- #1
spaghetti3451
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In chapter 1 of Peskin and Schroeder, the reaction ##e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}## is studied in detail. The related following paragraph is taken from page 4 of Peskin and Schroeder:
Both the electron and the muon have spin ##1/2##, so their spin orientations must be specified. It is useful to take the axis that defines the spin quantization of each particle to be in the direction of its motion - each particle can then have its spin polarized parallel or antiparallel to this axis. In practice, electron and positron beams are often unpolarized, and muon detectors are normally blind to the muon polarization. Hence one should average the cross section over electron and positron spin orientations, and sum the cross section over muon spin orientations.
I have the following questions regarding the content of the paragraph:
Both the electron and the muon have spin ##1/2##, so their spin orientations must be specified. It is useful to take the axis that defines the spin quantization of each particle to be in the direction of its motion - each particle can then have its spin polarized parallel or antiparallel to this axis. In practice, electron and positron beams are often unpolarized, and muon detectors are normally blind to the muon polarization. Hence one should average the cross section over electron and positron spin orientations, and sum the cross section over muon spin orientations.
I have the following questions regarding the content of the paragraph:
- Why is it useful to have the spin of each particle polarized parallel or antiparallel to the direction of its motion?
- Why does the fact that electron and positron beams are often unpolarized in practice imply that one should average the cross section over electron and positron spin orientations?
- Why does the fact that muon detectors are normally blind to the muon polarization imply that one sum the cross section over muon spin orientations?