# Naturalness and experiments

Is there an example where model building that is motivated only by Naturalness, has led to experimentally verified observations?

If the question is unclear, or if the reader wants more elaboration, then continue reading.

Naturalness is defined by 't Hooft as: "A theory with a parameter $m$ is natural if the limit where $m \rightarrow 0$ results in an enhancement of the symmetry of the theory."

For example, take fermions in the Standard Model, if you set their masses to zero then you restore chiral symmetry. And the log-divergent radiative corrections will vanish.

Now, take the Higgs boson (a scalar), if you calculate the loop correction the Higgs squared mass parameter, you'll get quadratic divergence. If you set the mass to zero, this won't help as you still have quadratic divergence. And no symmetry is restored.

If the scale of new physics is at the Planck scale or GUT scale, then you'll have to tune the mass of the Higgs by something like $10^{30}$.

If Supersymmetry exists, then the quadratic divergence cancels out. Also, the limit where the Higgs mass goes to zero will result in restoring SUSY. So, SUSY will give you a "natural" model.

However, I came across this article: "Is Naturalness Unnatural?" by Nobel laureate Prof. Burton Richter. It addresses three things: Naturalness (which what I'm concerned about), the cosmological anthropic principle, and the landscape in string theory.

Concerning Naturalness, in his view, in balancing between having a natural theory with extra parameters, and having a theory with huge fine-tuning (or as he says: somethings are simply initial conditions) but fewer parameter, the latter is more important, while the former can be misleading.

Hence, I'm tempted to ask, are there examples in the past where naturalness considerations led to experimentally verified results?

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One more comment that isn't really an answer: you can argue indefinitely about the role naturalness should play, and about whether the cosmological constant should make us give it up. But in the case of naturalness of the weak scale, the nice thing is that the LHC is going to give us an answer, and it's going to give it to us relatively soon. So there's no need for abstract debate; just wait a while, and we'll know. –  Matt Reece Jun 5 '12 at 16:13

There are several occasions in the past when naturalness has been experimentally confirmed. One of the nicest is the successful prediction of the mass of the charm quark by Mary K. Gaillard and Benjamin Lee. In the Standard Model, the GIM mechanism suppresses flavor-changing neutral current transitions. But if the charm quark were absent, this wouldn't be true, and a number of observables in kaon physics would be very different. Using one of these observables, the K-long/K-short mass difference, Gaillard & Lee realized that the mass of the charm quark needed to be low enough to cut off a divergence, putting it at about 1.5 GeV. The true mass turned out to be about 1.3 GeV, so their estimate was pretty accurate.

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This is true to some extend, but naturalness is somewhat secondary to the requirement of anomaly cancellation between the second generation quarks and second generation leptons. –  Ron Maimon Jun 5 '12 at 15:58
Sure. Or just fitting things in SU(2) multiplets, for that matter. But that doesn't tell you much about the mass. –  Matt Reece Jun 5 '12 at 16:06
Nice, Matt. @Ron, you're right but note that anomaly cancellation – as well as the completion into doublets – may also be classified as a requirement for a symmetry to be enhanced (the SU(2) gauge symmetry) so it fits into the 't Hooft definition of naturalness, anyway. The existence of a charm quark, or a light charm quark, was predicted by the enhanced symmetry with its absence and/or reduction of the number of independent divergences which is a similar condition. –  Luboš Motl Jun 5 '12 at 17:24