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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}
\label{eq:firstInt} X_{11} = \int {\rm d}\Omega {(f_A^\gamma)^2 \over S^0} \ , \ & {\displaystyle 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} \ , \\
& {\displaystyle X_{22} = \int {\rm d}\Omega {(f_A^Z)^2 \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)^2 \over S^0} \ .
\end{eqnarray}
...
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} \ , \ & {\displaystyle Y_{12} = \int {\rm d}\Omega {(f_A^\gamma + f_C^\gamma) \times (f_A^Z + f_C^Z) \over S^0}} & \ , \\
\label{eq:lastInt} & {\displaystyle Y_{22} = \int {\rm d}\Omega {(f_A^Z + f_C^Z)^2 \over S^0} } & \ .
\end{eqnarray}
The numerical results are presented in the next section for the case of the FCC-ee.