 Solution

For a measurement of the cross-section ratio with standard deviation $0.019R$, the separation of the fourth-lepton prediction from the ordinary prediction isThus the peak-ratio model predicts only about a one-standard-deviation shift in this observable. In contrast, the direct Z boson width changes by $167+84=251$ MeV, givingUnder these assumptions the direct width measurement is overwhelmingly more sensitive. These are separate expected displacements, using the supplied experimental uncertainties and fixed theoretical inputs; they are not a combined statistical significance. The $501/3$ single-neutrino normalization and the peak-energy assumption are the same as in e. If the alternative literal $501$ MeV per neutrino premise were used, the corresponding displacements would instead be $12.3$ and $254$ standard deviations, illustrating why that normalization must be stated.