[Halld-pid] TDCs for TOF

[Alexander Ostrovidov]

Hello,

In view of the CAEN 1290A vs F1 TDC choice, I looked at 
the pion-Kaon momentum separation with these 2 TDCs:

1. The best timing resolution we achieved with a single
TOF paddle in the cosmic ray tests in our lab was 
90 ps with CAEN 1290A and 103 ps with F1 TDC.

2. The minimal path length L for any particle will be 550cm 
(the distance from the center of the target to TOF). Actually,
this is the worst case scenario. With the longer path lengths,
the improvement in momentum separation becomes even slightly
better than what is shown below for a minimal path length.

3. I consider only TOF timing resolution and disregard the
contribution to the resolution from other factors like momentum 
measurement, path length, RF bunch start time, etc.  From the 
Fig.8.1 in the old IU report, it is obvious that even the smaller 
TOF resolution of 80ps already dominates everything else in 
the region of interest (where the 3-sigma envelopes for pion 
and Kaon  intersect).

4. Difference in the time of flight between pions and Kaons
as a function of their momentum is:

Delta(t) = [L/(p*c)] * [sqrt(p^2+Mkaon^2)-sqrt(p^2+Mpion^2)]

This dependence is shown on the attached plot.

5. Assuming 3-sigma envelope for both pi and K (i.e.,
their 6-sigma separation), the pion-Kaon envelopes will
overlap at 1.806 GeV with 6*103ps=618ps time separation,
and at 1.934 GeV with 6*90ps=540ps time separation.
In other words, we gain about 130 MeV of extra separation
in momentum by using 1290A instead of F1 TDC, and come
closer to the future RICH threshold.

Sasha

P.S. If necessary, I can generate some simple Monte Carlo
(like piKK or something like that) to give an estimate
of what this improvement means in terms of the number of
events, with definite PID, etc.

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