Analytic third-order QCD corrections to top-quark and semileptonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>u</mml:mi></mml:math> decays

Abstract

We present the first analytic results of next-to-next-to-next-to-leading-order (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi mathvariant="normal">N</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msup><a:mi>LO</a:mi></a:mrow></a:math>) 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 <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:msup><d:mrow><d:mi mathvariant="normal">N</d:mi></d:mrow><d:mrow><d:mn>3</d:mn></d:mrow></d:msup><d:mi>LO</d:mi></d:mrow></d:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi>m</g:mi></g:mrow><g:mrow><g:mi>t</g:mi></g:mrow></g:msub><g:mo>=</g:mo><g:mn>172.69</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>GeV</g:mi></g:mrow></g:math>. Additionally, we obtain the third-order QCD corrections to the dilepton invariant mass spectrum and decay width in the semileptonic <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>b</i:mi><i:mo stretchy="false">→</i:mo><i:mi>u</i:mi></i:math> transition. The perturbative series in the on-shell mass scheme exhibits poor convergence behavior. In the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mover accent="true"><l:mi>MS</l:mi><l:mo stretchy="true">¯</l:mo></l:mover></l:math> mass scheme, the scale dependence is greatly improved. A more precise determination of the CKM matrix element <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>V</p:mi><p:mrow><p:mi>u</p:mi><p:mi>b</p:mi></p:mrow></p:msub></p:math> could be obtained with such higher-order corrections. Published by the American Physical Society 2024