In the LEP collider, the energy in the center of mass system was about 200 GeV and, in many events, muons were produced. This simple exercise will show you that you need strong magnetic fields and large detecting chambers to detect 100 GeV muons.
a) Why can the energy of a muon produced in a LEP event never exceed 100 GeV?
b) Calculate the momentum of a 100 GeV muon. The rest (invariant) mass of the muon is 105.7 MeV.
c) The magnetic field in the ALEPH detector is about 1.5 Tesla. Calculate the radius of the trajectory of a 100 GeV muon in this magnetic field. Suppose that the muon moves perpendicular to the magnetic field.
d) Now suppose that your detector can measure a sagitta of about 1 mm. Using your previous result for the radius, calculate the length of Time Projection Chamber (TPC) necessary in a radial direction.
Click here for Solutions of exercise 5
This detector only gives you the momentum and charge of the particle. To identify the particle, you need additional detectors around the TPC, like the electromagnetic calorimeter, the hadron calorimeter and the muon chamber. If you add all these detectors up, you get a radial diameter of nearly twenty meters!