Pi0 Calibrations - Version 2.0

Do we need to redo the calibration?

Yes! Here is why:

  1. Hovannes's calibration was done years ago and is not documented (if it is please show me where).
  2. Our understanding of the detectors has improved a lot since then.
  3. Comparisons against the elastic few elastic events have shown disagreement. (link to Anusha's work)
  4. The eta mass reconstruction is poor. (no clear peak)
  5. Since it provides our only determination of the energy, it should be double checked!
  6. Pi0 mass reconstruction is not uniform.

Here is a result having roughly calibrated the lower half of bigcal for symmetric decays with a limited energy range (around 1100 MeV): Note second and third plots in the middle show the first and second clusters vertical position VS mass reconstruction.

Procedure

First, for each photon cluster, an energy and x-y position corrections are calculated from a GEANT4 based simulation trained neural network. This corrects for the fact that not all the energy is "visible" in the calorimeter and to get proper x-y position at the face of bigcal corrected for showers produced by particles off normal incidence (ie, an incident angle correction).

The calibration procedure roughly follows this paper. I do not know how Hovannes originally did his calibration (because it is not documented anywhere that I know of) but I believe he used this paper as well.

This procedure involves inverting a rather large matrix, which, in practice can be quite difficult. When calibrating the whole detector a 1744x1744 matrix needs to be inverted. Since the matrix is built with real data, it is not guaranteed to be invertible because some blocks may not have participated (significantly) in any pi0 events. In order to avoid complications, an eigen-decomposition of the matrix is performed and only blocks with eigenvalues that are not consistent with zero are used (since the inverted matrix is the sum of terms proportional to 1/eigenvalue).

Once the matrix is inverted, the solution to the equation for the small corrections for each block (E -> (1+epsilon)E). In the perfect world, the correction could be completed in one iteration, however, there are lots of backgrounds, noisy channels, and combinations of corrections which the data sample cannot determine. So the corrections are applied iteratively.

Only one percent of the calculated epsilon value is taken along with imposing a maximum allowable value. This avoid over-correction oscillations, which can happen quite easily, and allows for a smooth and steady convergence to the best values of epsilon.

Initial Attempts

Below are the diagnostic plots of an iteration. It is clear that some noisy channels need to be treated and that the corrections are large.

Calibration in pieces

Since the initial results were so large, I decided to take a more careful approach. After lots of work building a flexible calibration code, calibration can be performed on arbitrarily defined sections of bigcal. This is much better for a few reasons.

  1. The pi0 photon cluster separation is not that large (unlike the eta) and statistics are good even for small sections. They just need to span two quadrants.
  2. Noisy sections can be isolated.
  3. Can check that other sections are not biasing the results.
  4. Faster and easier matrix inversion.
  5. Can focus on calibrating hard to reach corners of bigcal after easier areas.

It is clear that when all of BigCal is calibrated at once, the peak looks OK. But when it is broken down into sections, there is clearly room for improvement Again, here the lower half has been re-calibrated:

Here are 3 iterations:

You will notice the top right plot converging towards zero. This is the difference between the calculated and actual masses squared.

Here is an example of the upper part of Bigcal after a few iterations:

Conclusion and Future Work



A lot more plots are found here.
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[IMG]pi0mass3_4.png 2015-01-09 17:56 34K 
[IMG]pi0Calibration_c1_fu..>2015-01-09 17:56 42K 
[IMG]pi0CalibrationCompar..>2015-01-09 17:56 34K 
[IMG]pi0CalibrationCompar..>2015-01-09 17:56 34K 
[IMG]pi0Calibration2_5_c1..>2015-01-09 17:56 59K 
[IMG]pi0Calibration2_5_2.png2015-01-09 17:56 19K 
[IMG]pi0Calibration2_0_c1..>2015-01-09 17:56 55K 
[IMG]pi0Calibration2_0_c1..>2015-01-09 17:56 55K 
[IMG]pi0Calibration2_0_c1..>2015-01-09 17:56 55K 
[IMG]hms_elastics_1.png 2015-01-09 17:56 27K 
[IMG]etamass_2.png 2015-01-09 17:56 36K 
[IMG]etamass2-1600_0.png 2015-01-09 17:56 27K 
[IMG]etamass2-1400_0.png 2015-01-09 17:56 28K 
[IMG]etamass2-1300_0.png 2015-01-09 17:56 28K 

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