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Top quark production at threshold with O(alpha_s^2) accuracy

Kirill Melnikov, Alexander Yelkhovsky

TL;DR

The paper computes the next-to-next-to-leading order corrections to the top quark pair production cross section at threshold in e+e- collisions by solving a non-relativistic Schrödinger equation with a corrected QCD potential and by matching to perturbative results. The approach resums Coulomb-type enhancements and includes subleading NNLO terms, yielding a final R(s) formula that incorporates both dynamic and kinematic corrections. The main finding is that NNLO corrections are large, comparable in size to NLO, with only modest residual scale dependence near the resonance, and the authors provide explicit constants and a numerical analysis to support a precise extraction of top properties. The work also details a numerical treatment of a singular 1/r^2 potential and demonstrates the reliability of direct matching to eliminate cutoff ambiguities.

Abstract

We calculate the next-to-next-to-leading order correction to the cross section for top quark pair production in e+e- annihilation in the threshold region, resumming all O [ (alpha_s/beta)^n (alpha_s^2, beta^2, alpha_s beta) ] terms of perturbation series. We find that the magnitude of the NNLO correction is comparable to the size of the NLO corrections.

Top quark production at threshold with O(alpha_s^2) accuracy

TL;DR

The paper computes the next-to-next-to-leading order corrections to the top quark pair production cross section at threshold in e+e- collisions by solving a non-relativistic Schrödinger equation with a corrected QCD potential and by matching to perturbative results. The approach resums Coulomb-type enhancements and includes subleading NNLO terms, yielding a final R(s) formula that incorporates both dynamic and kinematic corrections. The main finding is that NNLO corrections are large, comparable in size to NLO, with only modest residual scale dependence near the resonance, and the authors provide explicit constants and a numerical analysis to support a precise extraction of top properties. The work also details a numerical treatment of a singular 1/r^2 potential and demonstrates the reliability of direct matching to eliminate cutoff ambiguities.

Abstract

We calculate the next-to-next-to-leading order correction to the cross section for top quark pair production in e+e- annihilation in the threshold region, resumming all O [ (alpha_s/beta)^n (alpha_s^2, beta^2, alpha_s beta) ] terms of perturbation series. We find that the magnitude of the NNLO correction is comparable to the size of the NLO corrections.

Paper Structure

This paper contains 6 sections, 45 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The framework of the calculation
  3. Corrections to the Green function at the origin
  4. Numerical solution of the Schrödinger equation
  5. Matching and final result for $R$
  6. Conclusions

Figures (1)

  • Figure 1: $R_{\rm LO}$ (dotted lines), $R_{\rm NLO}$ (dashed lines), $R_{\rm NNLO}$ (solid lines) as a function of energy $\sqrt{s} -2m$, GeV. In all three cases, three curves correspond to different choices of the soft scale $\mu = 50\; {\rm GeV}$ (upper curves), $\mu = 75\; {\rm GeV}$ and $\mu = 100\; {\rm GeV}$ (lower curves). We also use $m = 175\; {\rm GeV}$, $\Gamma _t = 1.43\; {\rm GeV}$ and $\alpha _s (M_Z) = 0.118$ as the input parameters.