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Feynman Amplitude Q

  1. Nov 15, 2009 #1
    I'm having a problem calculating the Feynman amplitude for the scalar scattering process [tex] \chi^+ \chi^- \to \chi^+ \chi^-[/tex] for an interaction Lagrangian which is:

    [tex] \mathcal{L} = - g \chi^\dagger \chi \Phi - \frac{\lambda}{4} (\chi^\dagger \chi)^2 [/tex]

    So far I have the 2 Feynman Diagrams for [tex] \chi^+ \chi^- \to \Phi \to \chi^+ \chi^-[/tex] but I can't think/remember how many there should be for the quartic term. I'm thinking there should only be one diagram and hence only one contribution to the Feynman amplitude (which should be -i lambda/4), so the total amplitude becomes:

    [tex] (-ig)^2 \left(\frac{i}{(p_1 + p_2)^2 - M^2} + \frac{i}{(p_1 - k_1)^2 - M^2} \right) - \frac{i\lambda}{4} [/tex]

    where M is the mass of Phi boson, p_1 and p_2 are the incoming energy-momenta and k_1 and k_2 are the outgoing energy-momenta.

    Am I along the right lines?

    Thanks
     
  2. jcsd
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