Pseudorapidity distribution with the "Fit Method"

Recently, I posted an analysis of the eta distribution from the 54 GeV data, based on calibrated picoDst files.

As I pointed out there, the dNdeta distribution from the EPD was WAY too large.  I now know why, and I'll explain here:

In that analysis, I looped over Position (PP) and Tile (TT) and filled one single histogram, like this:

Double_t nMIP = Epd->GetTile(-1,PP,TT)->nMIP());
h_dNdeta->Fill(eta,nMIP);

Recall that StEpdTile::nMIP() returns the signal in that Tile, normalized by the 1-MIP Landau MPV for that Tile.  It is an intuitive, beautiful and simple way to do the analysis.  However, intuition fails us, unfortunately, and this method fails.  There are two reasons:

  1. The mean value of a Landau distribution is undefined, due to its long tail.  (See e.g. wikipedia)
  2. Any noise that gives spurious high ADC values (and there is always a count here or there) skew the distribution

In the nMIP() distributions, of the 93 tiles, there would be counts at nMIP>10 not infrequently.  There were occasional rogue counts at nMIP=30 or nMIP=40.  The chance that these are truly 40-MIP events is zero.  Putting an "upper cut" on nMIP would be artificial and would not actually eliminate the skew problem.  The only correct way to handle this is through fitting.