deletions | additions       diff --git a/Measurement of the Z invisible width from runs at E greater than M_Z.tex b/Measurement of the Z invisible width from runs at E greater than M_Z.tex  index cff6676..658e2b8 100644  --- a/Measurement of the Z invisible width from runs at E greater than M_Z.tex  +++ b/Measurement of the Z invisible width from runs at E greater than M_Z.tex 
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\subsubsection{The Z invisible width and the number of neutrinos}   Above the Z peak, the $\epemto {\rm Z}\gamma$ process provides a very clean photon-tagged sample of on-shell Z bosons, with which the Z properties can be measured. From the WW theshold scan alone, 10 million ${\rm Z}\gamma$ events will be produced in each experiment with a ${\rm Z} \to \nnbar$ decay. The three million ${\rm Z}\gamma$ events with leptonic Z decays will in turn provide a direct measurement of the ratio $\Gamma_{\rm Z}^{\rm inv}/\Gamma_{\rm Z}^{\rm lept}$, in which uncertainties associated with absolute luminosity or perfectly cancel. The 40 million such events with either hadronic or leptonic Z decays will also provide a cross-check of the systematic uncertainties and backgrounds related to the QED predictions for the energy and angular distributions of the high-energy photon. The invisible Z width will thus be measured with a statistical error corresponding to 0.001 neutrino family. Systematic uncertainty are expected to be at the same level or smaller. The data taken at $\sqrt{s} = 240$ or $350$ GeV will contribute to further reduce this uncertainty. It may also be determined by the starting desing study that a dedicated run at a smaller centre-of-mass energy (with -- with  both a larger luminosity and a larger ${\rm Z}\gamma$ cross section) section --  will be more appropriate for this important measurement. \\  {\em An overall, statistics-dominated, uncertainty of 0.001 is therefore considered as a reasonable target for the number of neutrinos at TLEP.}