Shaposhnikov Wetterich predicted 126 GeV Higgs in 2009

[Haelfix]

There are some serious theoretical problems with Shaposhnikov-Wetterich's proposal, although it does seem like an interesting partial solution to one (but not both) of the stability problems of the electroweak sector.

The biggest problem is that it doesn't even attempt to address the dozens of other problems that the standard model has, which would be fine, except that any additional resolutions to those problems will alter the running of the beta functions and alter many of the assumptions of the proposal, that is, unless the new physics were wrapped up in baroque constructions (hidden sectors, Higgs inflationary scenarios and the like) the exact details of which are problematic for cosmology and actually create highly nonminimal extensions of the standard model (the point that Nima is emphasizing where it seems like any new physics you can imagine is in some sort of trade off between naturalness and nonminimality).

Further, the prediction of the Higgs perse is actually not that impressive when you look at it from a certain point of view. It's very much related to the statement that a Higgs mass below 126 creates a scenario where the Higgs potential loses its absolute stability when run up to the Planck scale, so all it takes are assumptions that favor a data point right at the margin and presto you get your prediction.

A lot of this will become very clear in the next few years, as we get more precise precision electroweak observables that will squeeze the details on the Higgs potential and other relevant observables (top quark mass)

 

[mitchell porter]

Hi Haelfix, glad to see you comment on this.

Further, the prediction of the Higgs perse is actually not that impressive when you look at it from a certain point of view... all it takes are assumptions that favor a data point right at the margin and presto you get your prediction.

But how is that not worthy of attention? That's the mysterious thing. We have all this angst specifically about the value 125 or 126 GeV, about how to make that natural and about whether we should interpret it as finetuned. And, oh yeah, that value is also what you get if you make certain assumptions. Why is there relatively little interest in exploring variations of those assumptions, compared to the vigorous search for new natural models?

I understand the points you raise against the idea, in particular that it would be spoiled by most forms of BSM physics. I understand the possibility that it's just a coincidence. Still, I think the time is ripe for the scattered people who consider the SW type of explanation for the Higgs mass to be a serious contender for the truth, to get together. They could have a conference. Something like "The Higgs, Marginal Safety, and Minimalism in Physics Beyond the Standard Model".

The truth may well be a hybrid of "neo-minimalism" and "traditional baroque" - by the latter I mean the line of thought that encompasses GUTs, supersymmetry, and string phenomenology - but minimalism itself comes in different forms. There's minimalism that's "nothing but the SM up to the Planck scale" (the SW prediction is a great victory for this school of thought), and there's minimalism like "the simplest model that incorporates all the data". The "new minimal standard model" is an example of the latter, and this is a type of minimalism which by definition acknowledges the new data like neutrino masses and dark matter. Perhaps what needs to happen is embedding of the SW mechanism in something like the NMSM, and then investigation of how to hybridize that with "traditional baroque", so as to explain coupling unification, the structure of an SM generation, and all the other facts which really motivate GUTs and beyond.

 

[Haelfix]

I actually disagree with Nima about one thing. If I had to give up something, i'd give up minimalism.

It is often the case that what seems nonminimal from an effective field theory point of view, is actually ok from the perspective of the high energy theory. For instance, if we happened to discover a bunch of new Z' models floating around, I think a lot of people would be quite nonplussed on the face of it, but then it might really be elegant from say the stringy phenomenology perspective or perhaps some other type of high energy theory yet to be discovered.. Further from my perspective, the huge array of problems we face in physics is almost assuredly pointing towards a good deal of new as yet discovered physics. From my point of view, I can't imagine anything simple that could fit all the available data and contradictory threads.

On the other hand, I really don't know how to do physics with large amounts of finetuning. Anyone can do that, and all predictive power is ultimately lost.

 

[mitchell porter]

An example of minimalism that is also minimally consistent with standard ideas would be something which is just standard model up to a quantum gravity scale, where it then becomes string theory - either the superstring, in which case it's a type of supersplit supersymmetry, or a nonsupersymmetric string, perhaps like a Hellerman-Swanson cosmological solution. (For the opposite, "non-minimal", "neo-baroque" scenario, see the end of this comment.)

I'm mentioning this possibility mostly so we can see what's wrong with it. But first, what might one hope to be its features? A version of the Shaposhnikov-Wetterich mechanism might set the mass of the Higgs. It might specifically be the dilaton which first comes into play at the quantum gravity scale, causing a deviation from the pure SM beta functions, as in 't Hooft's notion of local conformal symmetry constraining the SM couplings. The Yukawas would come from the moduli or from corresponding attributes of a non-geometric phase.

What are the problems for this daydream manifesto? On the empirical side: evidence of gauge unification, neutrino masses, the dark sector and the CMB data need to be accounted for. On the theoretical side: there are probably technical problems in getting believable yukawas just from the moduli.

If we assume supersymmetry (but only at the string scale, so it doesn't interfere with the SW mechanism), then we will have gravitinos, perhaps those could be the dark matter? Given the susy-breaking scale, the mass is probably wrong, both for the early universe and for the present-day properties of dark matter. Perhaps susy can break in some unusual way, so that the usual relation between the gravitino mass and the susy scale doesn't apply.

This is a general issue in contemplating this class of possibilities: one wishes to use the conventional wisdom about how strings, susy-breaking, etc, work, in order to constrain and guide one's thinking; but one also wishes to be aware that theory itself may work differently than we have imagined. The only course of action seems to be to develop the scenario while simultaneously listing all the reasons why it shouldn't work.

Regarding gauge unification, there are definitely string models in which unification is deferred or blocked in some way. One can imagine pushing that up to the string scale, along with supersymmetry, again so as to give the SW mechanism a chance to work.

For neutrino masses and dark energy, I don't have any concrete "proposal", though I note that Hellerman-Swanson cosmology has quintessence, and perhaps neutrino masses could come from something like Tom Banks's cosmological supersymmetry breaking - virtual effects involving gravitinos at the cosmological horizon.

edit: The "neo-baroque" antithesis to this line of thought would involve looking for ways to meaningfully preserve something of the SW mechanism and calculation, while nonetheless having lots of new physics. For example, I'd like to know how far one can go towards making the SW mechanism consistent with the recent recovery of a Higgs mass in the right range within the G2-MSSM. My guess is, not far, but I couldn't say what the specific barriers to this theoretical consummation might be.

 

[mitchell porter]

Shaposhnikov-Wetterich watch: Shaposhnikov gave http://higgs.ph.ed.ac.uk/sites/default/files/higgs_symp.pdf at a symposium on the Higgs. It's a must read for all neo-minimalists: Shaposhnikov says that not only does he have an argument for the Higgs mass, but for the proposition that there is no new physics between Fermi scale and Planck scale (slide 27). Beyond-standard-model physics is to be explained with 3 right-handed neutrinos with keV-GeV scale masses (slide 41), and the Higgs can be the inflaton.

Matt Strassler, who also spoke at the symposium, noted the talk on his blog and promised to analyse it in a future post.

 

[tom.stoer]

wow

so there are two competing proposals for "SM with 126 GeV Higgs + neutrinos + no new physics"
- Shaposhnikov Wetterich
- Connes

Suppose the asymptotic safety scenario is correct:
a) there is nothing new to be expected out there
b) we don't have any idea where SM with its gauge group, 3 generations, Higgs, GR, 4-dim. spacetime, ... come from

 

[mitchell porter]

A new paper by F. Klinkhamer adds some context to the Shaposhnikov-Wetterich calculation, by listing their work alongside a few others (references 3-6), as just one example of a Higgs boson mass prediction deriving from ultra-high-energy boundary conditions.

 

[marcus]

Any concern about Hamber's paper? I haven't reviewed this but my impression is that Shaposhnikov is counting on gravity being asymptotically safe.

And what evidence (eg from Reuter, Percacci, and friends) we have for asymptotic safety depends on the cosmological constant running. But Hamber says:

http://arxiv.org/abs/1301.6259
Inconsistencies from a Running Cosmological Constant
Herbert W. Hamber, Reiko Toriumi
(Submitted on 26 Jan 2013)
We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the non-local effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem.
34 pages.

 

[mitchell porter]

My interest here is somewhat broader than the original argument. I'm also keeping an eye out for generalizations and for similar ideas, in which the Higgs mass can be deduced from something that happens at the Planck scale. I don't know how universal Hamber & Toriumi's argument is, nor whether Lambda needs to run in every SW-like scheme. So connections are interesting but we need to distinguish cases.

 

[MTd2]

I haven't reviewed this but my impression is that Shaposhnikov is counting on gravity being asymptotically safe.

Don`t you mean diff? But, what`s the problem in not being diff? Most of the variation happens during inflation and inflation is an event essentially causually disconnected. Diff should be protected in general.

 

[marcus]

Any concern about Hamber's paper? I haven't reviewed this but my impression is that Shaposhnikov is counting on gravity being asymptotically safe.

And what evidence (eg from Reuter, Percacci, and friends) we have for asymptotic safety depends on the cosmological constant running. But Hamber says:

http://arxiv.org/abs/1301.6259
Inconsistencies from a Running Cosmological Constant
Herbert W. Hamber, Reiko Toriumi
(Submitted on 26 Jan 2013)
...

Don`t you mean diff? ...

No, I actually meant what I said---in the 2009 paper we are discussing he is assuming that gravity is asymptotically safe. And the indications he points to, that this is reasonable to assume, all involve renormalization where BOTH of the two main coupling constants (G and Lambda, the c.c.) are allowed to run. All the numerical work I've seen that supports AS being plausible depends on letting Lambda run.

As a reminder, here is the 2009 paper we are talking about:
http://arxiv.org/abs/0912.0208
==quote==
Asymptotic safety of gravity and the Higgs boson mass
Mikhail Shaposhnikov, Christof Wetterich
(Submitted on 1 Dec 2009 (v1), last revised 12 Jan 2010 (this version, v2))
There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies...
==endquote==

I keep thinking that the way out of this could be for Hamber to turn out to be wrong, or for his result not to apply for some reason.

 

[mitchell porter]

I have just been reading "On the running of the gravitational constant", which atyy mentioned in another thread (and also see "The effective field theory treatment of quantum gravity", page 17 forwards) ... and it seems this is a far more direct challenge to asymptotic safety, and hence to the starting point of Shaposhnikov-Wetterich.

AS has both G and Lambda running, and so Hamber-Tomiuri's argument that Lambda doesn't run (and that it is in fact an emergent invariant scale) contradicts AS. But the running of Lambda doesn't matter for the prediction of the Higgs mass, whereas the running of G does.

 

[marcus]

...
AS has both G and Lambda running, and so Hamber-Toriumi's argument that Lambda doesn't run (and that it is in fact an emergent invariant scale) contradicts AS. But the running of Lambda doesn't matter for the prediction of the Higgs mass, whereas the running of G does.

I don't understand how it "doesn't matter", Mitchell. Shaposhnikov's scenario depends on the asymptotic safety of gravity---coupling constants converging to an UV limit. This has not been demonstrated to occur with a fixed value of Lambda.
This may not be the most direct challenge, but it surely must contribute to the difficulties this form of minimalism faces.

 

[mitchell porter]

I don't understand how it "doesn't matter"

Lambda doesn't appear in the formulas, G does. If Lambda was the only issue, you might hope to motivate the formulas in some other way. But problems with a running G are a direct challenge to the formulas.

Anber-Donoghue's criticism, by the way, is that the running of G is meant to encapsulate the momentum-dependence of many higher-order gravitational interaction terms, but that you can't do this in a way that is consistent across different scales and physical processes. There's no single "formula for the running of G", even within a single theory.

 

[marcus]

Lambda not running matters a LOT. So only G appears in some formula? So Lambda does not appear? The point is that as far as we know you do not get asymptotic safety of gravity without Lambda running.

 

[mitchell porter]

Asymptotic safety requires that all the parameters which do run, are expressible in terms of a finite number of quantities which approach fixed values at high energies. Apparently most of the work on AS does focus on (Lambda,G) running, so the contradiction with Hamber-Tomiuri is notable. However, the basic AS idea of a fixed point does not explicitly require that Lambda is involved. Meanwhile, Anber-Donoghue calls in question the very idea of a "running G", and running G does feature directly in SW, so even if a "Lambda-less AS" was devised, SW would still have a problem.

 

[marcus]

, so even if a "Lambda-less AS" was devised, SW would still have a problem.

That I certainly grant But in all the AS I've seen Lambda plays an essential role. Notably in the work of Reuter and Percacci and their co-authors that has been responsible ever since 1998 for getting people to take AS seriously. That's why I regard the result Hamber and Toriumi (we really should get the spelling of her name consistently right) as potentially damaging to AS itself and to any minimalist scenario that depends on it.

======================
EDIT: Finbar just called my attention to a paper of Astrid Eichhorn where she gives an AS treatment to UNIMODULAR gravity---a modification of Einstein GR in which Lambda plays a reduced role. This could give Shaposhnikov a way to work around the problem!

http://arxiv.org/abs/1301.0879
On unimodular quantum gravity
Astrid Eichhorn
(Submitted on 5 Jan 2013)
Unimodular gravity is classically equivalent to standard Einstein gravity, but differs when it comes to the quantum theory: The conformal factor is non-dynamical, and the gauge symmetry consists of transverse diffeomorphisms only. Furthermore, the cosmological constant is not renormalized. Thus the quantum theory is distinct from a quantization of standard Einstein gravity. Here we show that within a truncation of the full Renormalization Group flow of unimodular quantum gravity, there is a non-trivial ultraviolet-attractive fixed point, yielding a UV completion for unimodular gravity. We discuss important differences to the standard asymptotic-safety scenario for gravity, and provide further evidence for this scenario by investigating a new form of the gauge-fixing and ghost sector.
10 pages, 1 figure

 

[mitchell porter]

Just for reference, here are the diverse approaches to obtaining a Higgs mass from Planck-scale boundary conditions, listed by Klinkhamer (see comment #77 in this thread).

[3] C.D. Froggatt and H.B. Nielsen, “Standard model criticality prediction: Top mass 173 ± 5 GeV and Higgs mass 135 ± 9 GeV,” Phys. Lett. B 368, 96 (1996)

[4] K.A. Meissner and H. Nicolai, “Conformal symmetry and the Standard Model,” Phys. Lett. B 648, 312 (2007)

[5] M. Shaposhnikov and C. Wetterich, “Asymptotic safety of gravity and the Higgs boson mass,” Phys. Lett. B 683, 196 (2010)

[6] M. Holthausen, K.S. Lim, and M. Lindner, “Planck scale boundary conditions and the Higgs mass,” JHEP 1202, 037 (2012)

 

[marcus]

It's good there are diverse approaches, alternative to depending on standard Asymptotic Safe gravity. I remember the Meissner Nicolai approach from Nicolai's presentation in 2009 at the Planck Scale conference. No dependence on Reuter AS. It continues to be, for me, the kind of archtypical minimalist approach. But you undoubtedly have thought more about this and may have a different idea of how they stack up.

Just for reference, here are the diverse approaches to obtaining a Higgs mass from Planck-scale boundary conditions, listed by Klinkhamer (see comment #77 in this thread).

[3] C.D. Froggatt and H.B. Nielsen, “Standard model criticality prediction: Top mass 173 ± 5 GeV and Higgs mass 135 ± 9 GeV,” Phys. Lett. B 368, 96 (1996)

[4] K.A. Meissner and H. Nicolai, “Conformal symmetry and the Standard Model,” Phys. Lett. B 648, 312 (2007)

[5] M. Shaposhnikov and C. Wetterich, “Asymptotic safety of gravity and the Higgs boson mass,” Phys. Lett. B 683, 196 (2010)

[6] M. Holthausen, K.S. Lim, and M. Lindner, "1112.2415" JHEP 1202, 037 (2012)

 

[mitchell porter]

The conformal SM is the coolest idea in that list and it's now a working hypothesis for me. The AS prediction managed to get the correct value of the Higgs mass so there may be something deeply right about their equations, even if AS itself is wrong. Holthausen et al only concerns itself with RG flow calculations and not with the Planck-scale mechanism, and Froggatt & Nielsen is a whole other approach whose merits I can't judge (but it's the oldest paper and Wetterich is in the acknowledgments).

But the basic idea could be true and the true mechanism not yet discovered. Klinkhamer tries to get the Planck-scale boundary conditions from wormholes! And Froggatt & Nielsen speculate about gravitational nonlocality - see the end of their page 9. So AS and the CSM have special merits, but the answer could also be None Of The Above.

 

[marcus]

The conformal SM is the coolest idea in that list and it's now a working hypothesis for me. ... AS and the CSM have special merits, but the answer could also be None Of The Above.

About the Conformal Standard Model (CSM), which also looks to me like the coolest idea of those four minimalist proposals (!), I want to remind anyone new to the thread that Meissner and Nicolai just recently posted a new CSM paper. They aren't letting the idea drop.

http://arxiv.org/abs/1208.5653
A narrow scalar resonance at 325 GeV?
Krzysztof A. Meissner, Hermann Nicolai
(Submitted on 28 Aug 2012, last revised 20 Sep 2012)
We propose to identify the excess of events with four charged leptons at E ≈ 325 GeV seen by the CDF and CMS Collaborations with a new 'sterile' scalar particle characterized by a very narrow resonance of the same height and branching ratios as the Standard Model Higgs boson, as predicted in the framework of the so-called Conformal Standard Model.
4 pages, 2 figures. Phys.Lett. B718 (2013) 943-945

I'll also expand the reference to their 2007 CSM paper you gave in post #88:

http://arxiv.org/abs/hep-th/0612165
Conformal Symmetry and the Standard Model
Krzysztof A. Meissner, Hermann Nicolai
(Submitted on 15 Dec 2006, last revised 26 Mar 2007)
We re-examine the question of radiative symmetry breaking in the standard model in the presence of right-chiral neutrinos and a minimally enlarged scalar sector. We demonstrate that, with these extra ingredients, the hypothesis of classically unbroken conformal symmetry, besides naturally introducing and stabilizing a hierarchy, is compatible with all available data; in particular, there exists a set of parameters for which the model may remain viable even up to the Planck scale. The decay modes of the extra scalar field provide a unique signature of this model which can be tested at LHC.
13 pages, 6 figures. Phys. Lett. B 648, 312 (2007)

 

[mitchell porter]

I am peeved today, to see a flood of science journalism talking about "Higgs calculations show universe may end", with an anthropic tag-along saying "and maybe the Higgs mass was tuned so the universe would last just long enough to produce observers". There is a dismaying possibility that this new anthropic dogma will get most of the attention, even within physics, at the expense of attempts at causal explanation.

 

[atyy]

I am peeved today, to see a flood of science journalism talking about "Higgs calculations show universe may end", with an anthropic tag-along saying "and maybe the Higgs mass was tuned so the universe would last just long enough to produce observers". There is a dismaying possibility that this new anthropic dogma will get most of the attention, even within physics, at the expense of attempts at causal explanation.

It was worth it to hear in the comments that Mexico will outlast the universe, because the end of the universe will come at the speed of light, but in Mexico light is much slower, sometimes taking an infinite time to arrive after the switch has been flipped.

 

[typical guy]

I feel stupid every time I receive an answer to one of my questions but I continue to ask them anyway. So here goes:

1. Assume SOMEWHERE in the unobserved portion of the universe, a bubble forms (the new ground state discussed in this thread) and expands outwards at the speed of light. Will the bubble EVER reach us? In other words, the universe is expanding at an accelerating rate, possibly faster than c. If so then won't this bubble be constantly converting new space that's stretched?

2. Assuming that the universe would never be completely converted by the bubble, would other bubbles eventually form? A follow up, would these bubbles have the same exact ground state as one another and if not, what happens if they form close to one another and eventually collide?

3. Assuming that the universe is expanding too quickly for the bubble(s) to catch up with us, does that imply that previous higher energy states of the universe might be "laying around" somewhere expanding outwards so quickly that our spacetime cannot possibly eat it/them all away?

Thanks in advance and apologies if this has been asked before or if these questions seem stupid.

 

[mitchell porter]

typicalguy, you seem to have the right ideas - an instance of vacuum decay can't spread beyond the cosmological horizon of the point where it began, but any part of the universe that is in a false vacuum state is at risk of locally experiencing vacuum decay.

Other threads might be better for a general discussion of this issue (whether the Higgs field is in a false vacuum state, and the consequences if it is). If we discuss it further here, it should be specifically in the context of Higgs mass predictions like the one in the title.

 

[mitchell porter]

And there is something for SW fans to talk about here. In all our discussion we have hardly alluded to the fact that the SW prediction is on the boundary between stable vacuum and unstable vacuum. But it's not a coincidence; the vacuum instability occurs if the Higgs quartic coupling becomes negative at any scale, and the SW boundary condition is that the Higgs quartic coupling is zero at the Planck scale. So, it's right on the edge.

But I for one don't feel like I have a proper understanding of this. Is there some deep reason to expect that a quantum-gravitational mechanism for determining the Higgs mass would drive it to a metastable value?

 

[marcus]

typicalguy, you seem to have the right ideas - an instance of vacuum decay can't spread beyond the cosmological horizon of the point where it began, ...

typicalguy just for concreteness the distance to the horizon is currently around 15.7 or 15.8 billion ly.

I'm not sure such bubbles are able to form, but if they can, and one did, say 16 billion ly from us, today, then the effects could never reach us. for the reason you mentioned, accelerated expansion, out of causal range.

this calculator gives the past and future development of the cosmological event horizon (CEH):
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo6.html

The CEH is slated to gradually increase and converge to around 16.5 billion ly, as can be seen in the calculator's table output.

 

[Haelfix]

Whether the vacuum is stable, metastable or unstable has very little to do with details about quantum gravity, and almost everything to do with the exact value of the top quark mass and the mass of the Higgs. See figure 5

http://arxiv.org/pdf/1205.6497v1.pdf

Now, if you can find some unification proposal that links gravity to those two values (which I assure you everyone and their mother is trying to do right now), then be my guest, but right now it looks very much like its some sort of coincidence. I hate to use the A word, but well there's that too.

 

[mitchell porter]

Well, arivero likes to point out that the top yukawa is very close to 1. Though it is closest at low energies, if I am to believe Figure 7 (page 14) here. So all we need is a reason for the Higgs self-interaction to be zero in the far UV, some wacky UV/IR reason for the top yukawa to be almost 1 in the far IR, and we're done. :-)

 

[mitchell porter]

This paper, before it gets around to introducing its new model of BSM physics, actually states the case for a "desert" in some detail:

The standard model (SM) is extremely successful at predicting what we do not see - namely flavor changing neutral currents (FCNC), lepton family violation among charged leptons, proton decay or neutron oscillations, and (with the exception of the strong CP problem) large CP violating effects. These all follow from the fact that such processes require irrelevant operators in the SM and are therefore suppressed by the high energy scale associated with new heavy particles. By assuming a desert for many decades of energy above the electroweak scale, all of the above processes are strongly suppressed, providing a simple explanation for what we (don't) see...

There is tension in the SM, however, between the natural explanation of a desert for the absence of FCNC, lepton and baryon number violation, and CP violation on the one hand, and the fine tuning of the Higgs sector that comes with a desert on the other.

In other words: a desert is the natural explanation for why we don't observe many phenomena which otherwise ought to be possible; but then the Higgs appears to be finetuned... All the more reason, therefore, to take seriously those desert models which would provide a causal explanation of this finetuning.

 

[mitchell porter]

Via Peter Woit, a talk by Joseph Lykken reviewing a number of non-susy approaches to explaining the tunedness of the Higgs mass. (Woit also links to a more theoretical talk by Nathan Seiberg about the hierarchy problem, that is also worth reading.)

It seems that causal explanations of the tuned Higgs, like Shaposhnikov-Wetterich and Nicolai-Meissner, are beginning to be recognized as a distinct class of theory, alongside "unnatural" and/or anthropic finetuning (Arkani-Hamed) and new versions of SUSY which restore naturalness (numerous authors). This is heartening, and it's especially gratifying to see Lykken at the fore of this, since it was his soundbite about the metastability of the universe, and the flurry of media it generated, which prompted my dismay in comment #92.

In fact, Lykken not only reviews several possibilities, but he devotes the most attention to a model in which dark matter plays a role in a Nicolai-Meissner-like mechanism. That is, he combines "radiative electroweak symmetry breaking" - in which the destabilizing Mexican-hat self-interaction of the Higgs field (that is responsible for a ground state with a nonzero VEV, and thus for the Higgs mechanism) is induced by virtual effects - with high-energy boundary conditions that tune the resulting Higgs mass. In this model, the new particle which induces radiative EWSB is also the dark matter!

So not only are causal models of Higgs tuning beginning to be recognized, but they are being combined with BSM facts from elsewhere in physics. Perhaps this will even become a popular topic while we wait for the LHC to be switched on again...

edit: What would really be dramatic, is a model of a "causally tuned Higgs" which also explains the observation that the mass of the Higgs is half the sum of the Z, W+, and W- masses. Like the tuning of the Higgs mass, this isn't just something that was noticed after the discovery, it was actually used to predict the correct value. Unfortunately, the "theory" which produced that formula is nonsensical, so the formula really needs some other justification.

Also, like the Koide relation, it's a relation between low-energy masses which shouldn't have simple relations, because of renormalization group running. (This may be contrasted with theories like Shaposhnikov-Wetterich, where the low-energy Higgs mass acquires its value from a simple boundary condition at high energies.) So most physicists will dismiss it as numerology and a coincidence. But as Lykken says in his talk (slide 20), "dismissing striking features of the data as coincidence has historically not been a winning strategy..."

 

[the_pulp]

Look at this conference http://workshops.ift.uam-csic.es/WMH126/program.html at which Shaposhnikov participated and look in particular his pdf and video. It is more or less what he stated in his 2009 paper + some other papers that he wrote.

However, even though it sounds as the same conclusions, here he talks about a desirable mass of 129 Gev and not of 126 Gev, so here, the agreement with experiments (LHC) is not so good now. Do you know what changed in the estimation of this "optimal mass" between 2009 and 2013 that moved the number in 3 Gev?

 

[MTd2]

http://arxiv.org/abs/1205.2893v2

It seems 129+-6GeV.

There is a discussion about fit with a higgs cosmology here and the value of Higgs:

http://arxiv.org/abs/1311.4979