[G12] resolution of tagger in kinematic fitter

[Eugene Pasyuk]

This would be a double counting for high energy end. The offset form the nominal bin centroid is always less than the a bin width. 
What needs to be adjusted is E_beam. We always had it deviate from what MCC reports by ~0.1-0.2%, and even up to 0.5% occasionally. But this is multiplicative factor and affects all Eg the same way. 

-Eugene 

> From: "Lei Guo" <leguo at fiu.edu>
> To: "Eugene Pasyuk" <pasyuk at jlab.org>
> Cc: "Carlos Salgado" <salgado at jlab.org>, "g12 at jlab.org g12 at jlab.org"
> <g12 at jlab.org>
> Sent: Wednesday, February 10, 2016 4:22:24 PM
> Subject: Re: [G12] resolution of tagger in kinematic fitter

> I understand that the 2007 paper is about the correction and now the correction
> gets applied at cooking. However, there is uncertainty to that correction. So
> on top of the 0.001*e_beam, there should be additional 0.001*e_gamma, for the
> overall resolution.

> Sent from my iPhone

> On Feb 10, 2016, at 15:52, Eugene Pasyuk < pasyuk at jlab.org > wrote:

>> You are confusing two different things.
>> The tagger reconstruction returns the photon energy as a centroid of the E_bin.
>> The bin widths is almost a constant and is ~0.001*E_beam. The beam centroids
>> originally used are coming from the geometry of the tagger hodoscope and
>> magnetic field.
>> During g10 and g11 it was discovered that bin centroids are not what we thought
>> due to gravitational sag of the focal plane.
>> To determine the deviation from the expected values two methods were used. One
>> is the calibration you refer to, the other using kinematic fit of g11 data.
>> What you see in the tagger calibration paper is the accuracy of the centroid
>> offset from ideal.
>> Once this calibration was done we implemented those corrections in the tagger
>> reconstruction. So, in g12 cooked date it is already accounted for. So, this is
>> not and uncertainty but correction.
>> What is left is the bin width. The photon energy could be anything
>> E_bin(i)-Ebin_width/2<Eg<E_bin(i)+Ebin_width/2
>> The calibration gives us E_bin(i), but effects of the bin width should go in the
>> kinematic fit. Ebin_width ~ Ebeam*0.001 and it is essentially a constant over
>> focal plane. Carlos' note describes how to get the variance assuming uniform
>> energy distribution within E_bin.

>> -Eugene

>>> From: "Lei Guo" < lguo at jlab.org >
>>> To: "Carlos Salgado" < salgado at jlab.org >, "Eugene Pasyuk" < pasyuk at jlab.org >
>>> Cc: " g12 at jlab.org g12 at jlab.org " < g12 at jlab.org >
>>> Sent: Wednesday, February 10, 2016 3:01:22 PM
>>> Subject: Re: [G12] resolution of tagger in kinematic fitter

>>>> The uncertainty in the energy of the photon is 0.001* E_beam (per NIM and Eugene
>>>> P.)

>>> I copy and pasted from the 2007 tagger energy calibration NIM paper ():

>>> "In this report, we present the energy calibration of the Hall B bremsstrahlung
>>> tagging system at the Thomas Jefferson National Accelerator Facility. The
>>> calibration was performed using a magnetic pair spectrometer. The tagged photon
>>> energy spectrum was measured in coincidence with e + e - pairs as a function of
>>> the pair spectrometer magnetic field. Taking advantage of the internal
>>> linearity of the pair spectrometer, the energy of the tagging system was
>>> calibrated at the level of ±0.1%E γ . The absolute energy scale was determined
>>> using the e + e - e+e- rate measurements close to the end-point of the photon
>>> spectrum. The energy variations across the full tagging range were found to be
>>> < 3MeV”

>>>> The hodos were built such that this is true (different widths)

>>>> Then consider a counter of width (energy) "a" where the (assume) energy
>>>> distribution is flat: then Variance = sigma^2 = 1/a* int^a_0 E^2 dE = a^2/3

>>>> Therefore if we distribute the uncertainty over a counter (energy bin) the
>>>> variance is : sigma^2 = (0.001*E_beam)**2/3

>>>> =Carlos
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