Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Cross Section Difference Bhabha Scattering and Muon Pair Production
  1. Bhabha scattering (Replies: 6)

  2. Bhabha Scattering (Replies: 4)