Changes between Version 20 and Version 21 of DatabaseBasedAnalysis/Spectrum


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Timestamp:
Dec 3, 2019, 5:19:37 PM (10 months ago)
Author:
tbretz
Comment:

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  • DatabaseBasedAnalysis/Spectrum

    v20 v21  
    99\[\phi(E) = \frac{1}{A_0\cdot \Delta T}\frac{N(\Delta E)}{\epsilon(\Delta E)\cdot \Delta E}\]
    1010
    11 For simplicity, in the following, \(\Delta E\) will be replaced by just \(E\) but always refers to an average quantity in an given energy interval. Note that strictly speaking the average quantity is not independent of the event distribution in that interval so that the calculation are only exact if the correct distribution is assumed!
     11For simplicity, in the following, \(\Delta E\) will be replaced by just \(E\) but always refers to to a given energy interval.
    1212
    1313The total area \(A_0\) and the corresponding efficiency \(\epsilon(E)\) are of course only available for simulated data. For simulated data, \(A_0\) is the production area and \(\epsilon(E)\) the corresponding energy dependent efficiency of the analysis chain. For a given energy bin, the efficiency is then defined as
     
    1616
    1717where \(N_0\) is the number of simulated events in this energy bin and \(N=N_{exc}\) the number of *excess* events that are produced by the analysis chain.
     18
     19Note that the exact calculation of the efficiency \(\epsilon(\Delta E)\) depends on prior knowledge of the correct source spectrum \(N_0\). Therefore, it is strictly speaking only correct if the simulated spectrum and the real spectrum are identical. As the real spectrum is unknown, special care has to be taken of the systematic introduced by the assumption of \(N_0\).
    1820
    1921The number of excess events, for data and simulations, is defined as