[G12] g12: EC corrections and resolution

[Andrea Celentano]

Dear all,
I tried to derive photons corrections for MC and data, following the 
procedure described in this note: 
https://misportal.jlab.org/ul/Physics/Hall-B/clas/viewFile.cfm/2011-004.pdf?documentId=632
Basically, this is based on the exclusive reaction gamma p -> p pi+ pi- 
gamma, *where all the particles are measured*. The measured gamma 
3-momentum is compared to the 3-momentum obtained from a 1C kin. fit to 
the  gamma p -> p pi+ pi- (gamma) hypothesis.
For Kin. fit, I am using the package provided by MK. Simulations have 
been performed with MK DB and runIndex = 10.

After deriving MC corrections (and waiting for data to be skimmed), I 
also looked at photon resolution and covariance matrix for MC. For MC, 
cov. matrix can be determined comparing the "true" gamma 3-momentum with 
the measured one. The "true" 3-momentum can be the generated one, or the 
one obtained from the kin. fit. For data, the same procedure can be 
adopted, and the "true" gamma 3-momentum will be the missing one 
obtained from the kin. fit. However, when using as "true" 3-momentum the 
one obtained from the kin. fit, the resolution (i.e. the width of the 
"kin.fit-measured" distribution) is given by the (quadratic) sum of the 
error on the measured quantity, and the error on the missing photon 
3-momentum from kin. fit. If the latter is "small", it can be neglected.

I attach a plot (MC1.png) showing the MC distribution of:

* Generated photon energy - kin. fit photon energy (black)
* Measured photon energy - generated photon energy (red)
* Kin. fit photon energy - measured photon energy (green)

The width of the black curve is smaller than the one of the red curve, 
showing the the kin. fit photon energy error is much smaller than the 
measured photon energy error. This guarantees that the resolution 
studies based on comparing the kin. fit photon energy to the measured 
one are not biased.

I also attach a plot (MC2.png) showing the MC distribution of:

* Generated photon theta - kin. fit photon theta (black)
* Measured photon theta - generated photon theta (red)
* Kin. fit photon theta- measured photon theta (green)

In this case, the width of the "generated - kin. fit" distribution 
(black) is LARGER than the width of the "generated - measured" 
distribution (red), as if the experimental error on the measured photon 
theta angle is SMALLER than the error on the theta angle of the missing 
photon from kin. fit. If this is correct, the corresponding resolution 
can't be extracted using the kin. fit information as the "true" one: not 
a problem for MC, but for data.
Or, maybe, the EC simulation (gsim+gpp) is not smearing enough the EC 
response for angles - however, I checked that EC resolution determined 
from generated 3-momentum is compatible with what described, for 
example, in 
https://misportal.jlab.org/ul/Physics/Hall-B/clas/viewFile.cfm/2009-011.pdf?documentId=533

Do you think it may be possible that the error on the measured photon 
angle in EC is smaller than the missing-photon angle (after applying the 
kin. fit?). Note, finally, that the same conclusion applies even when 
not using the kin. fit, but just taking the missing photon 3-momentum 
from final state p, pi+, pi-.

Thanks!
Bests,
Andrea
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