Understanding the Fine Tuning Problem in Scalar Field Theories

In summary, the problem of fine tuning in mass renormalization of scalar field theories arises from the fact that the divergence in the mass of a scalar field is quadratic rather than logarithmic. This poses challenges in predicting the Higgs mass and has led to attempts to cancel the divergent terms through a cancellation condition. However, this has not been consistently achieved beyond one loop, leaving the problem unresolved. This issue does not exist in spinor electrodynamic, as seen in equation 62.25, where there is no fine tuning problem or quadratic divergence. The idea of cancellation was first proposed by Veltman in 1981 and is still being studied by researchers in the field.
  • #1
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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
 
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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.
 
  • #3
Thanks, Bill!

Can anybody comment on equation 14.43?
 

1. What is the concept of fine tuning scalar fields?

Fine tuning scalar fields refers to the precise adjustment of parameters in a scalar field theory in order to achieve a desired outcome or result. In physics, scalar fields are mathematical objects that assign a value to each point in space. Fine tuning these fields is often necessary in order to accurately describe physical phenomena or make predictions.

2. Why is fine tuning scalar fields important in scientific research?

Fine tuning scalar fields is important in scientific research because it allows for the development of accurate and predictive models of physical systems. By adjusting the parameters in a scalar field theory, scientists can better explain and understand complex phenomena, which can lead to new discoveries and advancements in various fields of science.

3. What are some examples of fine tuning scalar fields in practice?

One example of fine tuning scalar fields is in the Higgs field, which is responsible for giving particles their mass. In order to accurately describe the mass of particles, scientists had to fine tune the parameters of the Higgs field. Another example is in cosmology, where fine tuning of scalar fields is necessary to explain the expansion of the universe and the formation of galaxies.

4. How does fine tuning scalar fields relate to the concept of naturalness?

Naturalness is a concept in physics that suggests that fundamental properties and parameters should not require excessive fine tuning to produce realistic results. In the context of scalar fields, naturalness means that the parameters should be close to their "natural" values in order to accurately describe the physical system. Fine tuning scalar fields is often necessary to achieve naturalness in a theory.

5. Are there any limitations to fine tuning scalar fields?

Yes, there are limitations to fine tuning scalar fields. One limitation is that fine tuning can only take a theory so far. If the parameters become too finely tuned, the theory becomes less predictive and may not accurately describe the observed physical phenomena. Additionally, fine tuning can sometimes lead to the so-called "fine-tuning problem", where the reason for the precise values of parameters is not well understood or seems unlikely.

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