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Cross Section Difference Bhabha Scattering and Muon Pair Production

  1. Jan 28, 2009 #1
    how do the angular distributions of Bhabha Scattering

    [tex] e^+ e^- \Rightarrow e^+ e^- [/tex]

    and Muon pair production

    e+ e- [tex]\Rightarrow \mu^+ \mu^-[/tex]


    Phileas Fogg
  2. jcsd
  3. Feb 7, 2009 #2
    The difference is caused by the fact that there is an additional Feynman diagram in Bhabha scattering. (The electron process can occur by scattering OR pair annihilation/production, whereas the muon process can only occur by the latter.)

    This gives a scattering amplitude (in terms of the Mandelstam variables s,t,u) of

    M_mu = (u^2 + t^2)/s^2


    M_el = (s^2 + u^2)/t^2 + 2u^2/(ts) + M_mu

    The cross-section is proportional to the squares of these quantities. In the center-of-mass frame (same as the lab frame for a two-beam collider), s has no angular dependence, and

    t ~ 1-cos theta


    u ~ 1+cos theta

    So the relative angular dependence isn't hard to work out (though I don't know it offhand).
    (These values are all from Quarks and Leptons by Halzen & Martin)

    The rest is algebra. Note that this is a high-energy approximation, which assumes that the particle masses are negligible compared to the beam energy.

    (Hope this is what you were looking for!) :smile:
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