[G8b_run] Polarization comparison update

[dugger at jlab.org]

Hi,

Due to the JLab cyber attack limiting my ability to connect to the CUE I
will not be giving links to figures.

I have analyzed the 1.3, 1.5, and 1.7 GeV data using the corrected code.
For those that may be interested: I have placed an explanation of the
coding error at the bottom of this email.

Results:
My latest comparison for the overlap between the 1.3 and 1.5 GeV edges are
nearly identical to what I showed previously (within statistical errors of
the previous results).

New study:
I have made a comparison of (PhExp/PvExp)/(PhKen/PvKen), where

* PhExp/PvExp -> ratio of the para to perp polarizations determined by my
pi0 study.

* PhKen/PvKen -> ratio of the para to perp polarizations given by ken

Here is what I come up with:
Edge     eCounters     (PhExp/PvExp)/(PhKen/PvKen)
1.3       341-369       1.1   +/- 0.1
1.5       321-255       1.040 +/- 0.009
1.7       300-335       1.009 +/- 0.008

There is a good consistency between the pi0 determination of the
polarization ratio and the the ratio obtained using Ken's numbers. The 1.3
GeV edge has the largest inconsistency, but is within statistical error of
the optimal value of 1. The large statistical error is due to the ratio
having a large scatter about the mean value. The 1.5 edge has the largest
statistically significant deviation from the value of 1, but is within 5%
of optimal. The 1.7 edge has a very nice value for the ratio of ratios.

The ratio of Sigma in the overlaps are:
Overlap     Orientation     ratio
1.3-1.5      Para            0.933 +/- 0.008
1.3-1.5      Perp            0.94  +/- 0.01
1.5-1.7      Para            1.00  +/- 0.02
1.5-1.7      Perp            NA

Note: Because of the energy cuts made on the instantaneous edge and the
fact that the Perp setting spans a smaller energy region given in the
PolTbl, there is only one point for the 1.5-1.7 Perp comparison within the
fit region that determines the ratio. That single point has a statistical
error that overlaps 1, but I don't think it is right to report the number,
since the number of data points used to determine the ratio is
inconsistent with the other ratios given.

Now we can play game:
If we demand consistency between the two type of measurements and assume
that the 1.7 Para set is correct, then the 1.7 Perp is close to correct
and the 1.5 para must also be close to correct. The para/perp ratio taken
for the 1.5 set then forces us to lower the 1.5 perp set by 4 to 5%.
Lowering the 1.5 perp by 4-5% would bring the 1.3 to 1.5 perp overlap to
be within statistical uncertainty of the optimal value. We then say that
the 1.3 Perp setting is close to correct. We also use the assumed
correctness of the 1.5 para to say that the 1.3 para must be low by 6 to
7%. If we change the 1.3 GeV set by 6 to 7% we are still within
statistical uncertainty of the para to perp ratio for the 1.3 GeV set.

I hope that I did not mess up the math. However, the nature of the game
does not change. We have a lot of information about ratios and we can use
that information to help constrain the possible values of the
polarizations. Demanding that we have consistency between the ratios gives
us correction factors and when we propagate all of the error, we will have
systematics for the corrections. There will always be one overall constant
that is undetermined. In the above "game", I assumed the 1.7 GeV para data
set had good polarization values. More realistically, the 1.7 GeV para
edge could be off by some multiplicative factor. To deal with the
systematic uncertainty of the overall multiplicative number, we can look
at all the settings that are statistically consistent and estimate the
uncertainty in the overall multiplicative factor from the scatter within
those setting. My gut feeling is that we can get the systematics to within
a few percent (assuming that the 1.9 and 2.1 sets don't hold any big
surprises).

The future: I'm going to try and optimize the energy range for the
instantaneous edge cuts. First, I will remove the energy cut entirely,
then I will systematically change the energy cuts and look for the best
case scenario. I hope to have this study finished by Tuesday.

The coding error (if interested):
In the old PolTbls the number of edges was fixed to be 80 for all of the
g8b data sets. In Ken's new code, the number of edges in the PolTbl is
dependent upon the polarization orientation and run edge setting. In my
fortran code I placed a goto statement such that, if an event edge had a
value outside of the available edges in the PolTbl, it was possible that
the event processed as normal, but used the last valid PolTbl edge. This
is obviously wrong and I have now corrected the code.

Take care,
Michael