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 state-of-the-art determination of the bag parameters we predict: τ(B+)/τ(Bd0) = 1.082− 0.026+ 0.022, τ(Bs0)/τ(Bd0) = 0.9994 ± 0.0025, τ(D+)/τ(D0) = 2. 7− 0.8+ 0.7 and the mixing-observables in the Bs and Bd system, in good agreement with the most recent experimental averages.
Highlights
The theory expression for mixing observables is a product of perturbative coefficients and non-perturbative matrix elements
The sum rule is formulated in HQET, where quantum fluctuations with a characteristic scale of the order of the bottom-quark mass have been integrated out
The outline of this work is as follows: in section 2 we describe the details of the QCD-HQET matching computation focussing on ∆B = 2 operators
Summary
MB is the mass of the B meson and BQi = 1 corresponds to the VSA approximation. We note that the quark masses appearing in (2.12) are not MS masses which is the usual convention today [5, 46], but pole masses. We prefer the definition (2.11) for the analysis because the use of MS masses makes the LO ADM of the Bag parameters explicitly μdependent and prohibits an analytic solution of the RGE. At the end we convert our results to the convention of [5, 46] which we denote as. Where the AQ(μ) follow from AQ with the replacements mb → mb(μ) and mq → mq(μ). Similar to (2.11), we use for the HQET operators. The HQET bag parameters BQare determined from a sum rule analysis
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