# Self-energy in two scalar Yukawa interaction

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.

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$$^1$$).