SMD Residuals

First, here is a quick review of the cuts applied so far (numbered so that they correspond to the plot of the number of hits that survive each cut):

1. Seed towers with energy > 1 GeV are selected

2. The highest-energy 2x2 tower patch containing the seed tower is a hit if it has energy > 4 GeV

3. The hit is kept if the associated 2x2 preshower patch has energy > .32 MeV

4. The hit must have an SMD eta strip with energy > 10 keV (the highest-energy such strip and the three strips on either side form the cluster in the eta plane)

5. The hit must have an SMD phi strip with energy > 10 keV (the highest-energy such strip and the three strips on either side form the cluster in the phi plane)

6. The hit must not have SMD eta cluster energy < 55 keV and SMD phi cluster energy < 45 keV

With these cuts applied, we can implement a measurement of the SMD residual.  To determine this, we take the set of seven (to match the size of the cluster) strips to the right or left of the SMD cluster in the eta or phi plane, and for each set of strips sum the deposited energy.  The largest of the four values is our residual.  We can plot the log of the residual vs. the log of the average of the eta and phi cluster energies, in energy bins (as we expect that the residuals will be energy-dependent) for pizeros and gammas (note that these plots exclude those hits with residuals equal to 0, which is about half the sample in both cases):

Gamma:

Pi0:

These plots strongly suggest a cut requiring that the log of the residual be less than -5 or so.  In fact I implemented the cut log(residual)<-5.2, with results as follows for gammas, pizeros, and piminuses (the last included only for reference as the residual cut doesn't effect them much.  The bins on the cut results plot are as listed above, with the last bin being the residual cut:

Gamma:

Pizero:

Piminus:

This cut is perhaps a little strict: it could be loosened slightly or adjusted so that there is a separate cut for each energy bin.

We can examine the residuals in a different fashion by plotting the log of the ratio of the residual divided by the cluster energy from the plane the residual is taken from against the ratio of the smaller smd cluster energy to the larger smd cluster energy (after the above cut has been applied).  Note that the line at -11 in the lowest energy bin is actually for hits with zero residuals, which otherwise would not show up.

Gammas:

 

Pi0s:

 

These plots appear to be fairly similar, suggesting that the cut on the size of the residual is the main cut to be made here.

Important note: these results are naturally dependent on the definition of the cluster.  Currently the cluster is defined as a high strip and the three strips on either side, but it may be worth trying to redo everything with a cluster defined as the high strip and the two strips on either side to see if a narrower cluster gives more information about residuals without sacrificing too much information about the cluster.