Associating mcTracks with reconstructed points in the EEMC

In any resolution or efficiency determination, one must have some method for associating which mcTrack corresponds to which reconstructed point.  I feel the method which has been previously used for the EEMC (used by both Alice and Weihong) has some problems, and I suggest the following solution.

The previous method

Alice and Weihong both used a method where, for every pi0 candidate, one associates any and all mcTracks satisfying the following criteria:

  1. the mcTrack is a pi0 that originated from the primary vertex
  2. the value ((delta phi)^2+(delta eta)^2) is below some threshold, where (delta phi) is the difference between the phi of the momentum of the pi0 candidate and the phi of the momentum of the mcTrack, and similarly for (delta eta).

This has several disadvantages: first, the statistics are not preserved, as all tracks are associated with weight one, and multiple mcTracks may be associated with a given pi0 candidate and multiple pi0 candidates with a given mcTrack.  This is probably a minor effect, as rarely will there be multiple pi0s from the same vertex heading in almost the same direction.  The worse problem is that one has biased the results by ignoring all cases where no pi0 was generated with (phi, eta) near where one was reconstructed. While cases where the pi0 candidate is close to a generated pi0 are handled OK, cases where the the reconstructed pi0 is not close, or where there was no pi0 generated at all, are not handled at all.  In the case of resolution plots, it is essential that all cases are considered.  In the case of efficiency plots, one must argue that these ignored cases are background and that the background is properly modeled and subtracted.  Note: a significant background is when a single gamma is reconstructed as two gammas, (see Keith's work of Summer, 2010 and 2011) and we do not  have a good model of the shape of this background vs. pT or M_pi0.

New Method

For every reconstructed point on the EEMC, a number of mcTracks will be associated with weights, such that sum of the weights for a given reconstructed point equal 1.  The concept is to assign the weight according to how the energy the mcTrack deposited per SMD strip corresponds with strip-energies associated with the reconstructed point. The weights are determined by considering, for every SMD strip, the amount of energy deposited by a given mcTrack into the strip, and the strip-cluster weight (how much of the energy of the strip contributed to the energy of the cluster, i.e. if multiple clusters used the same strip).  The weight, before normalization, is then the sum over strips of the product of the mcTrack energy times the strip-cluster weight.  The same method can be done with the towers instead of the strips, but the resolution of the towers is not fine enough to yeild good results.   One can then choose to interpret the weights as one pleases, i.e. either associating the point with just the highest weight mcTrack, or using all mcTracks with their various weights.  In practise, using just the highest weight track works well. This method still has a few disadvantages, but overcomes the bias problem, allowing more accurate estimates of the resolution and efficiency of various algorithms.

The method has been implemented in www.star.bnl.gov/cgi-bin/protected/cvsweb.cgi/offline/users/sgliske/StRoot/StEEmcPool/StEEmcHitMaker/StMcEEmcHitMakerStrips.h and tested with the "Micky Mouse" Monte Carlo generator (i.e. feeding an ascii text file into Geant via starsim).