Conventional wisdom in the particle theory for about 30 years has been that the Standard Model has a huge “hierarchy” or “naturalness” problem, the solution to which is supposed to appear at the LHC via SUSY or some other new BSM physics. With no SUSY or other BSM physics appearing at the LHC, this conventional wisdom is now moving towards claims that fundamental physics has been shown by the LHC to be “unnatural”, with parameters that are environmental, artifacts of our position in the multiverse generated by the anthropic landscape of string theory. For an example of this, see Seiberg’s Now What? talk at Aspen (Arkani-Hamed also spoke, with presumably a similar point of view, although the talk is not available).

It seems to me that a much more logical conclusion to draw would be that the LHC has just shown that the hierarchy/naturalness argument was mistaken. I’ve never understood why people found it convincing, and have often argued about this here on the blog. From the “hierarchy” angle, the problem is why the ratio of the electroweak-breaking scale to the GUT or Planck scale is such a small number, but we don’t actually have any evidence for GUT physics or for quantum gravitational physics, so no good reason to be sure that such high scales are relevant to anything or the cause of a hierarchy problem. From the “naturalness” side, while the theory is renormalizable, one can worry about the sensitivity to high energies of its cutoff dependence, but it’s unclear to me why one should be that concerned about this. More worrisome is that the Higgs sector introduces most of the undetermined parameters of the SM, a much more serious defect of the standard theory.

Today at a workshop on The First Three Years of the LHC, Joe Lykken gave a talk on Higgs without Supersymmetry, in which he argues that there is no naturalness problem or need for supersymmetry, and makes a specific suggestion about how to think about the high energy behavior of the Higgs. He starts off with:

is there a Higgs naturalness problem?

•For decades the HEP community has asserted that naturalness is the central issue

•Simply put, we have assumed that either EWSB is natural, in which case we need to explain why, or that it is fine-tuned, in which case we also need to explain why

•I will argue that this is a false dichotomy,and that LHC results are hinting at a third path

then explains the standard dogma about quadratic sensitivity to the cutoff. He argues that the solution to this problem lies in properly understanding the scaling behavior of the Higgs, following ideas that go back at least to W. Bardeen in 1995 (see here). The fact that the renormalization group flow of the quartic term in the Higgs potential takes it to zero at high energies is interpreted as a suggestion that the right UV boundary condition is that the Higgs potential vanish. From there Lykken goes on to discuss more specific ideas, which may lead to observable new physics at LHC scales.

These aren’t really new ideas, but I think Lykken is drawing the right lesson from the LHC results: the naturalness argument for SUSY has now been shown to have been misguided, and it’s time not to give up and adopt the pseudo-science of anthropics, but instead to question the dogmas that have dominated the subject for decades.

Link for Lykken’s talk is a duplicate of Seiberg’s….

Flakmeister,

Works fine for me??

The Lykken link works fine for me as well. Also, Peter, you wrote:

‘…for SUSY has now been show to have been misguided…’, you meant to write ‘…shown…’

Mean and Anomalous,

Thanks, fixed.

Thx.. my bad (too many tabs flying around)….

Don’t be so hard on TeV scale SUSY…. it always struck me as a jobs program for experimentalists and theorists… Hell, at LEP2, one search analysis could give you 5 easy papers…. SUSY did have the benefit of providing testable predictions (even though you knew there was a lot of wiggle room)

As an outsider to this world, I had to look up on naturalness – indeed it seems strange to me that lack of naturalness should hint at anything. The universe seems to show structures at many different scales of Spacetime, how should a model representing such a universe exhibit “naturalness” as defined in wikipedia?

Frank,

The scales of various observed physics have some explanation in terms of our understanding of the astrophysics/physics (except I guess the size of the universe, the time back to the big bang is just an historical fact).

Very roughly, the idea of naturalness is that if even if you don’t know how to compute something, you expect it to be “naturally” of order 1 in the appropriate units. If it’s exponentially smaller, there should be some reason. People try and apply this to particle physics at scales such that we don’t have experimental evidence.

Then the question arises as to why the Higgs mass (or W, or Z, etc) is so small in units of the GUT or Planck scale. The answer may just be that there is no GUT scale and the Planck scale is irrelevant. The SUSY explanation is that fermionic superpartners 0f the Higgs have zero masses (before SUSY breaking), and this keeps the Higgs small small. You then expect the SUSY breaking scale to be what determines the mass. Thus the problem arising now, since the LHC has shown that the SUSY breaking scale must be quite a bit higher than the electroweak breaking scale.

This argument is made in various forms at the beginning of just about every review paper or talk on SUSY, and I’m just giving a crude version of it. Best I not go on about the details, but look for a more detailed version that might be readable.

Some of your collegues might have shown the string landscape is in fact falsifiable, by, erm… falsifying it

http://arxiv.org/abs/1303.4428.pdf

lun,

As they say in the abstract “if our results prove applicable to string theory…”

But please, that’s really off-topic, and I think the Lykken talk is a much more interesting subject.

The non-existence of SUSY in Nature is quite natural; I have expected this result since thirty years ago. Because there is no Nambu-Goldstone fermion, one must go to supergravity in order to make use of super-Higgs mechanism. However, I showed that the supergravity cannot be a fundamental theory. In my review paper of the manifestly covariant canonical formalism of quantum gravity published in 1983 (Publ. RIMS 19, 1095), I emphasized “It is not the right way to extend the Lorentz invariance of elementary particle physics at the level of determining the fundamental Lagrangian density.” (p.1125) The reason for this claim essentially arises from the fact that there is no spinor (linear) representation of general coordinate invariance. For more details, see my recent paper entitled “Space-time structure in the ultimate theory” (Intern. J. Mod. Phys. D 20 (2011) 253; DOI: 10.1142/S0218271811018809).

N. Nakanishi,

Please, this has nothing to do with Lykken’s talk about the Higgs which is the topic of this posting.

Yes, the Lykken talk is interesting, dove tailed very nicely with Strumia’s Moriond presentation. I am not a theorist but I do remember being struck by Bardeen’s infrared fixed point stuff in the early-mid ’90s. Glad to see that yet another old dog might be taught a new trick or at the very least get a few more walks around the park….

I took a gander at the Moriond talks and I was somewhat taken aback by the clearly palpable tone of the theory summary talk, given with a proverbial almost stiff upper lip in the face of what clearly may be the death knell of the HEP as an experimental science…. Ironically from its own astounding success…

I was also tremendously impressed by the quality of the experimental results from the LHC. It is clear that there are still truly excellent young people entering the field, I only hope that they find the oppurtunities they deserve….

Peter,

Lykken states that his ideas will lead to dark matter discoveries. While it is great to eliminate one dream world (susy) he makes the mistake to introduce another (dark matter). Why is it not possible to stop with these silly games? After all, we only need an explanation for the SM parameters – not more not less.

Kudos. Please keep your efforts at dispelling quantum theology – I wish it wasn’t necessary but this has been on for so longer than anyone anticipated. And worse, the matter at stake is not just absence of falsifiability anymore.

Thomas,

I’m not convinced by Lykken’s dark matter model, but it’s quite reasonable for him and others to pursue such ideas. A long shot, but at least not flogging a dead idea as in SUSY models.

“It seems to me that a much more logical conclusion to draw would be that the LHC has just shown that the hierarchy/naturalness argument was mistaken. I’ve never understood why people found it convincing, and have often argued about this here on the blog. From the “hierarchy” angle, the problem is why the ratio of the electroweak-breaking scale to the GUT or Planck scale is such a small number, but we don’t actually have any evidence for GUT physics or for quantum gravitational physics, so no good reason to be sure that such high scales are relevant to anything or the cause of a hierarchy problem.”

are there any theoretical, observational or experimental ramifications if your position is physically correct i.e there is no GUT or planck scale in nature?

dark,

I think the question to ask is whether there is any evidence for a GUT scale, or that the Planck scale has something to do with particle physics. A huge effort has gone on for decades trying to find such a thing, come up empty so far.

Peter Woit

if there is no GUT scale, does this mean there is no “unification” of 3 of the 4 forces? if there is no planck scale, does this mean there is no QG?

dark,

There may be some sort of “unification” of the SM forces (e.g. something that explains their relative coupling constants, and why SU(3), SU(2), U(1)). But there’s no evidence for the specific proposal of putting these groups into a larger group like SU(5) or SO(1o) and then introducing some new Higgs fields to break the symmetry back down. This has never been the most compelling idea. Not only does it not solve the problems introduced by the Higgs, it adds a whole new set of them with new problems (including the hierarchy problem).

We really know nothing about quantum gravity, including whether the Planck scale is even the correct scale at which its effects become important.

Peter,

Perhaps I’m missing something, but is it really the case that the loop corrections to the Higgs mass are only a problem if there is a new physics at the GUT or Planck scale? The questions seems to me to be, what is the appropriate cutoff scale for these loop corrections? You seem to be arguing that the cutoff for these loop corrections should be the EW scale without requiring any new physics at this scale. Is it not true that the appropriate cutoff should be the next highest scale at which new physics appears? Even in the case that there were not new physics at the GUT or Planck scales, then wouldn’t the corrections to the Higgs mass be expected to be infinite?

“There may be some sort of “unification” of the SM forces (e.g. something that explains their relative coupling constants, and why SU(3), SU(2), U(1)). But there’s no evidence for the specific proposal of putting these groups into a larger group like SU(5) or SO(1o) and then introducing some new Higgs fields to break the symmetry back down. This has never been the most compelling idea. Not only does it not solve the problems introduced by the Higgs, it adds a whole new set of them with new problems (including the hierarchy problem).”

Isn’t SO(10) embedded the whole string theory TOE research program? If you don’t think SO(10) broken by new Higgs field then in what sense is there any reason to expect stringy unification?

“We really know nothing about quantum gravity, including whether the Planck scale is even the correct scale at which its effects become important.”

you have this link

“For an example of this, see Seiberg’s Now What? talk at Aspen (Arkani-Hamed also spoke, with presumably a similar point of view, although the talk is not available).”

in Seiberg’s article he confidently claims QG is well known thanks solely to string theory do you agree?

One thing about GUTs is the large number of extra gauge bosons that are introduced. The Standard Model has 12 gauge bosons–8 gluons, the W+, the W-, the Z and the photon. If we go to SU(5), then we have 5^2-1=24 gauge bosons, double the number in the SM. SO(10) has 10*(10-1)/2=45 gauge bosons, nearly 4 times the number in the SM; SO(10) could also exist by itself as the gauge symmetry of nature without string theory, just as a GUT–all the quarks and leptons plus a sterile neutrino of a single family fit into its 16 rep. String theory once considered a gauge group of E8xE8; each E8 would have 248 gauge bosons, for a total of 496. Going from the SM to a large GUT is like generalizing a small town into New York City or Tokyo, almost literally. It seems a large price to pay to explain a handful of parameters. You have to introduce lots of extra Higgs fields to break everything down to the SM. It seems that the SM is simpler than a large GUT theory. Just out of curiosity, I once computed all the subalgebras of just one E8 using Dynkin diagram technology–it was amazing what was in there.

Also, if the strong and electroweak gauge symmetries arise for totally different reasons, there might be no reason that they should unify.

@kingray

wouldn’t those extra gauge bosons show up as new forces?

Also, if the strong and electroweak gauge symmetries arise for totally different reasons, there might be no reason that they should unify.

that’s what ive wondered about – one of the arguments for SUSY is gauge coupling.

dark, yes if you had a large GUT, the SM would be the tip of the iceberg. It would be a huge extrapolation. Where unification has worked before, it was more of a case of interpolation–Maxwell just added a term to the eponymous equations, Weinberg et al just added enough to get U(2).

dark, if everything fit in one simple GUT group, then technically there would only be one force, with lots of gauge bosons. One force seems to be associated with each gauge group: SU(3) is the strong force, SU(2)xU(1) the electroweak force, and SL(2,C) is the gravitational force. Sometimes the electroweak force is split into the electromagnetic and weak forces, but they are tangled.

Hi,

I find these ideas quite compelling, and I have long thought that introducing a cutoff regulator might be the unnatural thing to do if there are no new high scale particles coupling to the higgs. However, that idea is not new at all, and I think you make it look too much like it had been unknown or suppressed by the SUSY inquisition somehow, while the truth is that people are working on it all the time.

However, I don’t see how this (now also Lykken’s) idea – that the right boundary conditions for the higgs potential are such that it should vanish somewhere, are any more experimentally testable or any less pseudoscientific than superstring theory, which at least establishes a framework to accomodate the other known particles and forces.

Lykken seems to misunderstand the basics of QFT and RG.

M_ Planck (at last) provides a cutoff to his theory, and thus the relevant operators such as H^2 gets turned on with a coefficient of the size M_planck to some positive power.

In other words, the CFT is badly broken by gravity and cannot thus be invoked as a solution of the hierarchy problem unless some new separate symmetry forbids the relevant deformations. Take for instance QCD: it is natural because the dangerous strongly relevant operators, such as the quark masses, can be forbidden by the chiral symmetry, while the gauge interactions are only marginally relevant and give you the desired hierarchy via dimensional transmutation. SuSy and RS are other examples where gravity enters only through irrelevant deformations.

“Lykken seems to misunderstand the basics of QFT and RG.

M_ Planck (at last) provides a cutoff to his theory, and thus the relevant operators such as H^2 gets turned on with a coefficient of the size M_planck to some positive power.”

Obviously, he must try to avoid this via some kind of asymptotic safety scenario. Do you think this is impossible? If so, it certainly isn’t a “basic QFT” argument which says so.

@ Alex,

If the CFT is exact (e.g. unbroken by gravity which becomes part of it) then it is not clear how to actually have any flow in the IR in the first place. Moreover, while the Higgs potential seems almost reaching a fixed point in the deep UV, the yukawas are not and they keep running spoiling the picture. Not to mention that the Higgs quartic is actually becoming negative below the Planck scale. About the ERG methods that people use to promote asymptotic safety scenario, it doesn’t seems well suited for theories like gravity or YM where the operators that get omitted by the truncation of the effective action contain more and more derivatives.

BB,

The fact that a heavy top quark makes the quartic coupling go negative too early would indeed be a problem for the asymtotically safe gravity scenario I guess.

As far as the running of the Yukawas etc is concerned, yes, in DREG in the SM the quartic rises again due to the gauge couplings – also, not all gauge groups are asyptotically free.

Shaposhnikov and Wetterich argue that in their RG scheme, the combined running of SM+Gravity exhibits a modified Yukawa and gauge running. What the impact of the truncation is I am not competent at all, but I would hope that people at least have checked different ones to see what the impact is.

@Also, if the strong and electroweak gauge symmetries arise for totally different reasons, there might be no reason that they should unify.

are there any theories that explore this? what would be the experimental predictions from this?

I never quite got the naturalness argument’s reliance on the assumption that some arbitrary ratios be of order 1. Aren’t there, in a suitable measure-theoretic sense, infinitely “more” large numbers than numbers of order one for nature to choose from, if nature is going to choose parameters randomly?

Anon,

Only in the multiverse-mania world where if we don’t know how to calculate something we can never understand it, so it’s equally likely to be any number would your argument apply. More conventionally, the standard idea is that there are fundamental structural reasons why the numbers we calculate have roughly certain values. Even if you can’t calculate things exactly, if you have a good understanding of what governs the result of the calculation, you expect to be able to do an order of magnitude estimate.

dark,

Type II Superstring Models with separate brane stacks for the sm gauge groups dont involve unification.

Predictions are hard… No proton decay maybe

@ Alex says:

thx.

wouldn’t the simplest model though be “the strong and electroweak gauge symmetries arise for totally different reasons, there might be no reason that they should unify” + 4D QFT + GR no SUSY + DM is sterile neutrino ?

There is some discussion here of Lykken’s talk… So far, I am confused about how all these things are supposed to relate: (1) the argument from DimReg that the SM is technically natural after all, (2) the idea that the SM is tuned to metastability by special UV boundary conditions, and (3) the use of radiative EWSB in a Higgs-portal model. Are they logically disconnected but thematically similar, or are there supposed to be logical connections?

@ Mitchell Porter,

well, (1) is simply (very very) wrong. The hierarchy/naturalness problem has nothing to do with divergences and the regulator. The hierarchy problem is about the stability of hierarchically separated physical scales. BTW, even dim. reg. generates relevant dangerous operators via its finite mass terms.

(3) would be very important in order to generate an hierarchy (via dimensonal transmutation like in QCD) of scales but only if one can forbid the relevant deformations with a separate symmetry. Otherwise is simply plain tuning.

BB,

“The hierarchy problem is about the stability of hierarchically separated physical scales.”

Surely the people proposing this scenario will agree that heavy particles coupling to the Higgs will immediately constitute a new high scale also in DREG, which will make a light higgs unnatural. That’s just ordinary matching and running in DREG. They seem to disagree that the Planck scale counts as such a high scale in this scheme. In that sense DREG is important and crucially connected to the EW naturalness problem because it makes it possible to regulate QFT without having to introduce a huge scale invariance violation via a planck scale cutoff.

“BTW, even dim. reg. generates relevant dangerous operators via its finite mass terms.”

May I ask what exactly are you alluding to here?

Alex,

Above I was,alluding to the finite terms which are still quadratically sensitive to any new physics scale.

Even assuming that no fundamental scale, not even Planck, breaks the CFT in the UV, I don’t think there is anything deep in dimreg. As there is nothing deep in dimreg for gauge theories, it just makes the calculations easier. Moreover, one could work with another arbitrary regulator and add a conformal compensator to the cutoff scale, rendering it as practical as the dimreg one.

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The really compelling argument that Lykken makes is that an ultraviolet boundary condition of zero for one or more quantities including Higgs boson mass or couplings that runs with energy scale can set the mass scale for the Standard Model at some suitable UV boundary. This argument is similar in form to the SUSY argument that the GUT scale is set by the point at which the running of the coupling constants cause them to converge (a scale that conveniently coincides with the energy scale when the patterns of CMB variation that we observe arose). SUSY proponents have made much of the fact that the running SM coupling constants don’t converge at a single point, but a very subtle tweak to their running near their UV convergence chalked up to quantum gravity effects, for example, can easily resolve this issue which is essentially precisely what was done in the asymptotic safety based prediction of the Higgs boson mass.

The conclusion that the hierarchy problem is principally a problem of our flawed understanding of where fermion and boson masses in the SM come from, likewise makes sense. If some unknown mechanism drives the relative fundamental particle masses of the Standard Model, then the absolute masses flow naturally from any boundary condition for any particle mass, Higgs or otherwise, that can fix the mass scale of fundamental particle masses generally. Surely, the one thing almost everyone believes intuitively is that the many experimentally measured constants of the SM have some deeper relationship to each other. As much as anything we need “Within the Standard Model” (WSM) theories at this point that motivate the why’s of the moving parts in it, as much as we need “Beyond the Standard Model” (BSM) theories that give rise to “new physics.” The only place empirical evidence is telling us that we need “new physics” is in the gravitational/cosmology sector.

Thus, the particularly SM extension that Lykken explores in his talk isn’t terribly compelling. But, the notion that minimal modifications of the SM are the way to go, rather than one creating heaps of new particles and forces a la SUSY, is a good one. A better minimal SM modification than the one he discusses, for example, which still meets the test of adding particle/force content only to the extent absolutely necessary is the one discussed in “Gravitational origin of the weak interaction’s chirality” by Stephon Alexander, Antonino Marciano, Lee Smolin (Submitted on 20 Dec 2012) http://arxiv.org/abs/1212.5246 which fits the dark matter sector and gravity into the same degrees of freedom as the electroweak SU(2)*U(1) sector, with electroweak constituting the left handed and gravity constituting the right handed counterparts of each other, leading to a “massless graviton coupled to an SU(2) triplet of chirally coupled Yang-Mills fields. . . . [with] a Dirac fermion [that] expresses itself as a chiral neutrino paired with a scalar field with the quantum numbers of the Higgs.” In other words, in addition to a graviton and its intricate gravitational fields, it gives rise to a singlet sterile neutrino dark matter particle and a simple scalar inflaton and/or dark energy field.

What does it mean for a Dirac fermion to “express itself” as a “chiral neutrino paired with a scalar field”??