Analytic three-loop QCD corrections to top-quark and semileptonic $b\to u$ decays

TL;DR

This paper provides the first analytic N$^3$LO QCD corrections to top-quark decay width and semileptonic $b o u$ decays, significantly improving theoretical precision and reducing uncertainties.

Contribution

It presents the first analytic calculation of N$^3$LO QCD corrections for top-quark decay and semileptonic $b o u$ decays, focusing on dominant contributions and employing differential equations.

Findings

N$^3$LO corrections decrease the top-quark decay width by 0.667%.

Scale uncertainty is reduced by half at N$^3$LO.

Most precise top-quark width prediction is 1.321 GeV.

Abstract

We present the first analytic results of N$^3$LO QCD corrections to the top-quark decay width. We focus on the dominant leading color contribution, which includes light-quark loops. At NNLO, this dominant contribution accounts for 95% of the total correction. By utilizing the optical theorem, the N$^3$LO 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 LO 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 $m_t=172.69$ GeV. Additionally, we obtain the third-order QCD corrections to the dilepton invariant mass spectrum and decay width in the semileptonic $b\to u$ transition.