By H. Georgi
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Additional resources for Interactions in Modern Particle Theory - Weak Interactions
Neglect me compared to mE . Note: Try to get the answer from the µ decay rate actually calculating anything new. 2-7. Calculate the differential cross section dσ/dθ for e+ e− → µ+ µ− , in the center of mass system where θ is the angle between the momentum of the incoming e− and the outgoing µ− . Assume that the energy is large compared to mµ (so that the lepton masses can be ignored), but not large compared to MZ (so that only electromagnetic and weak-electromagnetic interference terms are relevant).
The SLC, the novel single pass collider at SLAC Weak Interactions — Howard Georgi — draft - March 25, 2010 — 47 also produces Zs in e+ e− annihilation. In this machine, the electrons can be polarized, so the interactions of the left-handed and right-handed electrons can be separately studied. Problems 2-1. √ 2 = Derive the relation MW 2e2 /8 sin2 θ GF . 2-2. Derive the analogous relation in a theory in which the left- handed electron and muon fields are in triplets (with all right-handed fields in singlets) under SU (2) × U (1) as follows: EL+ = νeL e− L ψeL ML+ = νµL µ− L ψµL where E + and M + are heavy (unobserved) lepton fields.
7). In general, αs (µ) = f (µ/Λ) were f (x) is some fixed function. 7) also exhibits the property of asymptotic freedom, which means formally that αs (µ) decreases as the renormalization point µ increases. Roughly speaking, αs (µ) is the strength of the QCD interactions between color charges separated by a distance of the order of 1/µ. Since we can turn asymptotic freedom on its head and see that αs (µ) increases as µ decreases, this suggests that something interesting happens for µ small, which is at large separations of color charges.
Interactions in Modern Particle Theory - Weak Interactions by H. Georgi