Consider a kinetic lagrangian of 2 Klein-Gordon-Foch fields $\varphi$ and $\chi$ with interaction term
$$\mathcal{L}_I=g^2\bar{\chi}\chi\bar{\varphi}\varphi.$$
Is theory with such interaction renormalizable? Is there any proof?
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6In which spacetime dimension? – Qmechanic Mar 28 '23 at 05:21
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3Hint: Dimensional analysis shows that it is renormalizable for $d\leq 4$. – Qmechanic Mar 28 '23 at 07:04
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1I disagree. That interaction can make a divergent graph with four $\varphi$ legs. – Connor Behan Mar 28 '23 at 20:56