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Scale dependence of top-quark cross section at $e^+e^-$ colliders near production threshold at NNNLO

Yuichiro Kiyo

TL;DR

The paper analyzes the scale dependence of the top-quark threshold cross section at $e^+e^-$ colliders, presenting a full NNNLO QCD calculation within NRQCD and separating resonant and non-resonant contributions. It demonstrates improved perturbative stability, with renormalization-scale uncertainties shrinking to about $5\%$ and finite-width effects remaining under control, especially near the $1S$ peak. The study finds tens of MeV shifts in the peak position across perturbative orders, translating into a potential top-quark mass precision of roughly $30$ MeV from threshold scans. The results support precise extraction of $m_t$ from threshold measurements and indicate that QED/electroweak corrections can be incorporated with existing tools for phenomenological analyses.

Abstract

The top-quark threshold cross section at $e^+e^-$ colliders near production threshold is investigated. We study the scale dependence of the cross section for $σ(e^+e^- \to ttX$) near $\sqrt{s} \simeq 2m_t$ and discuss the theoretical accuracy of the NNNLO prediction. We report that a threshold scan at an $e^+e^-$ collider would allow a determination of the top-quark mass with an accuracy of order 30 MeV.

Scale dependence of top-quark cross section at $e^+e^-$ colliders near production threshold at NNNLO

TL;DR

The paper analyzes the scale dependence of the top-quark threshold cross section at colliders, presenting a full NNNLO QCD calculation within NRQCD and separating resonant and non-resonant contributions. It demonstrates improved perturbative stability, with renormalization-scale uncertainties shrinking to about and finite-width effects remaining under control, especially near the peak. The study finds tens of MeV shifts in the peak position across perturbative orders, translating into a potential top-quark mass precision of roughly MeV from threshold scans. The results support precise extraction of from threshold measurements and indicate that QED/electroweak corrections can be incorporated with existing tools for phenomenological analyses.

Abstract

The top-quark threshold cross section at colliders near production threshold is investigated. We study the scale dependence of the cross section for ) near and discuss the theoretical accuracy of the NNNLO prediction. We report that a threshold scan at an collider would allow a determination of the top-quark mass with an accuracy of order 30 MeV.
Paper Structure (4 sections, 3 equations, 3 figures, 1 table)

This paper contains 4 sections, 3 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Threshold production cross section
  3. Scale dependence of cross section
  4. Conclusion

Figures (3)

  • Figure 1: Top-quark production cross section in QCD near threshold with $\mu=80~{\rm GeV}$ (left panel), and the relative renormalization-scale dependence (right panel). Here $R$ denotes the resonant contribution only.
  • Figure 2: Finite-width scale dependence of the resonant top-quark cross section at NLO, NNLO, and NNNLO for center-of-mass energies $\sqrt{s}=340 , 344$ , and $348 ~{\rm GeV}$, shown in the left, middle, and right panels, respectively.
  • Figure 3: Size of perturbative QCD corrections to the $R$-ratio at $\sqrt{s}=344~{\rm GeV}$ with $\mu=100~{\rm GeV}$ (upper panel), and their scale dependence for $\mu \in [50, 350]~{\rm GeV}$ (lower panel).