QED

Simple Examples

  1. Cross section: Electron-Muon Scattering

    As a first example of a QED process the cross section for electron-muon scattering in the CMS is determined. In first order of perturbation theory this is given by a single t-channel photon exchange.

    SPIN AVERAGED MATRIX ELEMENT SQUARED

    Neglecting the particle masses the spin averaged amplitude squared (having evaluated the corresponding traces) is given by
    spinaveragedamplitudesquared_emu
    This can be rewritten in terms of the Mandelstam variables:
    spinaveragedamplitudesquared_emu_mandelstam



    FLUX FACTOR

    The flux factor is given by
    emuscattering_fluxfactor



    PHASE SPACE FACTOR

    The phase space factor for the two-body scattering process is given by
    emuscattering_phasespace
    where the energy of the final state particles is determined by the scattering angle θ.

    Putting everything together results in
    emuscattering_differentialcrosssection.png
    where the high-energy limit is assumed, that is, the incoming and outgoing thre-momenta in the the CMS are assumed to be equal.
  2. Electron-Positron Annihilation