The HF background in the signal region (3+ jets) is about 14 events. Depending on how exactly you handle the component-by-componennt background, the uncertainty in the signal region varies from 1.3 to 1.6 events. There are 138 events in the region, of which about 106 are attributed to top. The systematic uncertainty is therefore around 1.5%. The lepton ID scale factor, as you correctly point out, is a much bigger uncertainty.

Please take a look at the following file for more details.

First, when Wbb is floated separately from Wc and Wcc, it wants a fit factor of 1.17+-0.23. Mitch sees 0.68+-0.35 if I read his tables right (0.75+-0.35 if he uses the data-based mass shape.) The discrepancy is 0.49+-0.42 for the MC shape and 0.42+-0.42 for the data shape. Already we have seen these are not the only resolutions. The vertex mass fit showed sensitivity to the precise mass shape used, and the data-based shape helps to reconcile them. We found a shift in the mistag estimate which affects the discrepancy. We should be sure to understand the Wc jet spectrum. Perhaps the bb-fraction of the non-W background could be different. And, of course, in the first place we should be mindful of the actual size of the discrepancy--about 1 sigma. There's quite a list of things to look at beyond Wc and the charm scale factor, and the work of reconciling them is going to be really important for lepton+jets analyses (and is an obvious place However, we do not purport to _measure_ an HF fraction (we've never studied the systematics of it) in this fit. The fit is a method of quantitatively demonstrating that (a) the cross-section result depends only at very high order on the HF fraction, (b) that we do not need to move the HF outside the quoted uncertainties, as many people previously believed might be, to explain the data, and (c) it doesn't matter much how the HF components are treated (all together, or separately.) But to answer the original question, if the Wbb fraction is pinned to 0.68 times its MII value, then the Wc fraction in the fit rises by 29%--though the overall fit to the data gets considerably worse. The cross-section changes by 0.8%.

There is absolutely no such assumption that the excess is W+HF to be explicit about. I even wonder if we're looking at the same equation, as #13 has no "N_other" in it--or wondering if maybe we have communicated poorly in the note? Even if we had considered "everything else as a big lump", there would still be no such assumption. The data affects both N_other and N_HF in the minimization. This is a misunderstanding of what the likelihood fit does and how the constraints work. By no means does equation 13 "set W+HF to roughly (N_data - N_other)"; equation 13 lets "other" and "HF" have an error-based tug-of-war over the event count N_i(sigmatt,FHF,FQCd, etc)--just as a likelihood fit should. The HF scale factor is treated exactly the same as every other one. It is in no way priveleged by the fit. There is in fact a reason the other F factors come out near one: fundamentally that their absolute errors are so small that the total event count _doesn't care_ what value they are set to. So only the constraint term cares, and keeps it near one. Put another way, very quickly the point is reached where it is on longer useful to trade off improving the Poisson term of the likelihood relative to the constraint term. Incidentally this kind of effect leads to an often-overlooked subtlety in pseudo-experiment trials which I'll leave for another day.) The rough size of the correlation matrix element uncertainty is about 0.10, so seeing 0.11 is consistent with no correlation. (A small positive correlation is probably made possible through the scale factor, though I've not calculated the size of that effect).