Shaposhnikov Wetterich predicted 126 GeV Higgs in 2009


by marcus
Tags: 2009, higgs, predicted, shaposhnikov, wetterich
tom.stoer
tom.stoer is offline
#19
Feb8-12, 01:44 AM
Sci Advisor
P: 5,307
I think it's amazing that such an enormous work and resulting profound insights can perhaps (!) be traced back to a wrong assumption ;-) That does not necessarily mean that the reults are wrong, of course

It would be interesting to find a close relationship between AS and LQG.

I saw some recent results on AS applied to Holst action with different results as for Einstein-Hilbert. This is striking.

The cosmological constant is treated differently in both approaches; in LQG one tries to incorporate it already when defining the algebraic foundations as a q-deformation of SU(2); in AS it behaves as a standard running coupling 'constant'; these two ideas seem to be incompatible at a very fundamental level.
marcus
marcus is offline
#20
Feb8-12, 02:19 AM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
Quote Quote by tom.stoer View Post
...
The cosmological constant is treated differently in both approaches; in LQG one tries to incorporate it already when defining the algebraic foundations as a q-deformation of SU(2); in AS it behaves as a standard running coupling 'constant'; these two ideas seem to be incompatible at a very fundamental level.
It's 12 midnight here and I'm falling asleep. Have to sign off soon. In one paper I read the physical meaning of q has to do with the scale of angular resolution. I'm not sure that the fuzziness of angle measurement can't run. But you're probably right. I'll think about it in the morning. Have to get to bed.

==================
Next morning. Feeling more waked up. I assume that there are several ways to incorporate Lambda in LQG. A few papers have been written exploring the way using q-deformation. I'll keep an eye out for alternatives. Ashtekar recently posted a paper about positive Lambda in LQC (no mention of q-deformation, I haven't read enough of it to paraphrase or comment.)

I think LQG is a side issue in this thread, but to address your point:
Quote Quote by tom.stoer View Post
assume asymptotic safety + standard model is consistent and physically correct; then all the enormous work on LQG and other QG theories would be based on the fundamentally wrong assumption that GR cannot be quantized using standard QFT methods - and would be pointless.
I think the fundamental assumption is to take the backgroundless ("no prior geometry" JA Wheeler) character of GR seriously: to ask if and how you can build a quantum field theory without any prior geometry. And make it conservative/minimalist in a sense: just 4D, no boundary, no extra jazz.
I think it's a worthy quest, exciting so far, generating many new ideas.

There might be some way to make AsymSafe QG backgroundless---they may have already done this and I simply missed it. Or the universe might really have a preferred geometry so that GR is basically wrong. So then one should not even try for a quantum field theory with no prior geometry.
Haelfix
Haelfix is offline
#21
Feb8-12, 02:37 AM
Sci Advisor
P: 1,663
I would say it the opposite way actually. LQG requires the asymptotic safety program as a necessary condition in order for it to have any hope of being theoretically consistent. That is, unless there are new hitherto unknown objects in the theory that could unitarize the physics in some novel way.

Anyway, there has been really interesting exact work and solutions in 2+1 pure gravity recently by Maloney et al.
http://arxiv.org/abs/arXiv:1111.1987

The belief is that there might be a mathematically rigorous proof in principle of the AdS/CFT relation in 3 dimensions just around the corner.

What is really interesting imo (if I was a quantum gravity guy and/or interested in LQG), is that they have found a partition function (strictly speaking the Ising model) and a pure quantum theory that has no semiclassical limit!

Doesn't that ring a bell!
marcus
marcus is offline
#22
Feb8-12, 11:14 AM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
I don't want to lose the main thread here which is the possible relevance of the Shapo-Wetter scenario related to their 126 GeV Higgs prediction. Since we've turned a page, here's a reminder (post #16) that Cai Easson cite Shaposhnikov Wetterich in their new paper proposing a Higgs curvaton mechanism that would have generated the observed CMB fluctuations in the AsymSafe QG context.

http://arxiv.org/abs/1202.1285
Higgs Boson in RG running Inflationary Cosmology
Yi-Fu Cai, Damien A. Easson
(Submitted on 6 Feb 2012)
An intriguing hypothesis is that gravity may be non-perturbatively renormalizable via the notion of asymptotic safety. We show that the Higgs sector of the SM minimally coupled to asymptotically safe gravity can generate the observed near scale-invariant spectrum of the Cosmic Microwave Background through the curvaton mechanism. The resulting primordial power spectrum places an upper bound on the Higgs mass, which for canonical values of the curvaton parameters, is compatible with the recently released Large Hadron Collider data.
5 pages

Cai Easson's reference:
[14] M. Shaposhnikov and C. Wetterich, Phys. Lett. B 683, 196 (2010) [arXiv:0912.0208 [hep-th]]

==Cai Easson page 1==
...In this paper, we propose that the Higgs boson may play an important role in the early inflationary universe if the gravitational theory is asymptotically safe. In the frame of AS gravity, the gravitational constant G and cos- mological constant Λ are running along with the energy scale, and thus vary throughout the cosmological evolution. It has been argued that if there are no intermediate energy scales between the SM and AS scales, the mass of the Higgs boson is predicted to be mH = 126 GeV with only several GeV uncertainty [14]. We find a suitable inflationary solution can be obtained in a cosmological system which contains a Higgs boson and AS gravity, along the lines of [15]. In this model, there are effectively two scalar degrees of freedom, one being the adiabatic mode and the other being an iso-curvature mode. We find the corresponding perturbation theory leads to both the primordial power spectrum for the curvature perturbation and the entropy perturbation. When the cutoff scale runs lower than a critical value, inflation abruptly ends and the Higgs field can give rise to a reheating phase. During this phase, the fluctuations seeded by the Higgs field can be converted into the curvature perturbation through the curvaton mechanism [16, 17]. We derive a relation between the spectral index of the primordial power spectrum and the Higgs mass. We confront this relation with the latest cosmological observations and collider experiment data, and find they are consistent under a group of canonical values of curvaton parameters.
==endquote==

[15] Y. -F. Cai and D. A. Easson, Phys. Rev. D 84, 103502 (2011) [arXiv:1107.5815 [hep-th]].
That might be interesting:
http://arxiv.org/pdf/1107.5815.pdf
Jordan-Brans-Dicke variant of GR.

[16]D. H. Lyth and D. Wands, Phys. Lett. B 524, 5 (2002)
http://arxiv.org/abs/hep-ph/0110002
Generating the curvature perturbation without an inflaton
David H. Lyth, David Wands
(Submitted on 28 Sep 2001)
We present a mechanism for the origin of the large-scale curvature perturbation in our Universe by the late decay of a massive scalar field, the curvaton. The curvaton is light during a period of cosmological inflation, when it acquires a perturbation with an almost scale-invariant spectrum. This corresponds initially to an isocurvature density perturbation, which generates the curvature perturbation after inflation when the curvaton density becomes a significant fraction of the total. The isocurvature density perturbation disappears if the curvaton completely decays into thermalised radiation...
8 pages.
MTd2
MTd2 is offline
#23
Feb8-12, 11:30 AM
P: 1,923
So, inflation, according to this view, is very closely related to the electroweak force. Maybe some neutrinos are transported by some sort of inflation, which makes it warp drive?
marcus
marcus is offline
#24
Feb8-12, 05:47 PM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
Quote Quote by MTd2 View Post
So, inflation, according to this view, is very closely related to the electroweak force. Maybe some neutrinos are transported by some sort of inflation, which makes it warp drive?
I'm not sure what your reasoning is but I'll try to comment. The Higgs field is not DRIVING inflation in the Cai Easson picture. I suspect what drives inflation is simply Lambda because in AS Lambda(k) increases without bound as the scale k increases.

So you could say that a uniform classical "dark energy" (which is simply the cosmo constant) is what motivates inflation.

What that leaves unanswered is what causes fluctuations which we observe in CMB and which we think were the seeds of structure. the CMB has temperature fluctuations of about 1/1000 of one percent.

So many people prefer to believe in an "inflaton" field instead of simply RG large Lambda.

But that "inflaton" idea leads to elaborate fairy tales of eternal proliferating bubble universes.

So Cai Easson just say look you do not need an "inflaton field" to explain the fluctuations, the fluctuations are already explained just right by the Higgs field!
So then one can go back to the large running Lambda (natural for AS) to drive inflation.
tom.stoer
tom.stoer is offline
#25
Feb8-12, 05:59 PM
Sci Advisor
P: 5,307
Quote Quote by Haelfix View Post
I would say it the opposite way actually. LQG requires the asymptotic safety program as a necessary condition in order for it to have any hope of being theoretically consistent. That is, unless there are new hitherto unknown objects in the theory that could unitarize the physics in some novel way.
I still don't see why LQG should be inconsistent (due to missing degrees of freedom) b/c totally different approaches claim something like that.
marcus
marcus is offline
#26
Feb8-12, 06:06 PM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
Hi Tom, didn't see your post. This is clarification in case other people are reading the thread.
Just to be sure everybody understands in the basic AsymSafe picture that Shapo-Wetter are using, and also Cai Easson, the whole idea is that the dimensionless versions of G and Λ go to finite values as the skale k goes to infinity.
Think of k as momentum or wavenumber or as inverse length. Then k2 is inverse area.
Now Λ is a constant curvature quantity, an inverse area. So the dimensionless number λ = Λ/k2. This is what goes to a finite limit as k→∞ (say the AS people Reuter Percacci and friends). The only way this can happen is if the dimensionful cosmo constant Λ becomes huge as k increases.

So as you go back in time towards the start of expansion (whether it is a Loop cosmology bounce or whatever however caused it) the energy density gets very big and k increases and so Λ becomes huge, so it is responsible for inflation. No "inflaton".

Cai Easson are just working out details of where the matter came from and the fluctuations.
It is a natural extension of the AsymSafe story.

==========another topic===============
Tom, since you and Haelfix continue being interested in the relation of Loop to AS (even though it might not be exactly on topic) I should put in a pointer to Ashtekar about LQC with positive cosmo constant. It is NOT a q-deformation in this LQC treatment---it is just a constant which presumably could run as one desires in AsymSafe.
http://arxiv.org/abs/1112.0360
Positive cosmological constant in loop quantum cosmology
Tomasz Pawlowski, Abhay Ashtekar
(Submitted on 1 Dec 2011)
The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC. Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum evolution is...
36 pages

The two have certainly not been joined yet! And with Loop cosmo in present form seem to me temporarily at least a bad match. But perhaps not ultimately incompatible.
Haelfix
Haelfix is offline
#27
Feb8-12, 10:24 PM
Sci Advisor
P: 1,663
"I still don't see why LQG should be inconsistent (due to missing degrees of freedom) b/c totally different approaches claim something like that."

I didn't say that!

What we do know about unitarity in quantum gravity is a bit of a subtle story, and i'd be glad to explain (or rather point the way through the literature) a little some time in another thread. The problem is you really do need to sidetrack into toy models where we have exact or almost exact solutions (2+1gravity, AdS/CFT and string theory) to get some hold where people are coming from on this subject. In some sense, you can see where things go wrong by removing objects from the spectrum.

In particular, the physics of quantum black holes and what may or may not happen with high energy scattering essentially dictates that something very special seems necessary to rescue the tangible insights (like the area law) that we know from semiclassical gravity.

This is why the whole business about needing a UV completion or having some sort of special divergence structure (like AS) in the perturbation series is so paramount.

Of course this is subtle business to phrase exactly. Even in the QFT context, i'm sure you remember haggling about what one means exactly by tree level partial wave unitarity violation in field theories, and to what extent we can trust those types of results. Here, b/c of subtleties with horizons, the story is complicated tenfold.

Anyway some other time maybe!
Harv
Harv is offline
#28
Feb9-12, 07:28 PM
P: 9
Quote Quote by Haelfix View Post
What is really interesting imo (if I was a quantum gravity guy and/or interested in LQG), is that they have found a partition function (strictly speaking the Ising model) and a pure quantum theory that has no semiclassical limit!

Doesn't that ring a bell!

Ding Ding!
marcus
marcus is offline
#29
Feb9-12, 10:36 PM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
Quote Quote by Harv View Post
Ding Ding!
You Ding?

Lorentzian spinfoam propagator
Eugenio Bianchi, You Ding
(Submitted on 29 Sep 2011)
The two-point correlation function is calculated in the Lorentzian EPRL spinfoam model, and shown to match with the one in Regge calculus in a proper limit: large boundary spins, and small Barbero-Immirzi parameter, keeping the size of the quantum geometry finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.
13 pages
http://arxiv.org/abs/1109.6538
Finbar
Finbar is offline
#30
Feb12-12, 01:27 PM
P: 343
Quote Quote by marcus View Post

So far (to my knowledge) AS is not background indep, in any straightforward way at least, because if there is no scale then how can things run with scale? Reuter has tried to work around this problem at least since 2006, often referring to it and to possible solutions.

AS is background independent in a straightforward sense no specific background plays a prominent role. In LQG there is no background so it is background independent in a trivial sense. In AS there is a background but the running of the beta functions are independent of the background.


Now if a specific background is used, to make a calculation possible with current techniques, the result is that all the beta functions can not be distinguished. For example working on Einstein spaces one cannot tell between scalar curvature squared and Ricci squared.


So you see the only way to test AS properly such that we know the actual properties of the fixed point is to make no choice as of background.
marcus
marcus is offline
#31
Feb12-12, 02:35 PM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
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
marcus is offline
#32
Feb12-12, 02:44 PM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
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
Finbar is offline
#33
Feb12-12, 03:36 PM
P: 343
Quote Quote by marcus View Post
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
marcus is offline
#34
Feb12-12, 04:24 PM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
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
marcus is offline
#35
Feb12-12, 04:50 PM
Astronomy
Sci Advisor
PF Gold
marcus's Avatar
P: 22,798
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
Finbar is offline
#36
Feb12-12, 06:11 PM
P: 343
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.


Register to reply

Related Discussions
22 July rumor: Higgs at 144 GeV and anti-Higgs at 350 GeV (comment?) High Energy, Nuclear, Particle Physics 25
Asymptotic safety of gravity and the Higgs boson mass (Shaposhnikov - Quarks 2010) Beyond the Standard Model 2
Predict Higgs mass by AsymSafety: Shaposhnikov and Wetterich Beyond the Standard Model 5
Wetterich's derivation of QM from classical Beyond the Standard Model 8
Loll cites Shaposhnikov (unimodular -> inflation+accel.) Beyond the Standard Model 2