Shaposhnikov Wetterich predicted 126 GeV Higgs in 2009

[marcus]

Hi Finbar, I've heard Reuter make that argument on several occasions. The lack of straightforward freedom from any prior geometry seems to bug him.

His argument is that you need a prior geometry to set things up, but it doesn't matter WHICH prior geometry you pick. You need something to get started, to define the betafunctions, to set up the RG flow etc. But then, if you believe his argument, you always get the same fixed point.

In a sense that should be satisfactory, but the whole thing is still a little iffy and nebulous.

What if you are dealing with a situation where GR has a singularity and there IS no metric to use as your prior metric. What if you are trying to study the very Early, or black holes etc.

Personally I'd like to see Asymptotic Safety as the RESULT of some more fundamental theory like Loop. I think AS will turn out to be extremely useful as an effective layer based on some deeper understanding of geometry.

 

[marcus]

Finbar, I'd be really interested to know your reaction to the new paper by Damien Easson and Yifu Cai.

It looks like we can dispense with the "inflaton" idea and get inflation just from the run-up of Lambda at high density. AS seems to have a conspiracy of running constants to ensure a bounce---G goes to zero and Lambda gets infinitely large.

A more fundamental theory would probably not have Lambda actually go to infinity, but that is a detail.

BTW Arizona State seems to have gathered some notable talent in cosmology e.g. Lawrence Krauss as well as Easson. Cai is one of the ASU postdocs. I think the Cai Easson paper is a gamechanger and it helps to put ASU on the map for me.

You can get it by googling "Cai Easson higgs cosmology" or even just "cai easson higgs"
http://arxiv.org/abs/1202.1285.

What I'm looking for is for LQG to provide fundamental support for Asym Safety which works around classical singularities where a naive Reuter version of AS might fail, and which can use AS as an effective way to model inflation, bounce, primordial BH evaporation and other things of interest.

 

[Finbar]

Hi Finbar, I've heard Reuter make that argument on several occasions. The lack of straightforward freedom from any prior geometry seems to bug him.

His argument is that you need a prior geometry to set things up, but it doesn't matter WHICH prior geometry you pick. You need something to get started, to define the betafunctions, to set up the RG flow etc. But then, if you believe his argument, you always get the same fixed point.

In a sense that should be satisfactory, but the whole thing is still a little iffy and nebulous.

What if you are dealing with a situation where GR has a singularity and there IS no metric to use as your prior metric. What if you are trying to study the very Early, or black holes etc.

Personally I'd like to see Asymptotic Safety as the RESULT of some more fundamental theory like Loop. I think AS will turn out to be extremely useful as an effective layer based on some deeper understanding of geometry.

You seem to be implying that the background field method is dodgy? It is a well established tool in QFT and I don't see any reason to question it.

AS says that there are no unphysical divergencies so such singularities should not be in the Hilbert space. On the other hand I see no reason to not include metrics with curvature singularities which are sufficiently weak.

 

[marcus]

How effective AS can be at modeling the "big bang" singularity or whatever replaces is is somewhat a matter of opinion. Here's what I mainly wanted to ask you about:
==quote post #32==
Finbar, I'd be really interested to know your reaction to the new paper by Damien Easson and Yifu Cai.

It looks like we can dispense with the "inflaton" idea and get inflation just from the run-up of Lambda at high density. AS seems to have a conspiracy of running constants to ensure a bounce---G goes to zero and Lambda gets infinitely large.

A more fundamental theory would probably not have Lambda actually go to infinity, but that is a detail.

BTW Arizona State seems to have gathered some notable talent in cosmology e.g. Lawrence Krauss as well as Easson. Cai is one of the ASU postdocs. I think the Cai Easson paper is a gamechanger and it helps to put ASU on the map for me.

You can get it by googling "Cai Easson higgs cosmology" or even just "cai easson higgs"
http://arxiv.org/abs/1202.1285.

What I'm looking for is for LQG to provide fundamental support for Asym Safety which works around classical singularities where a naive Reuter version of AS might fail, and which can use AS as an effective way to model inflation, bounce, primordial BH evaporation and other things of interest.
==endquote==

 

[marcus]

Safe gravity describes the Loop bounce (?)

Finbar, another point: you may have watched Steven Weinberg's invited talk at the Strings 2010 conference (in Texas that year) and recall that it was not about String but about Asym Safe gravity. He described his frustrations with trying to model the bang and inflation with AS.

It's a natural thing to try, given the growing recognition of early universe cosmology (euc) as an important arena for testing theories.

The very high energy density, high curvature, regime seems to be a Loop strong point, where it gets results. Being completely free of background geometry could be helping there.

So for any newcomers to the discussion I'll review the essential fact about Safe gravity:
the conjecture that the dimensionless forms of G and Λ run to finite numbers as the energy scale k → ∞.

But the dimensionless forms of the two couplings are g = k²G and λ = Λ/k².

That means as we go back to the alleged singularity, G as a physical quantity must go to zero and the physical Λ must grow without bound.

This is a clear recipe for a bounce.

Asymptotic Safe gravity is begging for a Loop basis.

 

[Finbar]

Personally I don't like the idea of the bounce. It may come out in some simple quantum cosmology setup but I think its due to there being to much simplicity in the model. The problem I see with the bounce is that it's a violation of the second law.


There is a long way to go in any theory of quantum gravity solving the problems of the early universe. A lot more research needs to be done before something like AS can get a grip on this.

 

[marcus]

... The problem I see with the bounce is that it's a violation of the second law. ...

I see you are focusing on (your) intuition about correctness, rather than on what the theories say.
What I wanted your reaction to is what I think is a significant overlap between Safe and Loop
(they could either turn out right or wrong descriptions of nature, that's secondary here).

I wonder if you have any thoughts on the observation that Safe seems to agree with Loop bounce---because going back in time you get G→0 and Λ→∞

============

As for your objection about entropy, for the law to apply the phase space must be continuously defined. I don't think you can even define the metric at the moment of the bounce, much less the gravitational entropy. So second law is moot.

 

[Finbar]

I see you are focusing on (your) intuition about correctness, rather than on what the theories say.
What I wanted your reaction to is what I think is a significant overlap between Safe and Loop
(they could either turn out right or wrong descriptions of nature, that's secondary here).

I wonder if you have any thoughts on the observation that Safe seems to agree with Loop bounce---because going back in time you get G→0 and Λ→∞

============

As for your objection about entropy, for the law to apply the phase space must be continuously defined. I don't think you can even define the metric at the moment of the bounce, much less the gravitational entropy. So second law is moot.

Actually I would say that the statement that you get G→0 and Λ→∞ is wrong. Its a meaningless statement to say G→n where n is a dimensionless number since G is dimensionful. Of coarse it is a subtle point when n=0 but I still think that it is a wrong statement and physically misleading.


Measured in meaningful units, i.e. the energy scale k which is being probed, both G and Λ are of order one close to the UV fixed point. So effects which are proportional to G cannot be neglected with respect to effects proportional to Λ at smaller distances.


So It is far from obvious whether there will be a bounce in AS. At least based on this reasoning.

 

[marcus]

I'll say the same thing but more carefully. I mean that the physical quantity Λ grows without bound, it becomes infinite *as a curvature* certainly not as a number (!) because it is not a number.
I did not mean what you thought I did, sorry. I just wrong Λ → ∞ as a shorthand to say that as a curvature term it gets infinitely large. You are quite correct to quibble about the language.

I'll repeat the simple explanation I gave earlier:

So for any newcomers to the discussion I'll review the essential fact about Safe gravity:
the conjecture that the dimensionless forms of G and Λ run to finite numbers as the energy scale k → ∞.

But the dimensionless forms of the two couplings are g = k²G and λ = Λ/k².

That means as we go back to the alleged singularity, G as a physical quantity must go to zero and the physical Λ must grow without bound.

This is a clear recipe for a bounce.

Asymptotic Safe gravity is begging for a Loop basis.

Finbar, the point I'm making is that in AS what goes to a finite number, like say 1.5 is the ratio of two physical quantities Λ /k² = λ → 1.5 (say )

For convenience we're using natural units where k can be interpreted as a wavenumber and k² as a curvature, so the ratio is dimensionless. So the limit in the UV with k growing without bound must have Λ grow without bound.

 

[marcus]

...So It is far from obvious whether there will be a bounce in AS. At least based on this reasoning.

It never occurred to me that there would be a bounce in AS. I certainly wouldn't say it is obvious! I don't think AS is sufficiently background independent so it is a partially lame theory which I don't suppose capable of resolving the cosmo singularity.

It may turn out that Loop can serve as a BASIS or vehicle to realize some AS insights. Because (by abuse of notation, of course they are not dimensionless numbers!) G→0 and Λ→∞.
That means what holds stuff together shrinks to nothing and what blows stuff apart gets huge. It is a recipe for a bounce. Loop can realize the bounce that AS suggests happens (but is too background dependent to be able to implement.)

That is why I speculate that Asym Safe gravity is begging to be put on a Loop basis.
And that part is clearly just a speculative guess.

Yesterday Frank Saueressig gave a superb talk on Asym Safe gravity. The video is here:
http://pirsa.org/12020088/
It can serve both as a clear introduction for newcomers and a report on some of the interesting things that have come up in recent AS research. Recommend anybody interested in AS to watch it.

 

[Finbar]

Marcus,

When you say that AS in gravity is not background independent what is it you are referring to?
AS safety is a scenario for a field theory with an UV fixed point. It doesn't pick out any specific background as playing a role. Where backgrounds appear is in the construction of tools in QFT to test AS. This happens in the RG approach. However lattice gravity is another way to test for AS and this doesn't use any backgrounds.

So I would conclude that there is nothing in the AS conjecture that requires a background.
When you say " I don't think AS is sufficiently background independent" really you refer to some of the tools used to test for AS. Indeed for the RG approach being able to calculate on an a totally arbitrary background is the biggest challenge. But I do view this as a technical challenge and not a conceptual one.


I think your speculation about a loop basis is interesting. Ultimately one would like to know which are the relevant i.e. IR repulsive operators for the UV fixed point. Perhaps a loop basis would shed some light on this.

 

[marcus]

... But I do view this as a technical challenge and not a conceptual one...

Reuter gave several talks addressing the conceptual challenge. As I recall 2007 at Morelia and 2009 at Perimeter. I could be misremembering which talks, I know he was concerned about it at the time, maybe it's been resolved since.

The point is what defines scale so that couplings can run. You seem to need a prior metric to give you an idea of scale so you can get set up in the first place. So Reuter had been challenged about the background independence of the theory and when I heard him talk about it he was using a prior metric to define scale and then arguing that the end result did not depend on which prior metric you choose to start with.
It was not clear that this argument really goes thru and gets you background independence, at least to me.

 

[Finbar]

Reuter gave several talks addressing the conceptual challenge. As I recall 2007 at Morelia and 2009 at Perimeter. I could be misremembering which talks, I know he was concerned about it at the time, maybe it's been resolved since.

The point is what defines scale so that couplings can run. You seem to need a prior metric to give you an idea of scale so you can get set up in the first place. So Reuter had been challenged about the background independence of the theory and when I heard him talk about it he was using a prior metric to define scale and then arguing that the end result did not depend on which prior metric you choose to start with.
It was not clear that this argument really goes thru and gets you background independence, at least to me.

If the beta functions are independent of the background then then they are background independent. It seems pretty clean cut to me. Once beta functions are explicitly shown to be independent of the background then you would have to agree that this is background independent. Technically it is very hard to do this because one has to evaluate traces in the RG equation without specifying the background. But I do not think there is any conceptual barrier to doing these calculations.

 

[atyy]

Maybe AS is background independent, which would be nice. But if it isn't, does that matter? As long as the non-Gaussian fixed point exists it'll be ok, isn't it?

BTW, why not a limit cycle?

 

[Finbar]

Maybe AS is background independent, which would be nice. But if it isn't, does that matter? As long as the non-Gaussian fixed point exists it'll be ok, isn't it?

BTW, why not a limit cycle?

If a specific background is used to look for fixed point say a sphere or an Einstein space then one cannot actually calculate the individual beta functions say for scalar curvature squared and Ricci squared. Thus you can not show whether the fixed point exists unless you keep the background arbitrary.

So you see there really is no choice in order to show AS you have to have background independence.

 

[marcus]

Thus you can not show whether the fixed point exists unless you keep the background arbitrary. ...

That is right and that is the kind of thing I was talking about when I mentioned Reuter struggling with this problem in 2007-2009. He raised the issue and made a big deal of it.
You have to show that the fixed point you get does not depend on the prior metric you start out with.

Now this can be done, I believe (although not every step was clear to me) in a NONSINGULAR case.
Where it could break, I think, is precisely in situations where Loop resolving a singularity.

So far AS has not been successful in resolving bang or hole singularities.
I was just reading a Cai Easson paper where they apply AS to BH and they get some results about low temp and slow evaporation of small BH which are similar to Loop results (Modesto) but, in fact, they do not cure the singularity. So it is very good, and parallels Loop, but it does not go all the way.

As long as you cannot handle classical singularities you do not have complete background independence.

 

[Max™]

Not sure if it's bad to bump this, but it was suggested by the similar threads link, and well, the prediction seems worth new consideration given the recent 125~ GeV boson announcement at the LHC.

 

[MTd2]

Philip fits with 126GeV with the most recent data! WOW!

http://blog.vixra.org/2012/07/04/higgs-live-vixra-combinations/

 

[mfb]

Given the large number of predictions, I would not interpret too much in an agreement. The collection has 5 predictions in the range 124-126 (and a similar density for lower and higher masses), all with different models.

Edit: They had another prediction of 150 GeV at the same time.

 

[marcus]

Not sure if it's bad to bump this, but it was suggested by the similar threads link, and well, the prediction seems worth new consideration given the recent 125~ GeV boson announcement at the LHC.

Philip fits with 126GeV with the most recent data! WOW!

http://blog.vixra.org/2012/07/04/higgs-live-vixra-combinations/

Shapo-Wetterich prediction was based on a certain premise about the Standard Model and about the way some parameters run. The experimental result confirming their prediction makes their PREMISE (that it was based on) kind of interesting. Maybe we should take a closer look at the key assumption they used.

Max thanks for reminding us of this.

Their assumption would, I think, have consequences for Quantum Gravity. So it is relevant to BtSM forum.
At first sight it seems to favor the Asymptotic Safety QG approach of people like Percacci and Reuter. But that is just at first sight and I wouldn't necessarily take it for granted.

 

[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.