# Feynman Amplitude Q

1. Nov 15, 2009

### div curl F= 0

I'm having a problem calculating the Feynman amplitude for the scalar scattering process $$\chi^+ \chi^- \to \chi^+ \chi^-$$ for an interaction Lagrangian which is:

$$\mathcal{L} = - g \chi^\dagger \chi \Phi - \frac{\lambda}{4} (\chi^\dagger \chi)^2$$

So far I have the 2 Feynman Diagrams for $$\chi^+ \chi^- \to \Phi \to \chi^+ \chi^-$$ 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:

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

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