Re: pair spectrometer comments/questions

[Dan Dale <dale@athena.physics.isu.edu>]

Hi,
  I am jumping into the middle of this discussion, so I apologize if I 
am not fully up to speed.
  First, and maybe this is something I can have explained to me at 
tomorrow's meeting, it is
not clear to me the motivation for using the pair spectrometer to 
measure the photon energy.
Since the tagger does this much better, I assume it is for some kind of 
check of something
in the tagger.
  If we do use the pair spectrometer to measure Egamma, a few additional 
things to consider
are (1) pair production opening angle and azimuthal angle of pair, (2) 
recoiling electron in
electron field pair production (this goes as Z, whereas nuclear field 
goes as Z^2, arguing for
a high Z converter), (3) pair production followed by bremsstrahlung (a 
(target thickness)^2
effect arguing for a thinner target and a lower Z target), (4) multiple 
scattering of leptons in
the target.
  For the PrimEx pair spectrometer, the detector segmentation was 
motivated by rates. Our
physics target is the same as the pair converter, so we segmented the 
detectors to knock
down the rates. If I understand things right, GluEx can just make the 
pair converter thinner.

                                                                      
-Dan Dale



Jim Stewart wrote:
> *Hello Hrachya
>
> I think I am missing something fairly basic in my understanding of the 
> pair spectrometer design. I do not understand how you chose the 
> detector sizes.
>
> The photon energy is the sum of the energy of the electron and positron
> E_gam = E_ele+E_pos
> The uncertainty in the photon energy is the uncertainty of the 
> electron and positron added in quadrature.
> (This assumes the two energy measurements are independent which is not 
> true. For example if the photon interacts +2mm off beam axis in the 
> radiator then the positron will appear to have a larger curvature and 
> therefore lower momentum than it really does where as the electron 
> will seem to have a higher momentum.)
> deltaE_gam = sqrt[(deltaE_ele)^2 +(deltaE_gam)^2)]
> From this I would conclude that the pair spectrometer should be 
> designed so that both arms have roughly the same precision.
>
> The factors that contribute to the uncertainty in the energy 
> measurement are:
> 1) Beam spot size
> 2) Uncertainty in magnetic field
> 3) Opening angle of the bremsstrahlung production (p_t effects)
> 4) Size of the detectors
> 5) Position uncertainty of the detectors.
>
> Am I missing anything other sources to the uncertainty?
>
> The opening angle of the bremsstrahlung cone is the one factor which 
> is affected by the overall length of the spectrometer. Here you can 
> probably somehow express the contribution to the uncertainty as a fn 
> of overall path length of the electrons/positrons.
>
> The determination of the optimal size detectors may be somewhat 
> complicated. You have to understand how the finite spot size effects 
> the momentum uncertainty depending on how large the magnet and drift 
> space are. Do you know how best to calculate this? I  would think a  
> MC study is needed here.
>
>
> ========================= comment on vertical wire =================
> Jim -  Also please talk about the possibility to use a vertical wire 
> to scan the beam instead of a foil target. This reduces the 
> uncertainty from the spot size.
>
> Hrachya: CB has an angular distribution and one has to accept all CB 
> cone by spot in foil, otherwise we measure something different from 
> what trigger contains.
>
> The suggestion was to scan the beam profile. If you have a vertical 
> wire then you can move it across the photon beam. Then you can measure 
> the profile and by adding the different x-bins a better energy 
> resolution. I would view this as a dedicated systematic study on the 
> photon beam. This could give a more precise measurement. I guess a lot 
> will depend on how accurately you can combine the different x 
> measurements into a combined measurement.
> Jim
> *