Renormalisation scale setting for D-mixing

TL;DR

This paper proposes a novel renormalisation scale setting method for D-meson mixing calculations, addressing large discrepancies between theoretical estimates and experimental results caused by GIM cancellations.

Contribution

It introduces a scale setting approach that individually adjusts scales for different quark contributions, improving the accuracy of heavy quark expansion predictions.

Findings

Reduces the discrepancy between theory and experiment for D-meson decay rates.

Maintains consistency with existing predictions for B-hadron lifetimes and decay rate differences.

Increases uncertainties for semi-leptonic CP asymmetries in B decays.

Abstract

A naive application of the heavy quark expansion (HQE) yields theory estimates for the decay rate of neutral $D$ mesons that are four orders of magnitude below the experimental determination. It is well known that this huge suppression results from severe GIM cancellations. We find that this mismatch can be solved by individually choosing the renormalisation scale of the different internal quark contributions. For $b$ and $c$ hadron lifetimes, as well as for the decay rate difference of neutral $B$ mesons the effect of our scale setting procedure lies within the previously quoted theory uncertainties, while we get enlarged theory uncertainties for the semi-leptonic CP asymmetries in the $B$ system.