Testing the unfolded rapidity distributions

As noted in the previous blogpost, dN/deta is "too well" reproduced by the unfodling algorithm, especially if one feeds the same EPD distribution to it as what was used to generate the response matrix. Here is a comparision, where the MC truth dN/deta and the unfolded dN/deta overlap point by point:

Now I did a test where I artificially distorted the input MC truth, by randomly keeping or discarding MC tracks based on their pseudorapidity. The logic was the following:

and the distribution was a Gaussian, with the mean and the sigma being variable. Below are a lot of plots from such checks, where always the red is the input MC truth and the blue is the unfolded dN/deta:

Reducing the width (sigma=10000,4,3,2,1)

(the first plot with sigma=10000 is there just as a test, there basically no modification of dN/deta was done)

Shifting the center (mean=-3,-2,-1,1,2,3) and reducing the width (sigma=3)


Ratio of unfolded result over input MC truth
All the above cases were used to produce a compilation of unfolding over MC truth results. Notably in the 2<|eta|<5 region, the ratio is approximately compatible with 1 within current uncertainties of the simulation (note that only 5 colors were used for the 11 cases, so this plot is basically just to give an idea of how good the reproduction is)

Uncertainty calculation

Clearly there above shown uncertainties are not correct, as the reproduction fails by a much larger amount. Hence different things were tried:

1. Calculate the uncertainties with one of the following methods:
   1. RooUnfold::ErrorTreatment::kNoError
   2. RooUnfold::ErrorTreatment::kErrors
   3. RooUnfold::ErrorTreatment::kCovariance
   4. RooUnfold::ErrorTreatment::kCovToy
2. Check the reconstructed (unfolded histogram):
   
3. Check the error matrix (lots are in the following order: kNoError, kErrors, kCovariance, kCovToy)
   
4. Calculate the uncertainties based on the error matrix:
   

Observation: while the uncertainties depend on the method (and on taking the covariance matrix into account), they still do not account for the large difference.

I suspect that this has something to do with midrapidity tracks leaving no hits in the EPD at all, these shall be accounted for somehow. As a first step, I checked the dN/deta distribution of MC tracks with EPD hits (and that of all MC tracks). Here are the resulting plots (in two vertical zoom versions):