deletions | additions       diff --git a/Statistical analysis.tex b/Statistical analysis.tex  index a81f078..0f98a12 100644  --- a/Statistical analysis.tex  +++ b/Statistical analysis.tex 
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\end{equation}  This analytical procedure is used in Ref.~\cite{Grzadkowski_2000} to determine the sensitivity to top-quark electroweak couplings in $500\,{\rm fb}^{-1}$ of ${\rm e^+ e^-}$ collisions at $\sqrt{s} = 500$\,GeV, with or without incoming beam polarization. In this article, the authors evaluate the covariance matrix with Eq.~\ref{eq:rate}, but they let the total number of events float by adding a fictitious multiplicative form factor $\delta_0$ in front of $S^0$ in Eq.~\ref{eq:optimal}, hence increase the rank of the covariance matrix from 8 to 9. It was checked that this work-around is numerically equivalent to using Eq.~\ref{eq:norate}, {\it i.e.}, to not use the total event rate in the likelihood.   It can be seen from Fig.~\ref{fig:distributions}, however, that $f_A^\gamma(x,\cos\theta)$ (top-left corner) is almost degenerate with the standard model contributions $S^0(x,\cos\theta)$ (bottom-right corner). Letting the normaization of the standard model contribution float is therefore bound to lead to very large statistical uncertainties on all form factors, as is observed in Ref.~\cite{Grzadkowski_2000}. For this reason, and as is done in Ref.~\cite{Baer_2013}, the present study includes the total event rate in the determination of the uncertainties, leading to an improvement by factors up to 50 with respect to not using it. In the first configuration of Ref.~\cite{Baer_2013}, only the three coefficients $F_{1V}^\gamma$, $F_{1V}^Z$ and $F_{1A}^Z$ are allowed to vary. The other five form factors are fixed to their standard model values. In this simplified situation, Eq.~\ref{eq:optimal} reads  \begin{equation}  S(x,\theta) = S^0(x,\theta) + delta F_{1V}^\gamma 2\sin\theta_W f_A^\gamma + delta F_{1V}^Z 2\sin\theta_W f_A^Z + delta F_{1A}^Z 2\sin\theta_W f_B^Z \ ,  \end{equation}  which leads to the following $3\times 3$ covariance matrix $V = 4\sin^2\theta_W {\cal L} X$ with  \begin{eqnarray}  X_{11} = \int {\rm d}\Omega {f_A^\gamma \times f_A^\gamma \over S^0} \ , & X_{12} = \int {\rm d}\Omega {f_A^\gamma \times f_A^Z \over S^0} \ , & X_{13} = \int {\rm d}\Omega {f_A^\gamma \times f_B^Z \over S^0} \ , \\  & X_{22} = \int {\rm d}\Omega {f_A^Z \times f_A^Z \over S^0} \ , & X_{12} = \int {\rm d}\Omega {f_A^Z \times f_B^Z \over S^0} \ , \\  & & X_{22} = \int {\rm d}\Omega {f_B^Z \times f_B^Z \over S^0} \ .  \end{eqnarray}