Abstract:The hadronic matrix elements of dimension-six ∆F = 0, 2 operators are crucial inputs for the theory predictions of mixing observables and lifetime ratios in the B and D system. We determine them using HQET sum rules for three-point correlators. The results of the required three-loop computation of the correlators and the one-loop computation of the QCD-HQET matching are given in analytic form. For mixing matrix elements we find very good agreement with recent lattice results and comparable theoretical uncertainties. For lifetime matrix elements we present the first ever determination in the D meson sector and the first determination of ∆B = 0 matrix elements with uncertainties under control -superseeding preliminary lattice studies stemming from 2001 and earlier. With our stateof-the-art determination of the bag parameters we predict:−0.8 and the mixing-observables in the B s and B d system, in good agreement with the most recent experimental averages.

Based on recent HQET sum rule and lattice calculations we present updated Standard Model predictions for the mass differences of neutral B mesons: ∆M SM s = 18.4 +0.7 −1.2 ps −1 and ∆M SM d = 0.533 +0.022 −0.036 ps −1 and study their impact on new physics models that address the present hints of anomalous data in b → s transitions. We also examine future prospects of further reducing the theory uncertainties and discuss the implications of a 2025 scenario with ∆M SM 2025 s = (18.4 ± 0.5) ps −1 . In particular, the latter yields upper bounds M Z 9 TeV and M S 3 30 TeV for the minimal Z and S 3 lepto-quark explanations of the b → s anomalies, respectively.

We consider the effects of a non-vanishing strange-quark mass in the determination of the full basis of dimension six matrix elements for B s mixing, in particular we get for the ratio of the V −A Bag parameter in the B s and B d system:−0.009 . Combining these results with the most recent lattice values for the ratio of decay constants f Bs /f B d we obtain the most pre-−0.0072 in agreement with recent lattice determinations. We find ∆M s = (18.5 +1.2 −1.5 )ps −1 and ∆M d = (0.547 +0.035 −0.046 )ps −1 to be consistent with experiments at below one sigma. Assuming the validity of the SM, our calculation can be used to directly determine the ratio of CKM elements |V td /V ts | = 0.2045 +0.0012 −0.0013 , which is compatible with the results from the CKM fitting groups, but again more precise.

We determine the mass of the bottom quark from high moments of the bb production cross section in e + e − annihilation, which are dominated by the threshold region. On the theory side next-to-next-to-next-to-leading order (NNNLO) calculations both for the resonances and the continuum cross section are used for the first time. We find m PS b (2 GeV) = 4.532 +0.013 −0.039 GeV for the potential-subtracted mass and m MS b (m MS b) = 4.193 +0.022 −0.035 GeV for the MS bottom-quark mass.