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  • Letter
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Analytic third-order QCD corrections to top-quark and semileptonic b→u decays

Long-Bin Chen1, Hai Tao Li2,*, Zhao Li3,4,5, Jian Wang2,5,†, Yefan Wang2,6,‡, and Quan-feng Wu3,4

  • 1School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China
  • 2School of Physics, Shandong University, Jinan, Shandong 250100, China
  • 3Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
  • 4School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 5Center for High Energy Physics, Peking University, Beijing 100871, China
  • 6Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, China

  • *Corresponding author: haitao.li@sdu.edu.cn
  • †Corresponding author: j.wang@sdu.edu.cn
  • ‡Corresponding author: wangyefan@sdu.edu.cn
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Phys. Rev. D 109, L071503 – Published 8 April, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L071503

Abstract

We present the first analytic results of next-to-next-to-next-to-leading-order (N3LO) QCD corrections to the top-quark decay width. We focus on the dominant leading color contribution, which includes light-quark loops. At next-to-next-to-leading order (NNLO), this dominant contribution accounts for 95% of the total correction. By utilizing the optical theorem, the N3LO corrections are related to the imaginary parts of the four-loop self-energy Feynman diagrams, which are calculated with differential equations. The results are expressed in terms of harmonic polylogarithms, enabling fast and accurate evaluation. The third-order QCD corrections decrease the leading-order decay width by 0.667%, and the scale uncertainty is reduced by half compared to the NNLO result. The most precise prediction for the top-quark width is now 1.321 GeV for mt=172.69  GeV. Additionally, we obtain the third-order QCD corrections to the dilepton invariant mass spectrum and decay width in the semileptonic b→u transition. The perturbative series in the on-shell mass scheme exhibits poor convergence behavior. In the MS¯ mass scheme, the scale dependence is greatly improved. A more precise determination of the CKM matrix element Vub could be obtained with such higher-order corrections.

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Phys. Rev. D 109, L071503– Published 8 April, 2024
  • Received 18 September 2023
  • Accepted 7 March 2024
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