[Frost] Target sign comparison study

[Michael Dugger]

Hi,

I have used Natalie's method to try and reproduce her results regarding 
the study of target polarization orientation.

I am calling Natalie's approach the half-Plane method. She sums all counts 
separately above and below the polarization plane to derive her results. 
This is essentially a two-bin phi method.

The expression I use for the half-plane method is
T = (1/P)*(Y1 - Y2)/(Y1 + Y2),
where
Y1 = (counts above polarization plane)/(incident photon count)
Y2 = (counts below polarization plane)/(incident photon count)

I define the counts below the polarization plane to include the phi angles 
between 120 and 300 degrees. All other angles are associated with being in 
the upper polarization plane.

For the half-plane method I obtain the plots (using my definition of 
target polarization sign):
Egamma = 775  -> http://www.public.asu.edu/~dugger/halfPlane775.gif
Egamma = 875  -> http://www.public.asu.edu/~dugger/halfPlane875.gif
Egamma = 975  -> http://www.public.asu.edu/~dugger/halfPlane975.gif
Egamma = 1075 -> http://www.public.asu.edu/~dugger/halfPlane1075.gif
Egamma = 1175 -> http://www.public.asu.edu/~dugger/halfPlane1175.gif
Egamma = 1275 -> http://www.public.asu.edu/~dugger/halfPlane1275.gif

where the panels represent:
upper left: Events from set 2 (runs in range 62297-62373)
upper right: Events from set 3 (runs in range 62374-62489)
bottom left: Events from set 4 (runs in range 62490-62604)
bottom right: Events from set 5 (runs in range 62609-62704)

Comments:
First off, this is some ugly stuff. The half-plane method should not be 
used. The CLAS efficiency issues are far too large for the half-plane 
method to give reliable results for the determination of T from FROST 
data. To help illustrate this point, compare the above results to the 
phi-bin method where set 3 and 4 are combined to resolve issues of 
detector efficiency:
Egamma = 775  -> http://www.public.asu.edu/~dugger/t775.gif
Egamma = 875  -> http://www.public.asu.edu/~dugger/t875.gif
Egamma = 975  -> http://www.public.asu.edu/~dugger/t975.gif
Egamma = 1075 -> http://www.public.asu.edu/~dugger/t1075.gif
Egamma = 1175 -> http://www.public.asu.edu/~dugger/t1175.gif
Egamma = 1275 -> http://www.public.asu.edu/~dugger/t1275.gif

The phi-bin method clearly compares much better to world data and the 
theoretical curves than the half-plane method.

However, one might be able to say that -very roughly- the half-plane 
method is good enough to help in distinguishing the sign of the target 
polarization. If this is true than I think that my half-plane results 
(using my definition of the target polarization sign) show that my sign 
definitions give consistent T results from set to set.

Another point that must be brought up is the fact that my results for the 
half-plane method, while no worse looking than Natalie's, do not match 
well with what Natalie has shown, and that we are using different signs of 
the target polarization for sets 4 and 5.

Conclusion:
We will need to come up with better agreement on the T comparisons to make 
any progress in resolving issues regarding the direction of the target 
polarization.

Take care,
Michael