Shaposhnikov Wetterich predicted 126 GeV Higgs in 2009

[marcus]

==quote post #2 of this thread==
In 2009 Shaposhnikov and Wetterich predicted that Higgs would be observed at 126 GeV based on the assumption of asymptotic safe gravity and that standard model couplings were asymptotically free. Their prediction of Higgs mass came in the same box with one that nature had no new physics between here and the Planck scale.

This is a startling conclusion. In other words, once electroweak symmetrybreaking is taken care of, the good old standard model behaves like a fundamental theory (not merely effective) and holds all the way to Planck. As a signature prediction they derive along with that the 126 GeV figure for Higgs mass.
http://arxiv.org/pdf/0912.0208
Asymptotic safety of gravity and the Higgs boson mass
Mikhail Shaposhnikov and Christof Wetterich
...
...
Thanks to Mitchell for reminding us of this this. Hermann Nicolai gave a talk in 2009 where he talked about this same "big desert" idea and referred to work by Shaposhnikov. It's a striking idea to say the least.

==endquote==

==quote Shaposhnikov and Wetterich conclusions paragraph==
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 m_H = m_min ≃ 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. Detecting the Higgs scalar with mass around 126 GeV at the LHC could give a strong hint for the absence of new physics influencing the running of the SM couplings between the Fermi and Planck/unification scales.
==endquote==

 

[marcus]

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.

I'm still wondering how Derek Wise's "field of observers" idea fits with this. (See post #1.)
He just posted a new paper on it, with co-author Steffen Gielen. It is on the MIP poll.
I don't think AsymSafety works at a basic level because it is not Background Independent (you need a scale in order for things to run with scale.)
But maybe AsymSafe QG works in the Derek Wise context.

Here is Derek's new paper:
http://arxiv.org/abs/1206.0658
Linking Covariant and Canonical General Relativity via Local Observers
Steffen Gielen, Derek K. Wise
(Submitted on 4 Jun 2012)
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables. The key is viewing dynamical fields from the perspective of a field of observers -- a unit timelike vector field that also transforms under local Lorentz transformations. On one hand, all fields are spacetime fields, covariant under spacetime symmeties. On the other, when the observer field is normal to a spatial foliation, the fields automatically fall into Hamiltonian form, recovering the Ashtekar formulation. We argue this provides a bridge between Ashtekar variables and covariant phase space methods. We also outline a framework where the 'space of observers' is fundamental, and spacetime geometry itself may be observer-dependent.
8 pages

 

[mitchell porter]

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?

 

[atyy]

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?

I think in AS, naturalness isn't an issue, since one has to be fine tuned to lie on the critical surface anyway.

 

[marcus]

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]

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]

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]

"Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models" by Estrada and Marcolli.

 

[marcus]

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]

"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]

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]

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]

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]

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]

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]

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:

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 m_H = m_min ≈ 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]

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]

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]

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]

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]

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.