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Considering the Lagrangian of two scalar fields in $d=4$: $$\mathcal{L}=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{1}{2}(\partial\chi)^2-\frac{1}{2}M^2\chi^2-g\phi^2\chi$$

What would be the self-energy (diagrams, first order) for the $\chi$-particle? The second particle confuses me somehow.

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The $\chi$ particle seems to be interacting with the $\phi$ particle only in the $-g\phi^2\chi$ term, so the 1-loop correction to the $\chi$ propagator would be a loop of 2 $\phi$ particles. The first 4 terms are the kinetic and mass terms of the particles, while the rest (in this case 1) are the interaction terms - they tell you what type of particles (and how many of each) can appear in any given vertex (only 1 in this case), as well as the coupling constant ( in this case, the coupling constant is $g$ and has dimension of mass$^1$).

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