Problem:
    The SMD provides the spatial resolution to discriminate between single direct photon showers and two neutral pion decay photon showers.  Given the SMD information, however, how exactly do we perform this discrimination?

In particular, we would prefer a discrimination algorithm that is either

• Insensitive to the loss of peak heights (in the case of small dynamic range of the SMD response)

or

• Insensitive to the loss of low energy depositions (in the case of low resolution of the SMD response OR a deliberate low energy threshold made due to poor simulation of low energy depositions)

Additionally it would be nice if the algorithm was robust against dead strips, but that criterion will have to wait a bit.

Solution(?):
    The first algorithm studied is the energy weighted sample kurtosis of the SMD shower.  Defined as

the kurtosis is a measure of "peakedness" of the shower.  Small values of the kurtosis correspond to showers with high shoulders (indicative of large energy deposition away from the peak as in pion decays) while larger values of the kurtosis correspond to showers with high peaks and long tails.  Note that any linear scaling of the SMD strip energies cancels, so the kurtosis is approximately invariant to the energy of the shower.
    The kurtosis is calculated for StGammaCandidates identified in eta-phi space with direct photons (signal) or not identified (background) using StGammaCandidates from both direct photon and 2006 jet simulations (appropriately weighted).
    To study the robustness of this method we place a low energy threshold on the SMD strips included in the calculation (kurtosis of the phi strips is along the x axis while the  kurtosis of the eta strips is placed along the y axis),

as well as a high energy threshold above with the SMD strips saturate

Conclusion:
In the end the kurtosis provides only a small amount of discrimination between direct photon candidates and background candidates.  Moreover, this discrimination power rapidly decreases as the lower energy SMD depositions are removed, hence this method would require decent SMD resolution and good simulation of the shower tails.  Let's see if we can do better.