Dimension-six matrix elements for meson mixing and lifetimes from sum rules

TL;DR

This paper uses HQET sum rules to accurately compute dimension-six matrix elements for meson mixing and lifetimes, providing results that agree with lattice data and offering new determinations especially in the D meson sector.

Contribution

It presents the first determination of lifetime matrix elements in the D meson sector and improves control over B meson matrix elements, surpassing previous lattice studies.

Findings

Good agreement with recent lattice results for mixing matrix elements.

First-ever determination of D meson lifetime matrix elements.

Predicted lifetime ratios and mixing observables align with experimental data.

Abstract

The hadronic matrix elements of dimension-six $\Delta F=0,2$ 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 $\Delta B=0$ 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: $\tau(B^+)/\tau(B_d^0) = 1.082_{-0.026}^{+0.022}$, $\tau(B_s^0)/\tau(B_d^0) = 1.0007\pm0.0025$, $\tau(D^+)/\tau(D^0) = 2.7_{-0.8}^{+0.7}$ and the mixing-observables in the $B_s$ and $B_d$ system, in good agreement with the most recent experimental averages.