Renormalization scale setting for D-meson mixing
Alexander Lenz, Maria Laura Piscopo, Christos Vlahos
Abstract
A naive application of the heavy quark expansion (HQE) yields theory estimates for the decay rate of neutral $D$ mesons that are 4 orders of magnitude below the experimental determination. It is well known that this huge suppression results from severe Glashow-Iliopoulos-Maiani cancellations. We find that this mismatch can be solved by individually choosing the renormalization 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 semileptonic $CP$ asymmetries in the $B$ system.