deletions | additions       diff --git a/Statistical analysis.tex b/Statistical analysis.tex  index 0e986ae..154a2fd 100644  --- a/Statistical analysis.tex  +++ b/Statistical analysis.tex 
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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) + 2\sin\theta_W - 2i\sin\theta_W  \delta F_{1V}^\gamma f_A^\gamma + 2\sin\theta_W - 2i\sin\theta_W  \delta F_{1V}^Z f_A^Z + 2\sin\theta_W -2i\sin\theta_W  \delta F_{1A}^Z f_B^Z \ , \end{equation}  which leads to the following $3\times 3$ covariance matrix $V $V_1  = 4\sin^2\theta_W \times {\cal L} \times X$ 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} X_{23}  = \int {\rm d}\Omega {f_A^Z \times f_B^Z \over S^0} \ , \\ & & X_{22} X_{33}  = \int {\rm d}\Omega {f_B^Z \times f_B^Z \over S^0} \ . \end{eqnarray}  In the second configuration of Ref.~\cite{Baer_2013}, only the two coefficients $F_{2V}^\gamma$ and $F_{2V}^Z$ are allowed to vary, which leads to the even simpler expression of Eq.~\ref{eq:optimal}  \begin{equation}  S(x,\theta) = S^0(x,\theta) - 2i\sin\theta_W \delta F_{2V}^\gamma (f_A^\gamma + f_C^\gamma) - 2i\sin\theta_W \delta F_{2V}^Z (f_A^Z + f_C^Z)  \end{equation}  and the following $2\times 2$ covariance matrix $V_2 = 4\sin^2\theta_W \times {\cal L} \times Y$, with   \begin{eqnarray}  Y_{11} = \int {\rm d}\Omega {(f_A^\gamma + f_C^\gamma)^2 \over S^0} \ , & Y_{12} = \int {\rm d}\Omega {f_A^\gamma + f_C^\gamma) \times (f_A^Z + f_C^Z) \over S^0} & \ , \\  & Y_{22} = \int {\rm d}\Omega {(f_A^Z + f_C^Z)^2 \over S^0} & \ .  \end{eqnarray}