Renormalisation scale setting for D-mixing
September 15, 2021
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
semileptonic CP asymmetries in the $B$ system.
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