1999/03/31 by T. Nagano, A. Ota, Ayako Ota +1
Mathematics · Physics and Astronomy · #Convergence (economics) #High-Energy Particle Collisions Research #Logarithm #Mathematical analysis #Mathematics #Normalization (sociology) #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quark #Renormalon #Resonance (particle physics) #hep-ph
paper · pdf · doi:10.1103/physrevd.60.114014
published as Phys. Rev. D 60, 114014 (1999) · 23 pages, LaTeX2e, 16 PostScript figures, uses graphicx.sty; Descriptions on the momentum distribution are enlarged; A derivation of the momentum distribution formula is added as an appendix; Other minor changes; In ver.4, comparison with O(alfs) final-state interaction corrections to momentum distribution added; two figures added
arxiv created 1999/07/01 · openalex publication_date 1999/11/05 · openalex created_date 2016/06/24 · arxiv updated 2016/08/24 · openalex updated_date 2026/08/05
Recently full O(\ensuremathαs2,\ensuremathαs\ensuremathβ,\ensuremathβ2) corrections to the threshold total cross section for e+e^\ensuremath-\ensuremath→tt have been calculated, and the reported corrections turned out to be unexpectedly large. We study how to reduce the theoretical uncertainties of the cross section. We adopt a new mass definition proposed by Beneke, which incorporates a renormalon-pole cancellation in the total energy of a static quark-antiquark pair. This improves the convergence of the 1S resonance mass, while the normalization of the cross section scarcely changes. We argue that resummations of logarithms are indispensable, since two largely separated scales dictate the shape of the cross section. As a first step, we resum logarithms in the Coulombic part of the tt potential, and observe a considerable improvement in the convergence of corresponding corrections. There still remain, however, large corrections, which arise from a 1/r2 term in the tt potential. We also calculate full O(\ensuremathαs2,\ensuremathαs\ensuremathβ,\ensuremathβ2) corrections to the momentum distributions of top quarks in the threshold region. Corrections to the distribution shape are of moderate size over the whole threshold region.