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Patrick Janot edited Statistical analysis.tex
about 9 years ago
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\end{equation}
which leads to the following $3\times 3$ covariance matrix $V_1 = 4\sin^2\theta_W \times {\cal L} \times X$ 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_{23} = \int {\rm d}\Omega {f_A^Z \times f_B^Z \over S^0} \ , \\
& & 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}
...
\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}