IDEA

In a previous blogpost, I checked what happens if one tries to unfold a simulated EPD dataset (ring-by-ring hit info) that is created by some distorted dN/dη distribution. The result was that the 2<|η|<5 region was unfolded well, even if the EPD dataset came from a different dataset than the one on which the response was trained. In simple words, I used one response matrix on various EPD datasets. Now let us try to do the opposite: unfold one EPD dataset with various response matrices!

The response matrices were trained on distorted HIJING data, where a Gaussian distortion with a center η₀ and a width σ was applied on the pseudorapidity distribution, with the following logic:

where the η₀ and σ values were the following:

Here the one with a width of 10000 essentially means "no distortion", the others are more and more distorted as σ gets smaller. And there are 6 versions where there is also a shift. Here is an illustration:

FIG 1: SUPPRESSION FACTOR

Then the response matrices from the above distorted samples were used to unfold another EPD dataset.

RESULTS

Here are the results for various response matrices and EPD datasets:

FIG 2: MC truth: η0=0 and σ=10000	FIG 3: MC truth: η0=0 and σ=4	FIG 4: MC truth: η0=0 and σ=3
FIG 5: MC truth: η0=0 and σ=2	FIG 6: MC truth: η0=0 and σ=1
FIG 7: MC truth: η0=+3 and σ=3	FIG 8: MC truth: η0=+2 and σ=3	FIG 9: MC truth: η0=+1 and σ=3
FIG 10: MC truth: η0=–3 and σ=3	FIG 11: MC truth: η0=–2 and σ=3	FIG 12: MC truth: η0=–1 and σ=3

LESSONS

1. In the 2<|η|<5 region, all matrices unfold the same dN/dη, except the one that was trained on a sample with σ=1, as this is too narrow, and there are basically barely any EPD hits.
2. If the response and the EPD data are from the same sample, then unfolding is exact.
3. If the EPD data is from the sample of with σ=1, then no response matrix can reasonably unfold it, except the one that was trained on exactly the same sample.

Here is a ratio plot for all of the above cases (except where σ=1), i.e. this contains 10x10=100 curves (10 EPD MC data unfolded with 10 different respones each):

FIG 13: UNFOLDING/MCTRUTH RATIO FOR PLOTS 2-12 (100 CURVES IN TOTAL)

Ultimately, I believe this shows that the unfolding works well in the 2<|η|<5 region, and the systematic uncertainty from the training sample choice can be estimated well, and accounts for the discrepancy in the central (|η|<2) and very forward/backward (|η|>5) regions.

 
To visualize that differently, let me show here the χ² maps of the two different ranges (EPD range: 2<|η|<5; other range: elsewhere):

FIG 14: UNFOLDING-MCTRUTH CHISQUARE MAP, 2<|ETA|<5	FIG 15: UNFOLDING-MCTRUTH CHISQUARE MAP, |ETA|>5 OR |ETA|<2

Besides the yellow cross corresponding to σ=1, the χ² values for the EPD pseudorapidity range are pretty reasonable, taking into account the number of datapoints (120).

APPENDIX