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Error propagation in Amplitude Analysis (view source)
Revision as of 17:29, 22 November 2011
, 17:29, 22 November 2011no edit summary
When considering the uncertainty on the overall integral, both the errors on the ''u'' parameters
When considering the uncertainty on the overall integral, both the errors on the ''u'' parameters
and those from the finite MC statistics will contribute. The part of the error on the intensity coming from the finite MC statistics is computed using the usual rules for error propagation. A subtle point easy to miss at this stage is that the errors on the <font face="Times">''I''</font><sub>αβ</sub> are correlated because they are computed on the same MC sample. Therefore, while the <font face="Times">''I''</font><sub>αβ</sub> is rank 2 in the partial wave index, its error is rank 4.
and those from the finite MC statistics will contribute. The part of the error on the intensity coming from the finite MC statistics is computed using the usual rules for error propagation. A subtle point easy to miss at this stage is that the errors on the <font face="Times">''I''</font><sub>αβ</sub> are correlated because they are computed on the same MC sample. Therefore, while the <font face="Times">''I''</font><sub>αβ</sub> is rank 2 in the partial wave index, its error is rank 4.
<math>
<math>
u_\alpha u_\beta^* u_{\alpha'} u_{\beta'}^*
u_\alpha u_\beta^* u_{\alpha'} u_{\beta'}^*
\left[ \frac{1}{N_{gen}^2} \sum_i^N{
\left[ \frac{1}{N_{gen}^2} \sum_i^N{
A_\alpha^{\gamma \delta}(x_i) A_\beta^{\gamma \delta *}(x_i)
A_\alpha^{\gamma}(x_i) A_\beta^{\delta *}(x_i)
A_{\alpha'}^{\gamma' \delta'}(x_i) A_{\beta'}^{\gamma' \delta' *}(x_i)
A_{\alpha'}^{\gamma'}(x_i) A_{\beta'}^{\delta' *}(x_i)
}
}
\right]
\right]