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Error propagation in Amplitude Analysis (view source)
Revision as of 18:43, 23 November 2011
, 18:43, 23 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.
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.
:<math>
:<math>
= \sum_{\alpha,\beta,\alpha',\beta'}^n{
= \sum_{\alpha,\beta,\alpha',\beta'}^n{
u_\alpha u_\beta^* u_{\alpha'} u_{\beta'}^*
u_\alpha u_\beta^* u_{\alpha'}^* u_{\beta'}
\left[ \sum_{\gamma,\delta,\gamma',\delta'}{ \rho_{\gamma\delta}\rho_{\gamma'\delta'}
\left[ \sum_{\gamma,\delta,\gamma',\delta'}{ \rho_{\gamma\delta}\rho_{\gamma'\delta'}
\frac{1}{N_{gen}^2} \sum_i^N{
\frac{1}{N_{gen}^2} \sum_i^N{
A_\alpha^{\gamma}(x_i) A_\beta^{\delta *}(x_i)
A_\alpha^{\gamma}(x_i) A_\beta^{\delta *}(x_i)
A_{\alpha'}^{\gamma'}(x_i) A_{\beta'}^{\delta' *}(x_i)
A_{\alpha'}^{\gamma'*}(x_i) A_{\beta'}^{\delta'}(x_i)
}}
}}
\right]
\right]