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Old Sep 9th 2013, 09:23 AM   #1
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Calculate trigger purity

Can anyone help me with this excercise? I can't really get it
It is about purity and efficiency of a trigger

A particles beam is made of K (95%) and π (5%) mesons. Beam hit a ToF detector that measure
τ_ =1600100 psec
and
τ_K = 2200150 psec
with a gaussian time distribution. Assume errors as gaussian's σ
If we set the trigger threshold τ_K = 1900 psec what purity of K mesons we get for the selected set?
Calculate the efficiency
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Old Sep 5th 2014, 09:05 AM   #2
SRB
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Start by calculating the number of standard deviations (σ) that the trigger threshold is for both τ_n and τ_K.
Hint, it will look something like this: σ_n = (1900-??00)/??0 and σ_K = (2200-?00)/??0

Then, on the τ_n side of the threshold, you will get a large portion of the 5% that are n particles and a small portion of the 95% that are K particles. Calculate those two values based on the σ_n and σ_K. S_nn = ???(σ_n)x0.05 S_nK = ???(σ_K)x0.95

On the τ_K side of the threshold, you will get a small portion of the 5% that are n particles and a large portion of the 95% that are K particles. Calculate those two values based on the σ_n and σ_K. S_Kn = ???(σ_n)x0.05 S_KK = ???(σ_K)x0.95

At this point, you can calculate the purity of both the n and K mesons. For example P_K = S_KK/(S_KK+S_Kn).

I'm not sure what definition of "efficiency" is being used. My guess would be E_K = ???(σ_K). In other words, one of the functions of σ_K that Iwant you to figure for yourself.
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