deletions | additions       diff --git a/Statistical analysis.tex b/Statistical analysis.tex  index bfc3561..e423da0 100644  --- a/Statistical analysis.tex  +++ b/Statistical analysis.tex 
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p(k) = {1 \over \sigma_{\rm tot} } { {\rm d}^2\sigma \over {\rm d}x {\rm d}\cos\theta } {\rm , with \ }   \sigma_{\rm tot} = \int { {\rm d}^2\sigma \over {\rm d}x {\rm d}\cos\theta } {\rm d}x {\rm d}\cos\theta .  \end{equation}  The covariance matrix obtained from the numerical minimization of the negative log-likelihood is then inverted to get the uncertainties on the form factors, $\sigma(\delta_i)$. It can be shown~\cite{Davier_1993} that, in the linear form given in Eq.~\ref{eq:optimal}, this method leads to optimal statistical uncertainties on the form factors. The functions $f_i(x,\cos\theta)$ are therefore called "optimal observables". It turns out~\cite{Diehl_1994} that the covariance matrix, hence the statistical uncertainties on the form factors, can be obtained analytically in the limit of large number of events, which is the case considered in this letter. If the total event rate is included in the derivation of the likelihood, as is the case in Eq.~\ref{eq:likelihood}, the elements of the covariance matrix $V$ are giveb given  by \begin{equation}  V_{ij} = {\cal L} \int { f_i \times f_j \over S^0} {\rm d}x {\rm d}\cos\theta \ ,  \end{equation}  while if the total event rate is not included in the likelihood, namely by removing the first term of the product in Eq.~\ref{sec:likelihood}, these elements take the form  \begin{equation}  V_{ij} = {\cal L} \left[ \int { f_i \times f_j \over S^0} {\rm d}x {\rm d}\cos\theta - {\int f_i {\rm d}x {\rm d}\cos\theta \int f_i {\rm d}x {\rm d}\cos\theta \over \int S_0 {\rm d}x {\rm d}\cos\theta} \right],  \end{equation}