Reanalysis of the top-quark pair production via the $e^{+}{e}^{-}$ annihilation near the threshold region up to N${}^3$LO QCD corrections

Abstract

In this paper, we present an improved analysis of the top-quark pair production via the process $e^{+}{e}^{-}\to {\gamma }^{\ast }\to t\bar{t}$ near the threshold region up to next-to-next-to-next-to-leading order (N${}^3$LO) QCD corrections. Near the threshold region, the top-quark velocity $v$ tends to zero, leading to Coulomb singularity. To achieve a reasonable prediction in the threshold region, we reconstruct the analytical expression for the Coulomb-terms up to N${}^3$LO accuracy by using the PSLQ algorithm, whose numerical values agree well with the previous N${}^3$LO-level calculations. It is found that the N${}^3$LO series still has sizable renormalization scale dependence, and to improve the precision of the series, we apply the Principle of Maximum Conformality to eliminate such scale dependence. After that, the Coulomb part is resummed into a Sommerfeld-Gamow-Sakharov factor, which finally leads to a much more reasonable behavior near the threshold region.

10 pages, 6 figures

References in corpus (15)

• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Fermionic contributions to the three-loop static potential
• Top-quark pair production near threshold at LHC
• Bound-state Effects on Top Quark Production at Hadron Colliders
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Massive vector form factors to three loops
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Top-quark forward-backward asymmetry in e+e- annihilation at NNLO in QCD
• Electroweak prodution of top-quark pairs in e+e- annihilation at NNLO in QCD: the vector contributions
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• Heavy-quark pair production at lepton colliders at NNNLO in QCD
• Precise perturbative predictions from fixed-order calculations
• Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis
• Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders

Cited by in corpus (5)

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• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
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• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator
• QCD corrections of $e^{+}{e}^{-}\to J/\psi +c+\bar{c}$ using the principle of maximum conformality