pair spectrometer comments/questions

[Jim Stewart <jstewart@jlab.org>]

*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
*