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Energy-Energy Correlation

The Energy-Energy Correlation is defined by [Bas78]

\mathrm{EEC}(\theta) = \sum_{i < j}
\frac{2 E_i E_j}{E_{\mathrm{vis}}^2} \,
\delta(\theta - \theta_{ij}) ~,
\end{displaymath} (298)

and its Asymmetry by
\mathrm{EECA}(\theta) = \mathrm{EEC}(\pi - \theta) - \mathrm{EEC}(\theta) ~.
\end{displaymath} (299)

Here $\theta_{ij}$ is the opening angle between the two particles $i$ and $j$, with energies $E_i$ and $E_j$. In principle, normalization should be to $E_{\mathrm{cm}}$, but if not all particles are detected it is convenient to normalize to the total visible energy $E_{\mathrm{vis}}$. Taking into account the autocorrelation term $i = j$, the total $\mathrm{EEC}$ in an event then is unity. The $\delta$ function peak is smeared out by the finite bin width $\Delta \theta$ in the histogram, i.e., it is replaced by a contribution $1 / \Delta \theta$ to the bin which contains $\theta_{ij}$.

The formulae above refer to an individual event, and are to be averaged over all events to suppress statistical fluctuations, and obtain smooth functions of $\theta$.

Stephen_Mrenna 2012-10-24