Consider the one loop corrections to the propagator and the vertex in ##\phi^4## theory in the attachment(adsbygoogle = window.adsbygoogle || []).push({});

The former gives an integral representation proportional to ##\int d^4 k/k^2## in ##4## dimensions while the latter gives a representation ##\int d^4 k/k^2 (k+p)^2## where ##p## is the momenta input into the vertex from the external legs. Power counting tells us that both diagrams are UV divergent. Can we predict a priori what the dependence on some UV cut off scale would like for both diagrams? I know that it would be a finite function of the cut off such that in the limit that this cut off is extended to infinity, the function diverges. But can we say anything about the functional dependence just by this power counting?

In the former case, the integral is quadratically divergent. So maybe something like ##\Lambda_{UV}^2## or ##\log (\Lambda_{UV}^2)##? The latter diagram is maybe just ## \propto \Lambda_{UV}##?

Thanks!

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# I Dependence on UV cut off on some $\phi^4$ diagrams

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