We compute next-to-next-to-leading order corrections to the decay width difference of mass eigenstates and the charge-parity (CP) asymmetry afs in flavour-specific decays of neutral B mesons. We include both current-current and penguin operators at three-loop order. All input integrals in the transition amplitude are reduced to a small set of master integrals which depend on the ratio of the charm and bottom quark masses. The latter are computed using semi-analytic methods which provide deep expansions around properly selected values of mc/mb. We provide numerical results for ∆Γ and ∆Γ/∆M, both for the Bd and Bs system, including a detailed uncertainty analysis. Using the experimental value for the mass difference ∆Ms we predict ∆Γs = (0.078 ± 0.015) ps−1. For the CP asymmetries we find <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>a</mi> <mi>fs</mi> <mi>s</mi> </msubsup> <mo>=</mo> <mfenced close=")" open="("> <mrow> <mn>2.27</mn> <mo>±</mo> <mn>0.13</mn> </mrow> </mfenced> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {a}_{\textrm{fs}}^s=\left(2.27\pm 0.13\right)\times {10}^{-5} $</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>a</mi> <mi>fs</mi> <mi>d</mi> </msubsup> <mo>=</mo> <mo>−</mo> <mfenced close=")" open="("> <mrow> <mn>5.19</mn> <mo>±</mo> <mn>0.30</mn> </mrow> </mfenced> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {a}_{\textrm{fs}}^d=-\left(5.19\pm 0.30\right)\times {10}^{-4} $</EquationSource> </InlineEquation>. Furthermore, we show that the ratios (∆Γs/∆Ms)/(∆Γd/∆Md) and ∆Γd/∆Γs can be predicted with high precision. The former quantity permits the prediction ∆Γd = (0.00215 ± 0.00013) ps−1 from the measurements of ∆Md,s and ∆Γs. We further discuss the impact of ∆Γd/∆Γs on the CKM unitarity triangle and present ready-to-use formulae which permit improved predictions once updated results for the operator matrix elements are available.

Complete next-to-next-to-leading order QCD corrections to the decay matrix in B-meson mixing at leading power

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2026年3月10日

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Ulrich Nierste,
Pascal Reeck,
Vladyslav Shtabovenko,
Matthias Steinhauser

摘要

We compute next-to-next-to-leading order corrections to the decay width difference of mass eigenstates and the charge-parity (CP) asymmetry a_fs in flavour-specific decays of neutral B mesons. We include both current-current and penguin operators at three-loop order. All input integrals in the transition amplitude are reduced to a small set of master integrals which depend on the ratio of the charm and bottom quark masses. The latter are computed using semi-analytic methods which provide deep expansions around properly selected values of m_c/m_b. We provide numerical results for ∆Γ and ∆Γ/∆M, both for the B_d and B_s system, including a detailed uncertainty analysis. Using the experimental value for the mass difference ∆M_s we predict ∆Γ_s = (0.078 ± 0.015) ps⁻¹. For the CP asymmetries we find $a_{fs}^{s} = (2.27 \pm 0.13) \times 10^{- 5}$ $ {a}_{\textrm{fs}}^s=\left(2.27\pm 0.13\right)\times {10}^{-5} $ and $a_{fs}^{d} = - (5.19 \pm 0.30) \times 10^{- 4}$ $ {a}_{\textrm{fs}}^d=-\left(5.19\pm 0.30\right)\times {10}^{-4} $ . Furthermore, we show that the ratios (∆Γ_s/∆M_s)/(∆Γ_d/∆M_d) and ∆Γ_d/∆Γ_s can be predicted with high precision. The former quantity permits the prediction ∆Γ_d = (0.00215 ± 0.00013) ps⁻¹ from the measurements of ∆M_d,s and ∆Γ_s. We further discuss the impact of ∆Γ_d/∆Γ_s on the CKM unitarity triangle and present ready-to-use formulae which permit improved predictions once updated results for the operator matrix elements are available.