Understanding the Fine Tuning Problem in Scalar Field Theories

[Lapidus]

What do people mean when they say that mass renormalization of scalar field theories confronts us with a fine tuning problem. It's said the divergence in the mass of a scalar field is quadartic, rather than logarithmic, this poses a fine tuning problem. Why and how, and what does that mean?

Take Srednicki's textbook http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf" , chapter 14, pdf page 116, say equation 14.43. Where is the quadratic divergence, where and how is there a fine tuning problem?
(I suppose the k^2+m^2 term has something to do with it.)

Why is there for spinor electrodynamic no fine tuning problem, no quadratic divergence? For example in the same book, pdf page 372, chapter 62, equation 62.25?

thank you

 

[Bill_K]

The idea originated with Veltman in 1981. In the course of trying to predict the Higgs mass he looked at the leading quantum corrections which come from a single internal loop. They're divergent and can be expressed in terms of a cutoff Λ, which might be Planck scale or might not, but in any case is very large. Higgs couples to both bosons and fermions, and the interesting fact is that the terms from bosons are positive while the terms from fermions are negative. Veltman said if the terms cancel it might explain how the Higgs mass can be small. He next tired to extend the cancellation condition to more than one loop, but was unable to do so consistently. Note that while the cancellation idea is attractive, it is not absolutely demanded by anything, there may very well be some other explanation for the Higgs mass, but people have tried to make it work and consider it a problem that it hasn't.

 

[Lapidus]

Thanks, Bill!

Can anybody comment on equation 14.43?