Throughout the previous decade Gia Dvali was arguing that there are $10^{32}$ copies of the standard model out there. Now, he made a U-turn and says that there is only 1. Or even less. Let me explain.

The reason why we are pretty sure that we are going to observe new phenomena in the LHC goes under the nickname unitarity of WW scattering. What hides behind this is, technically speakin, that the tree-level scattering amplitude of longitudinally polarized W bosons computed in the standard model without the Higgs particle grows as a square of the scattering energy, and at some point around 1 TeV it becomes inconsistent with unitarity, that is with conservation of probability. In the full standard model this problem is cured: the contribution from the Higgs exchange cancels the dangerously growing terms and the full amplitude is well behaving for arbitrary high energies. A slightly different mechanism is realized in technicolor theories, where the consistent UV behavior of the amplitude is ensured by the exchange of spin-1 resonances.

In spite of 40 years of intensive research we are only aware of these 2 ways of unitarizing the WW amplitude. Thus the LHC should see either the Higgs or new spin-1 resonances. Time will tell which of the 2 possibilities is realized in nature.

A paper last week by Dvali and co. suggests that there may be a 3rd possibility. The authors conjecture that the standard model without a Higgs and without any other embellishments could be a fully consistent theory, even though it appears to be in conflict with unitarity. They argue that the uncontrolled growth of the WW scattering amplitude is just an artifact of the perturbative approximation, while at the non-perturbative level the theory could be completely sane. The idea is that, as the scattering energy increases above TeV, the theory defends itself by producing "large" classical configurations during the scattering process. The higher the energy, we get the larger and more classical objects which then decay preferentially to many-body (rather than 2-body) final states. This way the 2-to-2 WW scattering remains unitary at energies above TeV. The authors, somewhat dully, call this mechanism classicalization. To put it differently, as we increase the scattering energy at some point we stop probing the physics at short distance scales; these small distances are screened from external observers, similar in spirit to black holes screening the short distance physics in transplanckian scattering when gravity is in the game.

If this is the case, what would it mean in practice, that is in experiment? Much as in technicolor, at TeV energies the LHC should observe resonances in WW scattering who ensure the unitarity of the perturbative amplitude in the low-energy effective theory. However, as the scattering energy is increased the resonances become more and more classical and spectacularly decay into many-particle final states. There is no new fundamental degrees of freedom at high energies, no new fundamental forces to discover, just the standard model and its non-perturbative classical dynamics.

Now, can this be true? The paper is rather cryptic, and provides few technical details. In this sense it feels like another emergent gravity. What it demonstrates is that in a class of theories that includes the standard model there exist classical solutions whose large distance behavior only depends on how much energy is sourcing it, and whose size grows in a universal way with the energy. The rest seems to be just words, and there is a long way to proving that classicalization can indeed lead to a fully consistent quantum theory. Nevertheless, given the scarcity of ideas concerning electroweak symmetry breaking, there is definitely some philosophical potential in the paper. We'll see whether it leads to something more concrete...

Update: See also Lubos' stance.

## 11 comments:

Well, duh. About time they started hopping on a reasonable bandwagon.

It is not the only non-perturbative mechanism proposed as alternative to the Higgs.

see e.g. arxiv.org/abs/0909.3340

I guess we will see soon enough...

Holy cow, Gia, please.

Introducing a non-curved quantum gravity to the 100 GeV energy scale (and indeed, if the link between high-energy and short distances breaks, it *is* a form of quantum gravity), just in order to be able to pretend that the ordinary Higgs boson doesn't exist...

Classicalons - the non-curved black holes. Wow. How are they supposed to be calculated? What equations do they obey? Why don't we have little green men instead of classicalons? This is no epistemological analogy because the black holes actually do solve the equations we know - a soldier in the World War I was enough to find the solution. But classicalons?

I wrote a few explanatory comments about Why there are no classicalons by Dvali et al.

My initial professional opinion on this is I bloody hope they are wrong because I suck at non-perturbative physics :(. Maybe I'll have a more interesting one after I've read the paper.

Nice to see you blogging again.

Thanks for reporting. And I also read Lubos' notes. Nobody seems to have said the very simple reason which makes this paper utterly wrong. (In fact, also their ideas about black holes are misguided but that is not relevant now.)

The point is that whatever it is that they propose, it cannot be QFT a-la Wilson. If the Higgs sector cures its own disease, at scales above the Higgsing scale there should something. Wilson only allows for a UV CFT, and hence, power-law scattering amplitudes.

Their proposal implies that at scales much above the Higgsing scale we do not have any UV CFT, and not even approximately UV CFT. Such theories are unfamiliar and surely violate the axioms of QFT.

Note that even Weinberg speculated at some point that the pion Lagrangian could have a fixed point in the UV. This is unlikely, but cannot be easily refuted. The correlation functions will be power laws. In their proposal the exponential decay of correlation is not consistent with any known set of axioms.

And since they have virtually no evidence that what they say can happen, the whole story can be safely ignored :)

Sorry for a double comment. The program told that there was error in the processing of the comment but it

had accepted it after all.

Dear Anonymous,

you wrote:

"Such theories are unfamiliar and surely violate the axioms of QFT."

Well, this is a bloody weak argument against their paper. After all, they're saying the same thing. It's unfamiliar - which means that if it were correct, it would be a (mini)revolution. But you actually don't propose any argument that it's wrong.

Does it violate the rules of a local QFT? You bet. After all, they say that it's meant to be analogous to quantum gravity which is not a local QFT (in the bulk). And what? This fact itself is their starting point, not an argument against the picture.

Cheers

LM

There are many people saying that the Higgs is not needed to cure unitarity. The most famous is Tini Veltman - Nobel Prize for physics on the renormalization of the weak interaction and some more aspects - who says that the Higgs is an artifact of the perturbation expansion. He suggests that no other trick or concept is needed, but that the Higgs will go away as soon as field theory is well understood.

Mark

Lubos: They are drawing an analogy with QG, but nowhere they openly admit that what they are saying violates the Wilsonian picture of QFT (or do they and I missed it?)

My impression is that they wanted to borrow these ideas from QG but actually suggest that they can be completely consistent with QFT in the specific context they are interested in. In particular, the very few computations that are presented in the paper are defintely done in the framework of QFT.

So I think my comment is to the point. If they understand that whatever they are doing is not consistent with the axioms of QFT they should say that. (Or you should tell me where it is written in their paper.)

Dear Anonymous, of course that they do say that it is not a Wilsonian QFT. (Is it a heresy? Of course that if they want to adopt the QG concepts, they must suppress the Wilsonian axioms just like QG does: it suggests that leaving the local QFT axiomatics is the ultimate heresy but it's surely not.)

For example, open the paper on page 4 (5 of 37) and it says:

"The phenomenon of classicalization is a non Wilsonian self-completion of the theory by localized particles becoming classical in deep-UV."

However, as I argue in my article, this completion is only consistent for quantum gravity. The subtle non-localities that make sub-Planckian distances inaccessible in QG are results of black hole microstates which correspond to classical metastable, high-entropy, quickly thermalizing objects independent of their "microscopic building blocks". These properties can't be satisfied outside quantum gravity.

To some extent, this is true even in the perturbative string theory that produces non-localities at the string scale - which is longer than the Planck scale at weak coupling. But strings are surely new objects with many degrees of freedom - internal excitations - that can't be composed out of the low-energy fields (coming from low-energy vibrations of strings).

Cheers

Lubos

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