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. Published by the American Physical Society 2024
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