Roy Aleksan edited Measurement of the Z invisible width from runs at E greater than M_Z.tex  over 10 years ago

Commit id: 85029932c594da8a50ed54596b767a98fbb37331

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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 threshold scan alone, the cross section of about 5~pb~\cite{cite:Abbiendi2000hh,cite:Heister2002ut,cite:Achard2003tx,cite:Abdallah2003np} ensures that 10 million ${\rm Z}\gamma$ events will be produced in each TLEP experiment with a ${\rm Z} \to \nnbar$ decay and a high-energy photon in the detector acceptance. 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 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. Similar measurements can be carried out from the large ${\rm ZH}$ sample collected at $\sqrt{s} = 240$ and $350$ GeV. The GeV, in which the  ${\rm Z}$ boson is inferred from the missing mass recoiling against a reconstructed ${\rm H}$, say in ${\bbbar}$. A statistical uncertainty of less than 0.004 could be reach and  will contribute to further reduce this the overall  uncertainty. It may also be determined by the starting design study that a dedicated run at a smaller centre-of-mass energy -- with both a larger luminosity and a larger ${\rm Z}\gamma$ cross section -- 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.}