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Shaposhnikov Wetterich predicted 126 GeV Higgs in 2009

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marcus
#55
Jul19-12, 10:48 PM
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Quote Quote by mitchell porter View Post
Something we need to understand is how this prediction relates to the hierarchy problem. Arguably the resolution to the hierarchy problem is the next big issue now that the Higgs has shown up. Are Wetterich and Shaposhnikov claiming that asymptotic safety resolves it, or are they saying something less than that?
http://arxiv.org/abs/0901.0011
See the passage starting at the bottom of page 2:

==quote Shapo et al==
Most of the research in BSM physics carried out during the past few decades was devoted to solving the gauge hierarchy problem. Many different suggestions were proposed concerning how to achieve the “naturalness” of electroweak symmetry breaking. These propositions are based on supersymmetry, technicolor, and large extra dimensions, among other ideas. Finding a solution to the gauge hierarchy problem, coupled with the need to solve observational and other fine-tuning problems of the SM, is extremely challenging. Most of the approaches postulate the existence of new particles with masses above the electroweak scale (ranging from 102 GeV to 1015–1016 GeV). As a result, the proposed theories contain a plethora of (not yet observed) new particles and parameters.

In this review, we describe a conceptually different scenario for BSM physics and its consequences for astrophysics and cosmology in an attempt to address the BSM problems named above without introducing new energy scales (that is, in addition to the electroweak and the Planck scales). In such an approach, the hierarchy problem is shifted to the Planck scale, and there is no reason to believe that the field theoretical logic is still applicable to it.
Below we show (following Refs. [4, 5] and a number of subsequent works) that this goal may be achieved with a very simple extension of the SM. The only new particles, added to the SM Lagrangian are three gauge-singlet fermions (i.e., sterile neutrinos) with masses below the electroweak scale. Right-handed neutrinos are strongly motivated by the observation of neutrino flavor oscillations. In Section 2 we review neutrino oscillations and introduce the corresponding Lagrangian. We summarize the choice of parameters of the Neutrino Minimal Standard Model (νMSM) in Section 3. In Section 4, we present a νMSM cosmology. We discuss the restrictions from astrophysics, cosmology, and particle physics experiments, as well as future searches in Section 5. In Section 6, we conclude with a discussion of possible extensions of the νMSM and potential astrophysical applications of sterile neutrinos.
==endquote==
MTd2
#56
Jul20-12, 12:32 AM
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In that paper(p.9):

"For the SM model to be a consistent field theory all the way up to the Planck scale, the mass of the Higgs boson must lie in the interval 126 GeV < MH < 194 GeV"

So, it's hard to find out now if it is valid up to the plank scale or not.
marcus
#57
Jul20-12, 12:45 AM
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Quote Quote by MTd2 View Post
In that paper(p.9):

"For the SM model to be a consistent field theory all the way up to the Planck scale, the mass of the Higgs boson must lie in the interval 126 GeV < MH < 194 GeV"

So, it's hard to find out now if it is valid up to the plank scale or not.
That paper was BEFORE the paper where they applied the asymptotic safety idea!

Much of what they say here CARRIES OVER to the paper where they predicted Higgs mass of 126 Gev.
mitchell porter
#58
Aug27-12, 06:02 AM
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"Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models" by Estrada and Marcolli.
marcus
#59
Aug27-12, 09:31 AM
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Yes!
Just in case any reader hasn't seen this memorable snap of Matilde
http://www.its.caltech.edu/~matilde/

=========================
My remark in post#52 applies even more strongly now:

"I would urge anyone interested to go back and read posts #1 thru #16 of this thread.
Especially #9-#16 where you get comments from:
Mitchell Porter
Thomas Larsson
O. Willeke
MTd2
Atyy
and also there's that reference to the Cai-Easson paper using AsymSafety to explain inflation.

AsymSafety is a very powerful idea and what Shapo-Wetter did was combine it with the "Big Desert" hypothesis.
The idea that the Standard Model is adequate up to Planck Scale.
That it doesn't really have any problems it can't take care of on its own.
To the extent this is true, it would have consequences for QG."
================

About that snap, part of what makes it a memorable photograph are savvy details like
the red backs of the classroom chairs
the loose black chaplin suit and black hike boots
the sly faun grin
the white skin exposed below the elbow

She deserves to be right about the spectral standard model and m_H.
=================

Just for reference, here is Cham-Connes "Resilience" paper:
http://arxiv.org/abs/1208.1030
MTd2
#60
Aug27-12, 01:39 PM
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"Ella esta en el horizonte. Me acerco dos pasos, ella se aleja dos pasos. Camino
diez pasos y el horizonte se corre diez pasos mas alla. Por mucho que yo camine,
nunca la alcanzare. >Para que sirve la utopa? Para eso sirve: para caminar."

She is in the horizon. I get closer by two steps, she gets away by two steps. I walk ten steps and the horizon runs ten steps away. No matter how long I walk, I will never get to her. What is the purpose of the utopia? This is the purpose: to walk.
marcus
#61
Aug27-12, 03:00 PM
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Matilde is good with literary quotes and has a strong side-interest in languages. Last year at Caltech she taught a onedayaweek informal class in Sanskrit for Modern Physicists.

And the title page quote on her course material is a comically apt quote from Goethe's Faust:
"So soll ich denn mit saurem Schweiss, Euch lehren was ich selbst nicht weiss"

I reckon she shares some of Robert Oppenheimer's interests, one who was familiar with Classical Indian philosophy and poetry, and I would guess with Goethe's Faust as well.


"Thus shall I then with sour sweat, teach you what I myself know not."
MTd2
#62
Aug27-12, 03:06 PM
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Correct me if I am wrong, but it seems that paper says the constants converge to 0 at high energy, instead of a small triangle "convergence" of the usual standard model. So, with AS, there is no need for supersymmetry, fpr the purpose of convergence of coupling constants, is that it?
mitchell porter
#63
Aug27-12, 11:23 PM
P: 751
I'm still very confused about the sense in which asymptotically safe theories exist and make predictions. Often asymptotic safety is called a hypothesis about the behavior of a theory, which would mean that it's essentially a mathematical property that is either true or false for a given theory. But then we have these "predictions" somehow derived from asymptotic safety, which makes it sounds like a physical hypothesis. Is there some sort of ansatz, implied by asymptotic safety, which is the true basis for the predictions?
Finbar
#64
Aug29-12, 04:55 AM
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Quote Quote by mitchell porter View Post
I'm still very confused about the sense in which asymptotically safe theories exist and make predictions. Often asymptotic safety is called a hypothesis about the behavior of a theory, which would mean that it's essentially a mathematical property that is either true or false for a given theory. But then we have these "predictions" somehow derived from asymptotic safety, which makes it sounds like a physical hypothesis. Is there some sort of ansatz, implied by asymptotic safety, which is the true basis for the predictions?


Asymptotic safety is a generalisation of asymptotic freedom. Both are a statement about the existence of a UV fixed point with certain properties. The distinct properties of the fixed points in a given theory and the renormalisation group flow away from them into the IR is what gives rise to the physical properties of the theory.

For example the discovery that QCD is asymptotically free and becomes strongly coupled in the IR lead to predictions such that it was accepted as the right theory of the strong nuclear force.

In QCD there is a known antsatz i.e. the bare action which can be used to define the path integral on the lattice say. This is because the fixed point is gaussian so we know what the relevant operators are. In asymptotic safety things are not that easy because the fixed point occurs where the theory is strongly coupled. One must instead solve the RG equations to find the form of the action in the UV and know which operators are relevant. What is known is how couplings have to scale at a non-gaussian fixed point. They have to run as there mass dimension for example Newton's coupling has to run as G ~ k^(-2) in four dimensions as we take the cut-off k to infinity. Further predictions can be made based an calculations which include a certain class of operators e.g. R, R^2, C^2 etc. and derive the beta functions for each couplings. Also one can include matter fields coupled to gravity and see what effect it has on the running of the matter couplings.
tom.stoer
#65
Sep6-12, 05:20 AM
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AS theories are in principle nothing else but a generalization of asymptotic free theories. So one has to do two things: prove that a theory is AS i.e. identify the fixed point, and find the correct trajectory in coupling space on which a specific representant (describing our world) lives.

Once these two problems have been solved an AS theory will make predictions.

But there are many problems - and Finbar mentiones a few of them.

The major problem I see is how to restrict the infinite dimensional coupling space to a finite subspace w/o changing phyical predictions. Even for asymptotocally free theories it is not clear to me why it is allowed to neglect infinitely many irrelevant operators (it's clear that we can neglect finitly many). This problem is even more difficult with AS theories b/c in some sense we use a finite dimensional subspace to 'proof' that the theory is AS. The assumption is that using more couplings this property still holds. But why should a theory remain AS once we include infinitly many more couplings for gravity and SM?
mitchell porter
#66
Sep6-12, 07:50 AM
P: 751
All right, well, at some point I will try to understand this Higgs prediction from the top-down, AS perspective. But it's also interesting to understand the minimal version of the argument - that would be the penultimate stage in the deduction from AS, the last stage before we arrive at "126 GeV".

If we look at the very end of http://arxiv.org/abs/0912.0208, they say:
Quote Quote by Shaposhnikov & Wetterich
In conclusion, we discussed the possibility that the SM, supplemented by the asymptotically safe gravity plays the role of a fundamental, rather than effective field theory. We found that this may be the case if the gravity contributions to the running of the Yukawa and Higgs coupling have appropriate signs. The mass of the Higgs scalar is predicted mH = mmin ≈ 126 GeV with a few GeV uncertainty if all the couplings of the Standard Model, with the exception of the Higgs self-interaction λ, are asymptotically free, while λ is strongly attracted to an approximate fixed point λ = 0 (in the limit of vanishing Yukawa and gauge couplings) by the flow in the high energy regime. This can be achieved by a positive gravity induced anomalous dimension for the running of λ. A similar prediction remains valid for extensions of the SM as grand unified theories, provided the split between the unification and Planck-scales remains moderate and all relevant couplings are perturbatively small in the transition region.
mitchell porter
#67
Oct3-12, 10:33 PM
P: 751
Another avenue of investigation would be to look for middle ground between a minimal, A.S.-inspired argument, and SM extensions designed to make the Higgs mass "natural". For example, there are many new supersymmetric models being proposed, in which new particles modify the RG flow so that a 125 GeV Higgs doesn't require finetuning. For that matter, just looking at the corrections which matter in the MSSM, and then comparing that to Shaposhnikov-Wetterich models, should be instructive.

edit: Some work which seems important as a rival case study is the application of the "multiple point principle" (MPP) to the "two Higgs doublet model" (2HDM). In 2007 (see slide 16) this was employed to derive a Higgs-mass upper bound of 125 GeV. Like asymptotic safety, the MPP is a hypothesis about the high-energy properties of the theory. And interestingly, the 2HDM is conceptually between the SM (with its single Higgs) and the MSSM (which has an "up Higgs" and a "down Higgs"). So it really does seem that an A.S.-like hypothesis can be applied, even in the context of a MSSM-like theory.

On a different note, I also want to call attention to the use of hypergeometric functions in Estrada and Marcolli (#58), to describe exact solutions to their RG equations. This makes me wonder if you could construct a theory by assuming the form of the RG solutions. This is potentially relevant, not just to explaining the Higgs mass, but to explaining some of the other numerology of the SM, such as the various Koide-like relations being discussed in other threads. That is, one could posit various hypergeometric RG trajectories with embedded Koide relations, and then try to construct beta functions consistent with those trajectories, and finally a Lagrangian consistent with those beta functions.
mitchell porter
#68
Dec14-12, 01:59 AM
P: 751
Peter Woit has a post up, linking to a talk by Nima Arkani-Hamed on naturalness. Remember the problem is that the Higgs mass sets the approximate scale of all the fermion masses, it is very small compared to the GUT or Planck scales, and so there is an issue of finetuning; and Arkani-Hamed has been promoting the idea that, along with BSM physics like weak-scale SUSY that could render the Higgs mass natural after all, we should consider the possibility that it is finetuned, and ask ourselves what a physics in which all the finetuning was concentrated in one parameter (perhaps by anthropic considerations) would look like. (His answer is "split supersymmetry".)

I made a comment remarking how curious it is that Shaposhnikov-Wetterich receives so little attention, despite having presented a 126-GeV-Higgs scenario three years ago. The comment was deleted, which is annoying, because a lot of real physicists do read that blog. Perhaps the relevance to Arkani-Hamed's talk wasn't clear - the point being that here is one of the leading particle theorists discussing the ways in which the Higgs mass might be explained, and he doesn't even mention Shaposhnikov-Wetterich. One may reasonably ask why this option isn't even on his radar.
tom.stoer
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Dec14-12, 02:04 AM
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it seems to be more interesting, more attractive, cool, ... to speculate about 11-dim. theories, SUSY with >100 free parameters, ... instead of doing physics, unfortunately
marcus
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Dec14-12, 01:12 PM
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Quote Quote by mitchell porter View Post
Peter Woit has a post up,... http://www.math.columbia.edu/~woit/wordpress/?p=5416 ...

I made a comment remarking how curious it is that Shaposhnikov-Wetterich receives so little attention, despite having presented a 126-GeV-Higgs scenario three years ago. The comment was deleted, which is annoying,...
I know. Peter Woit's stance seems to require that he suppress discussion of any research line theorists might be pursuing instead of You-Know-Superwhat.

I think he takes exaggerated care not to be labeled as an advocate of any particular program--wanting to qualify (as I think he does) as an objective, disinterested critic.

It is annoying. His blog could be more of a part of the solution---and help the community see its way around the current impasse---rather than simply spotlighting the problem.
Haelfix
#71
Dec15-12, 12:11 AM
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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
#72
Dec15-12, 01:26 AM
P: 751
Hi Haelfix, glad to see you comment on this.
Quote Quote by Haelfix View Post
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.


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