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# Fine Tuning

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There is a big debate going on in physics at the moment about the concept of what makes a theory "natural". Clearly there are certain properties which make a theory attractive, such as its ability to describe experimental observations, it simplicity and its predictivity (i.e. how well it contrains possible realities).

Naturalness is slightly more of an aesthetic concept which is why it often so controversial, but it has been used in the past and is still being used to prefer certain theories over others.

Its most 'scientific' manifestation is in what is known as 'fine-tuning'. The analogy often used is of a radio station transmitting on a very narrow frequency band. In order to pick up the signal you will have to wiggle the tuner about in very small amounts to find just the right frequency. If you go to far to the right or left you miss the signal. Using a radio with a very wide band over which you can track you will find it difficult to find a narrow band transmission.

This is a bit like some physics theories. Let's assume that the theoretical model contains a parameter $\lambda$ just like the wavelength of a signal that a radio picks up. However, for most values of $\lambda$ you find that the theory makes very physically unrealistic predictions (e.g. an unstable vacuum), and in order to get good physical predictions you need to have a very very specific value of $\lambda$. (In the anaology you need to tune the radio very carefully to pick up the signal.) This is called a 'fine-tuned' theory, and it has always been generally regarded as a very negative property for a theory to have.

The most famous example in my field is the mass of the Higgs boson in the Standard Model. There is a parameter in the theory which has to be fine tuned to approximately one part in 1030 in order to give a Higgs boson mass which is physically reasonable. Many people believe that this tells us that the Standard Model is wrong and must be replaced or extended.

However, this is really an aesthetic problem. In reality each parameter must have one value, so why should one value be regarded as any less likely than any other. I am curious as to what non-physicists' views of fine-tuning would be - do you think it is a problem?

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Seems to me that you have only so many degrees of freedom. If some parameters are fixed, you have fewer degrees for the remaining ones. There is only one reality, after all.

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I see it all as a matter of Refinement, Crude oil will still burn!

but refine it and you get many many more different fractions of the black gloop, each with their own different properties.

essentialy it`s all down to our ability using the current tools we have to make Observations, and deducing what we can from this data.

I dare say a good many things will be in question given greater tools to make observation previously not possible, and this fine-tuning will be one of the Best parts of Science, it always has been.

for every answer we get, there will be 10 more questions about it.

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I am a physicists and I feel a little uneasy about fine tuning.

On a technical note, I always wonder about the renormalisation of fine tuned parameters. Generally you could set it classically to a number and then quantum effects could alter this value.

So, Severian what symmetry protects the Higgs mass? As I am no expert at phenomenology, I guess it is gauge symmetry?

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On a technical note' date=' I always wonder about the renormalisation of fine tuned parameters. Generally you could set it classically to a number and then quantum effects could alter this value.

[/quote']

Yes, in fact that is the whole problem in the Standard Model. You set the value and then it is altered by the quantum effects, to the tune of 30 orders of magnitude. So you need to re-tune at every order in perturbation theory. (This is because the Higgs boson is a scalar and scalar field theories contain quadratic divergences.)

So, Severian what symmetry protects the Higgs mass? As I am no expert at phenomenology, I guess it is gauge symmetry?

The Standard Model has no such symmetry, so in the Satandard Model you eithe have to claim that there is no new physics (i.e. abandon quantum gravity altogether) or you the natural Higgs mass is 1019 GeV (which won't float).

There are two ways you can get around this:

1. Introduce a new symmetry. The symmetry which is most used is supersymmetry but it could be a new gauge theory that is broken at some higher scale so we haven't seen yet.

2. Think up some reason why the Planck scale (the characteristic scale of gravity) should be at 1TeV or so (which makes the natural Higgs mass also 1 TeV or so). The most popular way of doing this is using extra dimensions, so gravity is not weak because of the high Planck scale, but is weak because it is leaking into the extra dimensions.

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As a layman, I see it as a "fudge" or "fiddle factor", But I quite understand why physicists want to call it something else. The politics of physics needs politically correct terms, as much as any other industry.

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the Satandard Model

Oh dear. What would Sigmund say?

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Of course Severian it is comming back to me. I do now remember Dr de Carlos at Sussex saying something about supersymmetry is needed to fix the Higgs mass, I guess this is exactly what she was talking about. Supersymmetry protects the Higgs mass. Right?

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• 2 years later...
Of course Severian it is comming back to me. I do now remember Dr de Carlos at Sussex saying something about supersymmetry is needed to fix the Higgs mass, I guess this is exactly what she was talking about. Supersymmetry protects the Higgs mass. Right?

Yes, exactly. The quadratic divergence that contributes to the mass is exactly canceled.

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However, this is really an aesthetic problem. In reality each parameter must have one value, so why should one value be regarded as any less likely than any other. I am curious as to what non-physicists' views of fine-tuning would be - do you think it is a problem?

I think, if you're willing to accept a fine tuned higgs mass, then you have a real problem model building. If you're willing to throw out "naturalness" as a criteria, then publishing hep-ph papers should be easy

So how do you build models, if you only have to satisfy the LEP data and the WMAP bound?

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I think, if you're willing to accept a fine tuned higgs mass, then you have a real problem model building. If you're willing to throw out "naturalness" as a criteria, then publishing hep-ph papers should be easy

So how do you build models, if you only have to satisfy the LEP data and the WMAP bound?

Oh - don't get me wrong, I like supersymmetry and dislike fine-tuning. I agree that it is a problem we can't overlook. But this is not the view of many physicists. I was simply stating the contrary viewpoint to stimulate discussion.

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Maybe there's not much discussion because people don't understand what "tuning" is. This has been my experience, at least---most non-physicists don't see a real problem with it because they don't understand the problem.

The example I use is this:

A + B - C = D

Suppose I tell you that A, B, and C are all real numbers that are between 0 and 10. What do you expect D to be? Or, conversely, given all real numbers between 0 and 10, what would a random selection of A,B, and C produce for D?

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• 2 weeks later...

Or to phrase it another way (to apply the shock-paddles to this thread), in Ben's example, if it turned out that $D=3 \times 10^{-22}$ would you think that there should be a good reason why A + B and C almost cancel, or would you be happy saying it was just coincidence?

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Fine-tuning theories walks the dangerous line between ad hoc hypothesis and making a theory fit the data. I'd say that if they had to fiddle around to get a Higgs mass they like, then they can't use the Higgs mass as evidence for their theory. However, if the same fine-tuned parameter then allows additional accurate predictions, then these would be evidence.

In Ben's example, I'd expect D to be about 5, but of course it could be anything between -10 and 20. Since his example uses real numbers, I'm not sure what error margins I could put to say how surprised I'd be if the value were far different than 5. I guess that I could do some calculating, but it would be rather annoying and I think he just intended it as an example.

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Fine-tuning theories walks the dangerous line between ad hoc hypothesis and making a theory fit the data. I'd say that if they had to fiddle around to get a Higgs mass they like, then they can't use the Higgs mass as evidence for their theory. However, if the same fine-tuned parameter then allows additional accurate predictions, then these would be evidence.

Well, I don't know if "making the theory fit the data" is always a bad thing I'm sure if you could explain electroweak symmetry breaking without a higgs, in a similarly economical fashion (i.e. not "extended walking technicolor"), then you'd be invited many places to give many talks. The situation with the higgs mass is a bit intricate---the ONLY way we know how to break symmetries is to give scalar particles VEVs. Naturally, scalar particles are heavy, but we have a spontaneously broken symmetry at a low scale. So what can we do? Similarly, you could ask why the electron should have such a small mass and the top quark such a large one. Or why all three neutrinos have more or less the same mass, but none of the quarks and leptons do.

PS Sverian---do you know a good review of the precision electroweak observables/data? I have this Phys Rept article by Heinemeyer, Hollik and Weiglein.

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Well, I don't know if "making the theory fit the data" is always a bad thing

No, it is in fact always a good thing. Doing it in an ad hoc fashion is what is dangerous. The more naturally a theory fits the data, and the simpler the theory, the better. Fine tuning is somewhat like taking a measurement, but it would be even better if your theory gave the measurement.

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PS Sverian---do you know a good review of the precision electroweak observables/data? I have this Phys Rept article by Heinemeyer, Hollik and Weiglein.

Well, that is probably what I would look at too, but since Sven, Wolfgang and Georg are all good friends of mine, I might be a little biased. I seem to remember a nice review paper by Dominik Stoeckinger too - I will go look for it.

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