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

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.

11 pages, 2 figures

References in corpus (10)

• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• Measurement of the ratio B(t to Wb)/B(t to Wq) in pp collisions at sqrt(s) = 8 TeV
• Symbol Alphabets from the Landau Singular Locus
• Intersection theory rules symbology
• Analytic result for the top-quark width at next-to-next-to-leading order in QCD
• Measurement of the top-quark mass using a leptonic invariant mass in $pp$ collisions at $\sqrt{s}=13\text{TeV}$ with the ATLAS detector
• Extracting the Top-Quark Width from Non-Resonant Production
• QCD improved top-quark decay at next-to-next-to-leading order
• Top quark mass measurements at the $t\bar{t}$ threshold with CEPC

Cited by in corpus (8)

• Using the $W$ as a Standard Candle to Reach the Top: Calibrating Energy Correlator Based Top Mass Measurements
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• Toponium: the smallest bound state and simplest hadron in quantum mechanics
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Subtraction of the $t\bar{t}$ contribution in $tW\bar{b}$ production at the one-loop level
• Top-Quark Decay at Next-to-Next-to-Next-to-Leading Order in QCD
• FeAmGen.jl: A Julia Program for Feynman Amplitude Generation
• Approximate N${}^2$LO and N${}^3$LO QCD Predictions for $tW$ Production