Hello,

Junhua's recent results on fitting with scale factors are all available 
from http://nuclear.uwinnipeg.ca/ucn/bs/

To summarize his results:

He has provided scale factors for every graph in every paper under the 
assumption of a constant _percentage_ of the point-to-point uncertainty.
This is not a unique assumption.  In a systematically dominated 
experiment, it is VERY difficult to estimate the point-to-point 
uncertainty, which is one reason I am reluctant to put numbers like this 
in a paper.  If there were a sensible way to quote a relative chi2, I 
might change my tune on that.  I am open to suggestions.

Consequently, all fit uncertainties and chi2's are only meaningful in a 
relative sense.  The scale factors themselves should all carry an 
uncertainty of approximately 12%, which is our normalization systematic 
uncertainty, added in quadrature with an additional error due to our 
assumption about the pt-pt uncertainty.  I would claim an indication of 
that level of error is the comparison to the "by eye" scale factor, which 
I have added in to junhua_double.txt.  This suggests an uncertainty 
comparable with the normalization systematic uncertainty.  This is 
confirmed by Junhua's statement:  "I fit the double-differential 
distributions with both G4 and Penelope simulations, assuming 12% error on 
the data points." and the fact that the reduced chi2's in general works 
out to be around unity for that assumption.

Under this assumption, the Penelope chi2's tend to be lower than the 
Geant4 chi2's, as we expected qualitatively.

Were we to quote overall scale factors in our paper, the most reasonable 
thing would be something like those found in junhua_nibf_1df.txt which 
summarize the scale factor determined by chi2 minimization (again with 
some assumption for pt-pt uncertainty which I do not know) to ALL the 
data.  Again, I would say only the scale factor is meaningful in an 
absolute sense, the chi2 and error bar might be useful in some relative 
sense.  Again, in general, the scale factors (particularly for Penelope) 
would agree with unity within the current normalization systematic 
uncerainty.

In summary, I still recommend against including scale factors or chi2's in 
the paper.  The reasons are:
1.  It would require an estimation of pt-pt systematic uncertainties, 
which is difficult to do in a systematically limited experiment.
2.  The most reasonable scale factors we could quote would be on the 
NIBF's.

However, one thing I did learn from this study is that the "Conclusion" 
section currently in the paper is totally wrong.  Penelope wins in shape 
AND normalization.  I think probably there are a few other places where 
this could be cleaned up.  Additionally, I would recommend a sentence in 
the conclusion stating we did these Chi2 studies, that pt-pt uncertainties 
were difficult to estimate, and that the resultant scale factors for 
Penelope were in agreement with unity within the normalization 
uncertainty.

If there are no objections, I will make the appropriate changes to the 
paper.

Jeff

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