Hamber-Tomiuri vs Shaposhnikov-Wetterich?

  • Thread starter mitchell porter
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In summary: There seem to be two problems with the above approach: first, Reuter's solution of the resulting renormalization group equation for the two couplings G(k) and λ(k) is truncated to the Einstein and cosmological terms, a procedure which is more or less equivalent to the derivative expansion discussed previously. A nontrivial fixed point in both couplings (G∗,λ∗) is then found in four dimensions, generally with complex relevant eigenvalues ν−1, with some dependence on the gauge parameters...The first of those references - "Nonperturbative Evolution Equation for Quantum Gravity" by Reuter - also appears in Shaposhnikov-Wetterich as
  • #1
mitchell porter
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Marcus has suggested that "Inconsistencies from a Running Cosmological Constant" (Hamber & Tomiuri; PF thread) may cause problems for "Asymptotic safety of gravity and the Higgs boson mass" (Shaposhnikov & Wetterich; PF thread), because the latter relies on asymptotic safety, and asymptotic safety (apparently) assumes a running cosmological constant.

From my perspective, SW's idea is of broader interest than asymptotic safety (i.e. it might be derivable from some other assumption), and also I don't know much about asymptotic safety. And Hamber-Tomiuri don't mention asymptotic safety, and Shaposhnikov-Wetterich don't mention the cosmological constant. So we are dealing with ideas that have a life apart from each other.

But they do have an overlap, and it would be educational to see that there really is a contradiction, or even just to see what Hamber-Toriumi's argument looks like, applied specifically to Shaposhnikov-Wetterich's scenario.

So I propose that (at least to begin with) this thread should focus specifically on the theory defined by the Neutrino Minimal Standard Model with asymptotically safe quantum gravity. We should try to understand whether and why the cosmological constant runs in that theory, and we should try to understand Hamber-Toriumi's argument as it would be applied in the context of that theory. (Or theories, if there is more than one way to define asymptotically safe quantum gravity.)
 
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  • #2
mitchell porter said:
Marcus has suggested that "Inconsistencies from a Running Cosmological Constant" (Hamber & Tomiuri; PF thread) may cause problems for "Asymptotic safety of gravity and the Higgs boson mass"... And Hamber-Tomiuri don't mention asymptotic safety, and Shaposhnikov-Wetterich don't mention the cosmological constant. So we are dealing with ideas that have a life apart from each other.

But they do have an overlap,...

See bottom of page 29 of Hamber Tomiuri. The reference to Reuter's work [references 25, 26] is rather oblique
==quote==
The solution of the resulting renormalization group equation for the two couplings G(k) and λ(k) is then truncated to
[equation 107 inserted here]
the Einstein and cosmological terms, a procedure which is more or less equivalent to the derivative expansion discussed previously. A nontrivial fixed point in both couplings (G∗,λ∗) is then found in four dimensions, generally with complex relevant eigenvalues ν−1, with some dependence on the gauge parameters [26].
There seem to be two problems with the above approach...
==endquote==
Some Asymptotic Safety QG papers cited by Hamber Tomiuri.
[25] M. Reuter, Phys. Rev. D 57, 971 (1998);
M. Reuter and H. Weyer, Gen. Relativ. Gravit. 41, 983 (2009);
E. Manrique, M. Reuter and F. Saueressig, Annals Phys. 326, 463 (2011), and references therein.
[26] O. Lauscher and M. Reuter, Class. Quant. Grav. 19 483 (2002).
[27] D. F. Litim, Phys. Rev. Lett. 92 201301 (2004); P. Fischer and D. F. Litim, Phys. Lett. B 638, 497 (2006).
 
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  • #3
The first of those references - "Nonperturbative Evolution Equation for Quantum Gravity" by Reuter - also appears in Shaposhnikov-Wetterich as reference 5 (their A.S. references are items 1 to 10 in their bibliography). So clearly this paper by Reuter is the "ur-text" where we can seek some common ground.

As you say, the reference to Reuter in Hamber-Tomiuri is oblique. So the way to proceed is as follows: use Reuter to place the SW argument in its full AS context, then look at that through the eyes of HT.

The big picture is that we have some theory - nuMSM + Einstein gravity - which can be formally defined by a lagrangian. But then to get anything out of it we have to make assumptions, approximations, employ ansatze. The SW argument examines the running of various quantities under a particular ansatz. We should want to see how the c.c. behaves under that ansatz too, and then try out the HT critique.
 
  • #4


Looking over more recent papers, Shaposhnikov seems to be the main standard-bearer (rather than Wetterich). Of the two he seems more involved with developing vMSM ideas. Just my subjective impression. After that 2009 SW paper the followup has been been by Shaposhnikov collaborating with others, or so it seems.

Two recent Shapo vMSM papers we might focus on and assess their dependence on AS gravity, cc running in particular:

http://arxiv.org/abs/1301.5516 (this has no dependence on Asymptotic Safety, I think)

http://arxiv.org/abs/1205.2893 (this seems to involve AS, with cc running, but Hamber might be wrong)
 
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  • #5
I have a slightly better grasp on this now. Percacci's asymptotic safety FAQ was useful. A quick summary (not 100% reliable, but this is what I've gleaned from the papers):

Ordinary perturbative quantum gravity contains infinitely many undetermined couplings, the coefficients of terms of arbitrarily high order. Asymptotic safety posits that, because of a fixed point in the RG flow, only finitely many of these parameters need to be specified, rendering the theory predictive. These quantities will include Newton's constant, the cosmological constant, and presumably some assortment of higher-order couplings.

Shaposhnikov and Wetterich posit that the standard model plus gravity is asymptotically safe, but the only gravitational parameter they employ is Newton's constant, which controls the magnitude of the gravitational contributions to the beta functions (RG behavior) of the gauge couplings, top quark yukawa coupling, and Higgs self-coupling. The Higgs mass prediction comes from a few extra assumptions about the sign and high-energy behavior of these quantities.

Hamber and Tomiuri examine quantum gravity through a variety of formalisms, and in each case conclude that the cosmological constant doesn't run. They do not explicitly use Wetterich's exact renormalization group equation (ERGE), which is used in asymptotic safety, but make a few comments on the A.S. program.

So there is considerable "logical distance" between the arguments of HT and the arguments of SW. Also, we need to remember that different theories, formalisms, and ansatze may give different results. Pure gravity in one dimension, and gravity+SM in another dimension, might have different RG properties, for specific mathematical reasons. A particular "result" may be an artefact of an approximation, going away when more detail is included. It's even possible that both sides (in the QG debate here) are wrong, that real gravity is not asymptotically safe and that the c.c. runs! As we try to resolve the "contradiction", we should bear in mind such possibilities.
 
  • #6


A bit off-topic: Shaposhnikov (as you might expect) was one of the more than 100 co-authors of a white paper about righthand neutrinos.
http://arxiv.org/abs/1204.5379
Light Sterile Neutrinos: A White Paper
I imagine that he and a lot of other people are excited by the recently revised WMAP9 report
http://arxiv.org/abs/1212.5226
Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, J. Dunkley, M. R. Nolta, M. Halpern, R. S. Hill, N. Odegard, L. Page, K. M. Smith, J. L. Weiland, B. Gold, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, E. Wollack, E. L. Wright
(Submitted on 20 Dec 2012 (v1), last revised 30 Jan 2013 (this version, v2))...
...
31 pages, 12 figures
Jester at Resonaances has a comment "How many neutrinos are in the sky?" that was picked up by Peter Woit. http://resonaances.blogspot.com/
http://resonaances.blogspot.com/2013/01/how-many-neutrinos-in-sky.html
It is suggested that the answer is 4, not 3.
__________________
 
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  • #7


mitchell porter said:
...
The big picture is that we have some theory - nuMSM + Einstein gravity - which can be formally defined by a lagrangian. But then to get anything out of it we have to make assumptions, approximations, employ ansatze. The SW argument examines the running of various quantities under a particular ansatz. We should want to see how the c.c. behaves under that ansatz too, and then try out the HT critique.

I think looking at the big picture of nuMSM + Einstein gravity is the right way.
Hamber Toriumi does cast doubt on AS, but it might be wrong, or it might not apply for some technical reason.

So that side of the nuMSM idea might still be OK, the business with AS gravity and the Higgs prediction. But still more exciting right now is the prospect of explaining Dark Matter, which has become more substantial with HINSHAW ET AL. WMAP9 finding that their socalled "Neff" ≈ 4 rather than around 3.
Neff is measured from the microwave background and is the effective number of non-interacting neutrino-like species.

===================
Some conflicting news. A "Pre-Planck cosmological parameters" paper appeared today featuring Neff = 3.24 ± .39 instead of the Neff = 3.84 ± .40 (from combined data sets) that one sees in the Hinshaw et al. "WMAP9" report I mentioned earlier.
See Erminia Calabrese et al. Cosmological Parameters from Pre-Planck CMB Measurements
http://arxiv.org/abs/1302.1841
 
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Related to Hamber-Tomiuri vs Shaposhnikov-Wetterich?

1. What is the Hamber-Tomiuri vs Shaposhnikov-Wetterich model?

The Hamber-Tomiuri vs Shaposhnikov-Wetterich model is a theoretical framework in particle physics that attempts to explain the origin of the mass of elementary particles. It is based on the concept of spontaneous symmetry breaking, which is the idea that the laws of physics are the same in all directions, but the universe exhibits a broken symmetry due to a hidden mechanism.

2. How does the Hamber-Tomiuri vs Shaposhnikov-Wetterich model differ from other models?

The main difference between the Hamber-Tomiuri vs Shaposhnikov-Wetterich model and other models is the use of the Wetterich equation, which describes the evolution of the effective potential of the Higgs field. This equation is used to calculate the Higgs mass and coupling constants, which are then compared to experimental data to test the validity of the model.

3. What are the implications of the Hamber-Tomiuri vs Shaposhnikov-Wetterich model?

If the Hamber-Tomiuri vs Shaposhnikov-Wetterich model is correct, it would provide a deeper understanding of the fundamental forces and particles in the universe. It would also explain the origin of mass and potentially lead to a unified theory of all the fundamental forces, including gravity.

4. How is the Hamber-Tomiuri vs Shaposhnikov-Wetterich model tested?

The Hamber-Tomiuri vs Shaposhnikov-Wetterich model is tested by comparing its predictions to experimental data, such as measurements of the Higgs mass and coupling constants. If the predictions match the data, it provides support for the model. Additionally, scientists can use computer simulations and mathematical calculations to further test the model's predictions.

5. What are the current challenges in the study of the Hamber-Tomiuri vs Shaposhnikov-Wetterich model?

One of the main challenges in studying the Hamber-Tomiuri vs Shaposhnikov-Wetterich model is the complexity and difficulty of the Wetterich equation, which involves high-dimensional integrals and is not easily solved analytically. This makes it challenging to make accurate predictions and test the model's validity. Additionally, the model may need to be modified or combined with other theories to fully explain all aspects of particle physics.

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