Greetings from Mainz, where I have the pleasure of covering a meeting for you without having to travel from my usual surroundings (I clocked up more miles this year already than can be good from my environmental conscience).
Our Scientific Programme (which is the bigger of the two formats of meetings that the Mainz Institute of Theoretical Physics (MITP) hosts, the smaller being Topical Workshops) started off today with two keynote talks summarizing the status and expectations of the FLAG (Flavour Lattice Averaging Group, presented by Tassos Vladikas) and CKMfitter (presented by Sébastien Descotes-Genon) collaborations. Both groups are in some way in the business of performing weighted averages of flavour physics quantities, but of course their backgrounds, rationale and methods are quite different in many regards. I will no attempt to give a line-by-line summary of the talks or the afternoon discussion session here, but instead just summarize a few
points that caused lively discussions or seemed important in some other way.
By now, computational resources have reached the point where we can achieve such statistics that the total error on many lattice determinations of precision quantities is completely dominated by systematics (and indeed different groups would differ at the several-σ level if one were to consider only their statistical errors). This may sound good in a way (because it is what you'd expect in the limit of infinite statistics), but it is also very problematic, because the estimation of systematic errors is in the end really more of an art than a science, having a crucial subjective component at its heart. This means not only that systematic errors quoted by different groups may not be readily comparable, but also that it become important how to treat systematic errors (which may also be correlated, if e.g. two groups use the same one-loop renormalization constants) when averaging different results. How to do this is again subject to subjective choices to some extent. FLAG imposes cuts on quantities relating to the most important sources of systematic error (lattice spacings, pion mass, spatial volume) to select acceptable ensembles, then adds the statistical and systematic errors in quadrature, before performing a weighted average and computing the overall error taking correlations between different results into account using Schmelling's procedure. CKMfitter, on the other hand, adds all systematic errors linearly, and uses the Rfit procedure to perform a maximum likelihood fit. Either choice is equally permissible, but they are not directly compatible (so CKMfitter can't use FLAG averages as such).
Another point raised was that it is important for lattice collaborations computing mixing parameters to not just provide products like fB√BB, but also fB and BB separately (as well as information about the correlation between these quantities) in order to help making the global CKM fits easier.