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The following is a review of error propagation needed to compute the errors on the normalization integrals and the intensity sum that is based on them.  Consider the estimator for the intensity for a given PWA solution, based on a sum over a Monte Carlo sample with N_gen phase space events generated and N reconstructed and passing all cuts.  A subtle point easy to miss at this point is that the errors on the ''I''_{αβ} are correlated because they are computed on the same MC sample.  Therefore, while the ''I''_{αβ} is rank 2 in the partial wave index, its error is rank 4.

The following is a review of error propagation needed to compute the errors on the normalization integrals and the intensity sum that is based on them.  Consider the estimator for the intensity for a given PWA solution, based on a sum over a Monte Carlo sample with N_gen phase space events generated and N reconstructed and passing all cuts.  <math>

<math>

I=\frac{1}{N_{gen}}\sum_i^N{

I=\frac{1}{N_{gen}}\sum_i^N{

   \sum_{\gamma,\delta}{\rho_{\gamma\delta}

   \sum_{\gamma,\delta}{\rho_{\gamma\delta}

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. A subtle point easy to miss at this stage is that the errors on the ''I''_{&alpha;&beta;} are correlated because they are computed on the same MC sample.  Therefore, while the ''I''_{&alpha;&beta;} is rank 2 in the partial wave index, its error is rank 4.

 

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