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1

Let us suppose that that the Standard Model is an effective field theory, valid below a scale $\Lambda$, and that its bare parameters are set at the scale $\Lambda$ by a fundamental, UV-complete theory, maybe string theory. The logarithmic corrections to bare fermion masses if $\Lambda\sim M_P$ is a few percent of their masses. The quadratic correction to ...

0

The fine tuning you describe isn't present in the $\phi^4$ model. You need some some other heavy fields around to see it. For example, couple your $\phi$ to a heavy fermion of mass M, Then when you will have a shift in your mass $\delta m^2 \sim M^2$. There will be other factors of $\pi$ and coupling constants and such, but the problem remains - for large M ...

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Dimensional regularization (i.e., dim-reg) is a method to regulate divergent integrals. Instead of working in $4$ dimensions where loop integrals are divergent you can work in $4-\epsilon$ dimensions. This trick enables you to pick out the divergent part of the integral, as using a cutoff does. However, it treats all divergences equally so you can't ...

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