# Calculating EEMC tower ideal gains and expected MIP response

This is a quick summary of how one goes from a measured MIP peak to a final tower gain.

In the attached spreadsheet, I use the EEMC tower boundaries in eta (lower table) to determine the average eta per bin and the ideal gain in each bin, assuming our goal ("ideal") is to have an e.m. shower of transverse energy ET = 60 GeV saturate the 12-bit ADC, that is, land in channel 4096.  This calculation is independent of assumed sampling fraction.  The result appears in column H in the lower table, and is highlighted in yellow.

For a calibration based on MIP's, we also need to know the actual energy deposited by the MIP as it traverses all of the scintillator layers, so we need to know the total thickness of scintillator (for normal incidence) and the dE/dx of a MIP.  These values appear in cells L5 and M5, respectively.  All calculations are keyed to these cells, so changing these cells will propagate to all other columns.

Finally, to connect ideal gains with MIP energy depositions (so we can arrive at the quantity of direct interest for a MIP-based calculation: in which ADC channel (above pedestal) should the MIP peak appear?), we also need to know the calorimeter sampling fraction.  I have used 5%, which is in cell G5.  Again, changing this one cell value will fill the rest of the tables accordingly.

With these assumed values (60 GeV, 4096 channels, 99 mm, 0.20 MeV/mm, 5% - all in row 5) one can now determine the ADC channel (above pedestal) in which the MIP peak will appear, if the gain is "ideal".  These are given in column N of the upper table and highlighted.  For each tower, the ratio of the actual (measured / fit) MIP peak channel to this ideal channel is the factor by which the ideal gain needs to be multiplied to arrive at the "true gain" per tower, which is what is loaded into the database.

N.B.  I just cut and pasted these two tables together, so there is some overlap between them.  Several columns relate to estimating number of photo-electrons (pe) and high voltage (HV) and can be ignored.

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