Trying a new formula to calculate the cluster sigmaMax

Cluster sigmaMax is a varaible that is used primarily to categorize the Yiqun clusters before the shower fitting is attempted. It is assumed that this variable, at a given energy, is good a signature to distinguish 2 photon from 1 photon clusters. Consequently, it plays a crucial role in the issues of di-photon merging and single photon splitting.

So far we had difficulty matching the distribution of this variable between data and MC. For one thing, the way it is defined, (second moment of cell coordinates weighted by energy) it is very sensitive to the soft towers in the cluster, and as a result the 1-count issues like the noise and pedestal uncertainty really changes the distiritbution.

Other problem we have is that above 55GeV, its effectiveness in distinguishing 2 photon from 1 photon clusters drops significantly. Two of the main reasons for this seem to be that 1. it is too sensitive to the soft junk, and 2. it is also very sensitive to the topology of the cluster. That is, whether the cluster is in the center of a cell or not. Both factors broaden the distribution for the clusters significantly.

While ultimately improving the shower fitting will be the best way to improve the reconstruction, we've tried a few different formulas to calculate the sigmaMax as a relatively quick and easy fix to the practical issues.

It turns out that a weighting scheme based on the suggestion by Jan works the best in alleviating these symptoms. That is, we use ln(E) instead of E as our weights, while suppressing the soft towers. Here we used minimum tower energy requirement of 0.5GeV to be included in the sigmaMax calculation.

This seems to have two major effects.

1. It obviously removes most of the sensitiveness to soft junk, thereby making the data-MC comparison easier and also sharpen up the distribution.

2. it greatly reduces the topology-dependent effect, which again sharpens the distribution.

Data-MC comparison for the old and new sigmaMax scheme

1. Old and New Esum vs. SigmaMax for Inner Events

2. Old and New Esum vs. SigmaMax for Edge Events