Pion Two Body Decay Simulation: Efficiency and Impurity Analysis

[spaghetti3451]

Hi I had to write a program to simulate the pion branching fraction in a pion two body decay.

To begin with, the pion decays either to a positron or to a muon which again decays to a positron.

So, the pion beam hits a target and decays at rest to positrons. Then the positrons fly off in random directions. I have written a piece of code that randomises the direction of the momentum of the positrons.

The positrons then hit a spherical shell (the detector) which extends in theta from 40 degrees to 140 degrees and in phi from -pi to pi.

I have been told that in a real experiment, there is no way to know if the pion decayed originally to a muon or a positron except from the measured positron energy, but that in this simulation, we can “cheat” and see how well we would be able to do in the real experiment.

So, I had to choose ranges of the measured energy that selected relatively pure samples of the two different sources of positrons.

Then I had to find the efficiencies for selecting each type of decay(what fractions of events of the correct type are selected).

Then I had to assume that the pion decays to equal numbers of muons and positrons and find the impurity of my selections (how many of the decays ascribed to each type are not actually
correct).

I don't understand why I have done the above.

Also, there is this extra question:

The actual decay rate of the pion to a positron is approximately only 10^−4 of the rate to the muon; what extra difficulties would this cause?

Any hep would ve greatly appreciated.

 

[mfb]

Then I had to assume that the pion decays to equal numbers of muons and positrons and find the impurity of my selections (how many of the decays ascribed to each type are not actually
correct).

Use a pure sample of decays to muons, get the fraction that is misreconstructed as positron decays.
Use a pure sample of decays to positrons, get the fraction that is misreconstructed as muon decays.

Based on that you can get the purity of each selection (in data) for every possible ratio of branching fractions. For 1:1 you'll see that you get a nice separation in both cases, but with 10^-4 the same approach will make a mess out of the positron selection: It is possible that you now have more muon decays than positron decays in it!