PHYS673 Problems September 25, 1996

1. Show how a discriminator may be used to introduce a fixed deadtime after each YES signal from a coincidence unit.
2. What is the accidental rate for triple coincidence if , , and are the singles rate in three counters?
3. Assume that the outputs from the readout electronics of two MWPCs are proportional to the number of hit wires. Show how commercial fast electronics may be combined to give a signal when there are two hits in the first chamber and four hits in the second.
4. An elastic scattering experiment has three detectors in the forwardly scattered direction (F), three detectors in the backwardly scattered direction (B), and three additional detectors (M) to monitor the overall event rate from the target. Lay out the electronics necessary to determine the elastic scattering rate. Suppose that you are suspicious that beam structure with a period of 70 ns is causing accidentals. What additional circuitry would be required to monitor the accidental rate?
5. An experiment is to be done at a colliding beam accelerator with bunched beams and a luminosity per bunch collision L (i.e. L is the instantaneous luminosity integrated over the bunch collision time). Suppose that it is not possible to interpret events unambiguously if more than one interaction occurs per bunch collision.
   1. If the cross section for interesting processes is and the total cross section is , then find the mean number of interesting events per bunch collision.
   2. What is the probability of getting one and only one interesting event per bunch collision?
   3. What is the mean number of background events per bunch collision?
   4. What is the probability of getting zero background events per bunch collision?
   5. What is probability of getting one and only one interesting event per bunch collision and nothing else?
6. Design a sub-trigger for a fixed target accelerator experiment that produces a signal OPEN whenever there are two downstream tracks with an opening angle greater than . Include a description of the detectors, their arrangement, and electronics.
7. The dominant decay mode of the meson is

   

   Design a trigger to study the decay mode. What can you do to minimize the background from ?

8. The charmed D meson has a  cm and a significant branching ratio into a K plus pions. Design a trigger to study D decays.
9. Show that the fraction F of potential events that can be recorded by a data acquisition system is

   

   where R is the trigger rate and is the time needed to readout an event. What trigger rate can be tolerated if the deadtime fraction should be less than 10% and if the readout time is 2  s.

10. Define the sensitivity S of a trigger to be the rate at which good events are recorded. Show that the sensitivity of a two-level trigger is

    

    where p is the purity of the event sample selected by the second-level trigger, R is the first-level trigger rate, t is the second-level decision time, f is the fraction of events that pass the second-level trigger, and is the readout time. Examine the quantities in this equation to determine under what conditions a two-level trigger can make a significant improvement in sensitivity.

11. Suppose that a calorimeter experiment defines a good trigger event to be any one in which the sum ( ) of the magnitudes of the deposited transverse momenta equals or exceeds a threshold value (q). Assume that the probability of getting an event with transverse momentum p is and that the calorimeter can only resolve to within , where . Show that the ratio r of the probability of getting a trigger in which the actual is less than q to the probability of a good trigger is .

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