We update the Standard Model (SM) predictions for the lifetimes of the B+, Bd and Bs mesons within the heavy quark expansion (HQE), including the recently determined NNLO-QCD corrections to non-leptonic decays of the free b-quark. In addition, we update the HQE predictions for the lifetime ratios τ (B+)/τ (Bd) and τ (Bs)/τ (Bd), and provide new results for the semileptonic branching fractions of the three mesons entirely within the HQE. We obtain a considerable improvement of the theoretical uncertainties, mostly due to the reduction of the renormalisation scale dependence when going from LO to NNLO, and for all the observables considered, we find good agreement, within uncertainties, between the HQE predictions and the corresponding experimental data. Our results read, respectively, Γ(B+) = <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mn>0.587</mn> <mrow> <mo>−</mo> <mn>0.035</mn> </mrow> <mrow> <mo>+</mo> <mn>0.025</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {0.587}_{-0.035}^{+0.025} $</EquationSource> </InlineEquation> ps−1, Γ(Bd) = <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mn>0.636</mn> <mrow> <mo>−</mo> <mn>0.037</mn> </mrow> <mrow> <mo>+</mo> <mn>0.028</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {0.636}_{-0.037}^{+0.028} $</EquationSource> </InlineEquation> ps−1, Γ(Bs) = <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mn>0.628</mn> <mrow> <mo>−</mo> <mn>0.035</mn> </mrow> <mrow> <mo>+</mo> <mn>0.027</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {0.628}_{-0.035}^{+0.027} $</EquationSource> </InlineEquation> ps−1, for the total decay widths, τ (B+)/τ (Bd) = <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq4.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mn>1.081</mn> <mrow> <mo>−</mo> <mn>0.016</mn> </mrow> <mrow> <mo>+</mo> <mn>0.014</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {1.081}_{-0.016}^{+0.014} $</EquationSource> </InlineEquation>, τ (Bs)/τ (Bd) = <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq5.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mn>1.013</mn> <mrow> <mo>−</mo> <mn>0.007</mn> </mrow> <mrow> <mo>+</mo> <mn>0.007</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {1.013}_{-0.007}^{+0.007} $</EquationSource> </InlineEquation>, for the lifetime ratios, and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">B</mi> <mi>sl</mi> </msub> <mfenced close=")" open="("> <msup> <mi>B</mi> <mo>+</mo> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{B}}_{\textrm{sl}}\left({B}^{+}\right) $</EquationSource> </InlineEquation> = <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq7.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfenced close=")" open="("> <msubsup> <mn>11.46</mn> <mrow> <mo>−</mo> <mn>0.32</mn> </mrow> <mrow> <mo>+</mo> <mn>0.47</mn> </mrow> </msubsup> </mfenced> <mo>%</mo> </math></EquationSource> <EquationSource Format="TEX">$ \left({11.46}_{-0.32}^{+0.47}\right)\% $</EquationSource> </InlineEquation>, <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">B</mi> <mi>sl</mi> </msub> <mfenced close=")" open="("> <msub> <mi>B</mi> <mi>d</mi> </msub> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{B}}_{\textrm{sl}}\left({B}_d\right) $</EquationSource> </InlineEquation> = <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq9.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfenced close=")" open="("> <msubsup> <mn>10.57</mn> <mrow> <mo>−</mo> <mn>0.27</mn> </mrow> <mrow> <mo>+</mo> <mn>0.47</mn> </mrow> </msubsup> </mfenced> <mo>%</mo> </math></EquationSource> <EquationSource Format="TEX">$ \left({10.57}_{-0.27}^{+0.47}\right)\% $</EquationSource> </InlineEquation>, <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq10.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">B</mi> <mi>sl</mi> </msub> <mfenced close=")" open="("> <msub> <mi>B</mi> <mi>s</mi> </msub> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{B}}_{\textrm{sl}}\left({B}_s\right) $</EquationSource> </InlineEquation> = <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25980_Article_IEq11.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfenced close=")" open="("> <msubsup> <mn>10.52</mn> <mrow> <mo>−</mo> <mn>0.29</mn> </mrow> <mrow> <mo>+</mo> <mn>0.50</mn> </mrow> </msubsup> </mfenced> <mo>%</mo> </math></EquationSource> <EquationSource Format="TEX">$ \left({10.52}_{-0.29}^{+0.50}\right)\% $</EquationSource> </InlineEquation>, for the semileptonic branching ratios. Finally, we also provide an outlook for further improvements of the HQE determinations of the B-meson decay widths and of their ratios.

Total decay rates of B mesons at NNLO-QCD

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2025年4月15日

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Manuel Egner,
Matteo Fael,
Alexander Lenz,
Maria Laura Piscopo,
Aleksey V. Rusov,
Kay Schönwald,
Matthias Steinhauser

摘要

We update the Standard Model (SM) predictions for the lifetimes of the B⁺, B_d and B_s mesons within the heavy quark expansion (HQE), including the recently determined NNLO-QCD corrections to non-leptonic decays of the free b-quark. In addition, we update the HQE predictions for the lifetime ratios τ (B⁺)/τ (B_d) and τ (B_s)/τ (B_d), and provide new results for the semileptonic branching fractions of the three mesons entirely within the HQE. We obtain a considerable improvement of the theoretical uncertainties, mostly due to the reduction of the renormalisation scale dependence when going from LO to NNLO, and for all the observables considered, we find good agreement, within uncertainties, between the HQE predictions and the corresponding experimental data. Our results read, respectively, Γ(B⁺) = ${0.587}_{- 0.035}^{+ 0.025}$ $ {0.587}_{-0.035}^{+0.025} $ ps⁻¹, Γ(B_d) = ${0.636}_{- 0.037}^{+ 0.028}$ $ {0.636}_{-0.037}^{+0.028} $ ps⁻¹, Γ(B_s) = ${0.628}_{- 0.035}^{+ 0.027}$ $ {0.628}_{-0.035}^{+0.027} $ ps⁻¹, for the total decay widths, τ (B⁺)/τ (B_d) = ${1.081}_{- 0.016}^{+ 0.014}$ $ {1.081}_{-0.016}^{+0.014} $ , τ (B_s)/τ (B_d) = ${1.013}_{- 0.007}^{+ 0.007}$ $ {1.013}_{-0.007}^{+0.007} $ , for the lifetime ratios, and $B_{sl} (B^{+})$ $ {\mathcal{B}}_{\textrm{sl}}\left({B}^{+}\right) $ = $({11.46}_{- 0.32}^{+ 0.47}) %$ $ \left({11.46}_{-0.32}^{+0.47}\right)\% $ , $B_{sl} (B_{d})$ $ {\mathcal{B}}_{\textrm{sl}}\left({B}_d\right) $ = $({10.57}_{- 0.27}^{+ 0.47}) %$ $ \left({10.57}_{-0.27}^{+0.47}\right)\% $ , $B_{sl} (B_{s})$ $ {\mathcal{B}}_{\textrm{sl}}\left({B}_s\right) $ = $({10.52}_{- 0.29}^{+ 0.50}) %$ $ \left({10.52}_{-0.29}^{+0.50}\right)\% $ , for the semileptonic branching ratios. Finally, we also provide an outlook for further improvements of the HQE determinations of the B-meson decay widths and of their ratios.