirnov (BSS).
  • Figure 2: The total normalised photon-induced $t\bar{t}$ cross section $R$ at the LC versus the c.m. energy in the threshold regime at LO (dotted curves), NLO (dashed) and NNLO (solid). Hoang--Teubner used the 1S mass scheme with $m_t^{1S}=173.68$ GeV, Melnikov--Yelkhovsky the kinetic mass at $15$ GeV with $m_{t, 15\,\hbox{\scriptsize GeV}}^{\rm kin}=173.10$ GeV, and Beneke--Signer--Smirnov and Yakovlev the PS mass at $20$ GeV with $m_{t, 20\,\hbox{\scriptsize GeV}}^{\rm PS}=173.30$ GeV. The plots have been generated from results provided by the groups Hoang--Teubner (HT), Melnikov--Yelkhovsky (MY) and Beneke--Signer--Smirnov (BSS) and Yakovlev.