Clockworks. [Img via dwan1509]. |

High energy physics is like this. Twenty years ago, it was extra dimensions, then we had micro black holes, unparticles, little Higgses – and the list goes on.

But there hasn’t been a big, new trend since the LHC falsified everything that was falsifiable. It’s like particle physics stepped over the edge of a cliff but hasn’t looked down and now just walks on nothing.

The best candidate for a new trend that I saw in the past years is the “clockwork mechanism,” though the idea just took a blow and I’m not sure it’ll go much farther.

The origins of the model go back to late 2015, when the term “clockwork mechanism” was coined by Kaplan and Rattazzi, though Cho and Im pursued a similar idea and published it at almost the same time. In August 2016, clockworks were picked up by Giudice and McCullough, who advertised the model as a “a useful tool for model-building applications” that “offers a solution to the Higgs naturalness problem.”

Gears. Img Src: Giphy. |

Before the LHC turned on, the most popular solution to the Higgs naturalness issue was that some new physics would show up in the energy range comparable to the Higgs mass. We now know, however, that there’s no new physics nearby, and so the Higgs mass has remained unnatural.

Clockworks are a mechanism to create very small numbers in a “natural” way, that is from numbers that are close by 1. This can be done by copying a field multiple times and then coupling each copy to two neighbors so that they form a closed chain. This is the “clockwork” and it is assumed to have a couplings with values close to 1 which are, however, asymmetric among the chain neighbors.

The clockwork’s chain of fields has eigenmodes that can be obtained by diagonalizing the mass matrix. These modes are the “gears” of the clockwork and they contain one massless particle.

The important feature of the clockwork is now that this massless particle’s mode has a coupling that scales with the clockwork’s coupling taken to the

*N*-th power, where

*N*is the number of clockwork gears. This means even if the original clockwork coupling was only a little smaller than 1, the coupling of the lightest clockwork mode becomes small very fast when the clockwork grows.

Thus, clockworks are basically a complicated way to make a number of order 1 small by exponentiating it.

I’m an outspoken critic of arguments from naturalness (and have been long before we had the LHC data) so it won’t surprise you to hear that I am not impressed. I fail to see how choosing one constant to match observation is supposedly worse than introducing not only a new constant, but also

*N*copies of some new field with a particular coupling pattern.

Either way, by March 2017, Ben Allanach reports from

*Recontres de Moriond*– the most important annual conference in particle physics – that clockworks are “getting quite a bit of attention” and are “new fertile ground.”

Ben is right. Clockworks contain one light and weakly coupled mode – difficult to detect because of the weak coupling – and a spectrum of strongly coupled but massive modes – difficult to detect because they’re massive. That makes the model appealing because it will remain impossible to rule it out for a while. It is, therefore, perfect playground for phenomenologists.

And sure enough, the arXiv has since seen further papers on the topic. There’s clockwork inflation and clockwork dark matter, a clockwork axion and clockwork composite Higgses – you get the picture.

But then, in April 2017, a criticism of the clockwork mechanism appears on the arXiv. Its authors Craig, Garcia Garcia, and Sutherland point out that the clockwork mechanism can only be used if the fields in the clockwork’s chain have abelian symmetry groups. If the group isn’t abelian the generators will mix together in the zero mode, and maintaining gauge symmetry then demands that all couplings be equal to one. This severely limits the application range of the model.

A month later, Giudice and McCullough reply to this criticism essentially by saying “we know this.” I have no reason to doubt it, but I still found the Craig

*et al*criticism useful for clarifying what clockworks can and can’t do. This means in particular that the supposed solution to the hierarchy problem does not work as desired because to maintain general covariance one is forced to put a hierarchy of scales into the coupling already.

I am not sure whether this will discourage particle physicists from pursuing the idea further or whether more complicated versions of clockworks will be invented to save naturalness. But I’m confident that – like a toddler’s phase – this too shall pass.

## 19 comments:

Hi Sabine,

I guess you do not know that a solution exists (first paper in 2012 or so, and now complete or close - I think), where all the gearing coefficients come from 2, 3, 7, 19 and pi, and where alpha and other couplings (of this model) are gear ratios which are computed from the same numbers.

Best,

J.

Behaving gear trains are a special case. Heretical chains, or loops, or Borromean rings of meshed gears can work,

https://www.youtube.com/watch?v=qGAnmRb66s0

https://www.youtube.com/watch?v=v=fFsA6hDc7z8

https://www.youtube.com/watch?v=5Mf0JpTI_gg

Physics spurns an obvious and testable vacuum structure. Gravitation and particle theory curve fittings can be empirically sourced. If not true, it terminates in fewer than eight papers, a small number.

Is "diagnonalizing" actually a thing, or just a typo? I suspect you meant "diagonalize", but if it's a thing can you offer a brief definition, please, as the internet seems quite unhelpful on the matter.

Otherwise, keep up the great writing,

s.

hardas,

Sorry, it's a typo - I fixed that. Yes, I mean diagonalize. If you diagonalize the matrix you have the eigenvalues on the diagonal and can just read them off. Best,

B.

'I fail to see how choosing one constant to match observation is supposedly worse than introducing not only a new constant, but also N copies of some new field with a particular coupling pattern. '

That's because you fundamentally misunderstand Quantum Field Theory. It's fine though.

Must say I really enjoy your take-downs of current high energy theoretical physics. :D

It's a real shame that "publish or perish" has reduced a subject with such a great past record to fashion-chasing, parameter tweaking and media hype.

Any hope of change on the horizon ?

A.

Gatto,

Humor me and explain your comment. Come on, just give it a try. Give me one rational justification for this, one that isn't based on aesthetic reasoning.

Hi Sabine,

I want to comment on "one that isn't based on aesthetic reasoning" - with which I agree with you. The Bohr model was not aesthetic, but very explanatory and eventually reductionist. I think physics has now taken the opposite path, like noting truly explanatory is needed - like (seen on this blog) "we have the right equations to model nature". In my opinion that is plain wrong. The point never was to model, but firstly to explain. Likewise, it was never to make predictions.

Best,

J.

I'm not necessarily talking about clockworks, which I find just a nice model building curiosity, but I though your sentence wasn't either.

All solution of the hierarchy problem consist in 'adding N copies of some new field with a particular coupling pattern'. The coupling pattern is typically enforced by a symmetry. This in turn allows to EXPLAIN a number that would be otherwise put by hand.

It is not aesthetic reasoning, it just the desire to understand a stunning empirical observation. This is the starting point of Science. Luckily, Science was already there when you were born.

Gatto,

Are you a physicist yourself or are you just repeating something you heard elsewhere? Why do you think it's better to put in several fields (plus numbers) by hand than to put in one number by hand? Sure this is aesthetic reasoning. Really, I think you don't know what you are even talking about.

I'm repeating something heard elsewhere obviously. Exactly like you are.

Let me understand your reasoning, what's the maximal number of field N I can add to explain a single number. At which point I enter the realm of 'aesthetic reasoning'? And what is exactly the criterion defining this upper bound?

There is the classical example of the electron mass being fine tuned without doubling all degrees of freedom and imposing certain relations among couplings as imposed by Lorentz invariance, but I find it somewhat pretentious.

I don't even want to talk about technical hierarchies, but small numbers in general.

The spectrum of the SM fermions is weird. Is it technically unnatural? No. Do you physicists have any satisfying explanation for it? No. Would we like one. Yes. The point is that exactly because a small electron mass is natural you cannot point to a definite energy scale where to look for a solution. It could well be beyond any foreseeable experimental reach.

Why is the electric dipole moment of the neutron so small? Do we care about it? It is just a small number right? I guess we should care. Maybe an axion is a solution. Should you look for it? I guess you should, but according to your logic it is not really clear whether you should. It seems to depend on how many fields are needed to get this axion.

Finally the hierarchy problem. That's hard. But you know where to look according to bread and butter quantum field theory. Around the weak scale. And there are theories requiring new fields with appropriate coupling that would be able to turn a coincidence into understanding. So it makes absolute sense to look, and it doesn't make much sense to say "I told you so" because a) i guess not many scientists would care b) it doesn't add anything to the actual understanding even if you were right.

There can of course be good questions and bad questions. Doing Science is about asking questions. It may turn out the hierarchy problem is a bad question as the aether was, but this would again require a deeper understanding, which doesn't come from saying 'I told you so'.

Gatto,

Not sure what you think I'm repeating other than myself, which evidently I'm forced to do constantly. Yeah, sure, aesthetic considerations aren't a priori bad. They can work. Just that, if they don't, scientists shouldn't get stuck on them. So how often do you think should we repeat the attempt to "prettify" the standard model when the outcome has been - over and over again - that such attempts lead to nothing?

I don't think you understand my reasoning. If you add only one additional field with one additional number, you have already added more axioms than would be required by just one additional number. Yeah, science is about asking questions. It's also about realizing when a question is a dumb question.

Thanks Dr. H., for your very clear explanation of the "clockwork" mechanism.

As you say, a single large number seems less "unnatural" than a bunch of fields with their interaction coefficients. However the clockwork approach has one big advantage. It allows one to predict particles and interactions (associated with the fields) to be found with a collider, so it could conceivably be experimentally demonstrated someday. Whereas if one says the number is "just the way it is" there's nothing to test.

This approach has, famously, worked very well in the past. For example electroweak theory postulated a lagrangian which explained electro / weak interactions. It included a new scalar field, Higgs, which was found. If it hadn't been, then no matter how elegant the theory, it couldn't be accepted. Same with this clockwork explanation. If the predicted particle(s) are found then it's right, otherwise not. It doesn't matter how "aesthetic" it is or isn't, nor how many copies of fields are involved.

The problem is that in many cases the mass of the predicted particle is not known. So if it's not found in the current generation collider, theoreticians just say it must be at a higher mass. Although specific versions of the theory can be disproven it seems they can always tweak it to "explain" why the masses must be beyond our current capability. So something like this clockwork idea can never really be disproven. Similarly, if we don't find supersymmetric partners with LHC they can always just say they're at a higher mass. A million years from now they might still be advocating superstring theory, still without any experimental evidence.

There's no real solution to the problem. Postulating a new theory (ie, a lagrangian) to explain something like "unnatural" numbers is surely legitimate theoretical physics. If your intuition says it's too Rube-Goldbergish, too unlikely, I think you're right. But if someone else, like Gatto, wants to pursue it, I say, go for it!

Just don't ask me to fund it.

George,

The Higgs was *not* a prediction made on aesthetic grounds. It was a prediction based on the requirement of mathematical consistency (loss of unitarity). Indeed the Higgs was (when it was first introduced) widely thought of as an ugly fix. The prediction for the LHC also wasn't specifically that the Higgs would have to be found but that some new physics had to appear around that energy scale.

Take away: Consistency is a good guide. Beauty is a bad guide.

As a matter of fact these kind of posts don't teach anything to anybody and just end up damaging the image of HEP in the public eye, as testified by the last line of previous post "Just don't ask me to fund it.".

The Rattazzi, Kaplan paper has 53 citations since November 2015, so this whole discussion is just plain ridiculous. There is no big trend, there is nobody asking any money to anybody.

But again, what do you expect from someone believing that the SM without the Higgs would be "mathematically inconsistent" or lose unitarity.

There is no reason to stop exploring higher and higher energies, simply because we don't know what it is there. There are obvious human limitations to deal with, like money, but there is a clear scientific case to keep exploring smaller and smaller distances. Exactly like you would like to visit a new continent that you just discovered. I guess you would say "Meh, just another piece of dirt".

Gatto,

I dunno where you're coming from but on my planet 53 cites in a year is a lot.

I didn't say that the SM without the Higgs would be mathematically inconsistent. I said the standard model without Higgs and any other new physics would violate unitarity, which is an inconsistency - it's incompatible with the probabilistic formulation.

"As a matter of fact these kind of posts don't teach anything to anybody and just end up damaging the image of HEP in the public eye, as testified by the last line of previous post "Just don't ask me to fund it."."qft. Get a life.

B.

The similarity to toddlers is uncanny. Even the predictable, "I know!" response when you point out something obvious to them.

Your writing is as always delectable. Can't wait for the book.

"Ben Allanach reports from Recontres the Moriond"Should be "Recontres

deMoriond, n'est-ce pas? (Although originally in France, this series of meetings, starting in 1966, is now held just across the border in Italy.)Is it "just" your opinion or general consensus that this is the most important particle-physics meeting? (There are several Recontres de Moriond; I've often been to the cosmology meeting, which is every two years in even-numbered years; next year is 17--24 March.)

Phillip,

Oops, sorry about this. Looks like a spell-check bummer. It is just my opinion. Let me know if you find something like a "general consensus" on anything in particle physics ;)

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