Patrick Janot edited Statistical analysis.tex  about 9 years ago

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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) +delta F_{1V}^\gamma  2\sin\theta_W \delta F_{1V}^\gamma  f_A^\gamma +delta F_{1V}^Z  2\sin\theta_W \delta F_{1V}^Z  f_A^Z +delta F_{1A}^Z  2\sin\theta_W \delta F_{1A}^Z  f_B^Z \ , \end{equation}  which leads to the following $3\times 3$ covariance matrix $V = 4\sin^2\theta_W \times  {\cal L} \times  X$ 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} = \int {\rm d}\Omega {f_A^Z \times f_B^Z \over S^0} \ , \\