Improved analysis of the decay width of t→Wb up to N3LO QCD corrections

In this paper, we analyze the top-quark decay <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>t</a:mi><a:mo stretchy="false">→</a:mo><a:mi>W</a:mi><a:mi>b</a:mi></a:math> up to next-to-next-to-next-to-leading order (<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>) QCD corrections. For the purpose, we first adopt the principle of maximum conformality (PMC) to deal with the initial perturbative QCD (pQCD) series. Then we adopt the Bayesian analysis approach, which quantifies the unknown higher-order terms’ contributions in terms of a probability distribution, to estimate the possible magnitude of the uncalculated <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msup><g:mrow><g:mi mathvariant="normal">N</g:mi></g:mrow><g:mrow><g:mn>4</g:mn></g:mrow></g:msup><g:mi>LO</g:mi></g:mrow></g:math> terms. In our calculation, an effective strong coupling constant <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:msub><j:mrow><j:mi>α</j:mi></j:mrow><j:mrow><j:mi>s</j:mi></j:mrow></j:msub><j:mo stretchy="false">(</j:mo><j:msub><j:mrow><j:mi>Q</j:mi></j:mrow><j:mrow><j:mo>*</j:mo></j:mrow></j:msub><j:mo stretchy="false">)</j:mo></j:mrow></j:math> is determined by using all nonconformal <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mo stretchy="false">{</n:mo><n:msub><n:mi>β</n:mi><n:mi>i</n:mi></n:msub><n:mo stretchy="false">}</n:mo></n:math> terms associated with the renormalization group equation. This leads to a next-to-leading-log PMC scale <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msubsup><r:mi>Q</r:mi><r:mo>*</r:mo><r:mrow><r:mo stretchy="false">(</r:mo><r:mi>NLL</r:mi><r:mo stretchy="false">)</r:mo></r:mrow></r:msubsup><r:mo>=</r:mo><r:mn>10.3048</r:mn><r:mtext> </r:mtext><r:mtext> </r:mtext><r:mi>GeV</r:mi></r:math>, which can be regarded as the correct momentum flow of the process. Consequently, we obtain an improved scale-invariant pQCD prediction for the top-quark decay width, e.g., <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msubsup><v:mi mathvariant="normal">Γ</v:mi><v:mi>t</v:mi><v:mrow><v:mi>tot</v:mi></v:mrow></v:msubsup><v:mo>=</v:mo><v:mn>1.3120</v:mn><v:mo>±</v:mo><v:mn>0.0038</v:mn><v:mtext> </v:mtext><v:mtext> </v:mtext><v:mi>GeV</v:mi></v:math>, whose error is the squared average of the uncertainties from the decay width of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>W</y:mi></y:math>-boson <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi mathvariant="normal">Δ</ab:mi><ab:msub><ab:mi mathvariant="normal">Γ</ab:mi><ab:mi>W</ab:mi></ab:msub><ab:mo>=</ab:mo><ab:mo>±</ab:mo><ab:mn>0.042</ab:mn><ab:mtext> </ab:mtext><ab:mtext> </ab:mtext><ab:mi>GeV</ab:mi></ab:math>, the coupling constant <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi mathvariant="normal">Δ</eb:mi><eb:msub><eb:mi>α</eb:mi><eb:mi>s</eb:mi></eb:msub><eb:mo stretchy="false">(</eb:mo><eb:msub><eb:mi>m</eb:mi><eb:mi>Z</eb:mi></eb:msub><eb:mo stretchy="false">)</eb:mo><eb:mo>=</eb:mo><eb:mo>±</eb:mo><eb:mn>0.0009</eb:mn></eb:math>, and the predicted <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mrow><jb:msup><jb:mrow><jb:mi mathvariant="normal">N</jb:mi></jb:mrow><jb:mrow><jb:mn>4</jb:mn></jb:mrow></jb:msup><jb:mi>LO</jb:mi></jb:mrow></jb:math>-terms. The magnitude of the top-quark pole mass greatly affects the total decay width. By further taking the PDG top-quark pole mass error from cross-section measurements into consideration, e.g., <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi mathvariant="normal">Δ</mb:mi><mb:msub><mb:mi>m</mb:mi><mb:mi>t</mb:mi></mb:msub><mb:mo>=</mb:mo><mb:mo>±</mb:mo><mb:mn>0.7</mb:mn><mb:mtext> </mb:mtext><mb:mtext> </mb:mtext><mb:mi>GeV</mb:mi></mb:math>, we obtain <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msubsup><pb:mi mathvariant="normal">Γ</pb:mi><pb:mi>t</pb:mi><pb:mrow><pb:mi>tot</pb:mi></pb:mrow></pb:msubsup><pb:mo>=</pb:mo><pb:mn>1.312</pb:mn><pb:msubsup><pb:mn>0</pb:mn><pb:mrow><pb:mo>−</pb:mo><pb:mn>0.0192</pb:mn></pb:mrow><pb:mrow><pb:mo>+</pb:mo><pb:mn>0.0194</pb:mn></pb:mrow></pb:msubsup><pb:mtext> </pb:mtext><pb:mtext> </pb:mtext><pb:mi>GeV</pb:mi></pb:math>. Published by the American Physical Society 2024