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Shaposhnikov Wetterich predicted 126 GeV Higgs in 2009

  1. Dec 13, 2011 #1

    marcus

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    Let's try to see the S&W prediction in connection with Derek Wise's beautiful paper on Cartan gravity and symmetry breaking.

    http://arxiv.org/abs/1112.2390
    The geometric role of symmetry breaking in gravity
    Derek K. Wise
    (Submitted on 11 Dec 2011)
    In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry of the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.
    4 pages. Contribution written for proceedings of the conference "Loops 11" (Madrid, May 2011)
     
    Last edited: Dec 14, 2011
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  3. Dec 13, 2011 #2

    marcus

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    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

    ==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 mH = mmin126 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==

    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.
     
    Last edited: Dec 14, 2011
  4. Dec 13, 2011 #3

    marcus

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    Now what I'm wondering is if the Derek Wise paper can have any relevance. Does anyone see a possible connection? Off hand one would say not.

    But the Wise paper is, in my view, beautiful, deep, and revolutionary. By and large physicists have always used FLAT tangent spaces. Or more generally a VECTOR BUNDLE, a fiber bundle where the fiber is basically Euclidean. Wise generalizes from that and says they ought to allow curved fibers---homogeneous spaces, as in Cartan geometry.

    What happens when you try to do AsymSafe gravity in the context of Cartan geometry? And then what happens to Shapo&Wetterich's idea when you translate that into the context of Cartan geometry?

    I'll not try to answer these questions. I'll rely on the verdict of others. If there's nothing of interest here, so be it. If anyone thinks so, please let me know.
     
    Last edited: Dec 14, 2011
  5. Dec 15, 2011 #4
    A very interesting prediction, I do have a question though, marcus can you elaborate a bit on what you meant by: "Their prediction of Higgs mass came in the same box with one that nature had no new physics between here and the Planck scale. " Does that imply in some sense that as we go smaller in scales the laws remain the same? Thanks.
     
  6. Dec 15, 2011 #5

    marcus

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    Vikram I think you have read what they said correctly and understand it at least as well as I do. So I can only say "yes that is what it seems to mean."

    The laws remain the same, the coupling constants continue to run, and (in the scheme they are proposing) no new physics enters to affect the running.

    The figure of 126 GeV is a consequence of all that. So it can serve as a kind of test or experimental signature indicating that their scheme could be right. Or, if it turned out not to be 126, or close to that, then that would discredit/falsify their idea.
    ==========================

    One way to formally write down the "running" of constants with scale is to use the wavenumber or momentum scale "k", also thought of as reciprocal length. And let k→∞.
    that is like what you said: consider smaller and smaller length scale.
    And the "running" is just the gradual change in some of the constants g(k) in the theory which are allowed to vary with scale (e.g. according to "renormalization group flow equations")

    You may be familiar with all this but in case you are not:
    "asymptotic free" means that g(k) → 0 as k goes to infinity. this is characteristic of the interaction of quarks. They don't feel attraction for each other when very very close. They are "free" of influence from each other, in the limit as they get close. ("asymptotic" means "in the limit as k→∞)

    "asymptotic safe" means that g(k) → γ some finite number if you start from correct values of the coupling constants which can be determined at some scale by experimental measurement. You only have to determine a finite set of numbers by experiment, at accessible, and then the renormalization group equations will guide you home to the correct limiting values of the constants. That is what "safe" means.

    You can probably google "asymptotic safety" and find out more. Steven Weinberg got the idea of it around 1976-1979.

    Their scheme assumes that most SM couplings run but are "free", except (as they say) for the Higgs self-interaction λ. And they want gravity to be Einstein except that the basic constants in the Einstein equation G and Lambda should run, or more exactly their dimensionless versions should run, and be "safe". That is a version of gravity which has been extensively studied by Percacci (SISSA Trieste) and by Reuter (U. Mainz). You can google it. Weinberg has gotten interested in it again after some years of doing other stuff.

    It looks as though regular Einstein gravity might actually be asymptotic safe. But no one is completely sure about that. Still, IF it is and if what they say is right about the SM couplings, then on that basis they make TWO consequences:
    1. 126 GeV Higgs
    2. SM and Einstein gravity shall act like fundamental theories and work all the way to Planck scale (i.e. no new physics enters the picture to affect how the couplings run).

    I am just restating what I quoted in post #2, from

    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

    Their predictions are very bold and testable. They can be falsified if they are wrong. This, at least, is a virtue. Theory guys should try to only make theories that can be readily falsified if they are wrong. And Shaposhnikov Wetterich at least do this. (Many other theorists fail to obey this rule.)
     
  7. Dec 15, 2011 #6
    You remember my name, sweet! In any case, I remember reading something related. A paper showed that the idea of quantum foam having a widely different physics was actually wrong and in that paper the authors showed that the laws remain the same through plank scales. The 126 GeV prediction is still quite amazing to me. Also thanks for the explanation.
     
  8. Dec 15, 2011 #7
    How could there not be new physics? We still have to explain dark matter and dark energy.
     
  9. Dec 15, 2011 #8

    marcus

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    Shaposhnikov Wetterich do not say there will be no new discoveries in physics :biggrin: They are talking about an intervening scale between electroweak and planck that influences the running.
    Here is the quote again so we can read it carefully:

    A similar prediction remains valid for extensions of the SM [such] 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.​

    Regarding "dark matter" Shapo-Wetter's scheme seems robust and flexible enough for some sort of dark matter particle to show up and join the SM party. You'd have to ask them about it.

    As for "dark energy", more and more that looks simply like the cosmological constant and this constant runs (along with Newton G) in AsymSafe GR in a controlled way to finite values. I think there is no "dark energy" problem in Shapo-Wetter context, since they incorporate AsymSafe GR.
     
    Last edited: Dec 16, 2011
  10. Dec 16, 2011 #9
  11. Dec 16, 2011 #10

    marcus

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    Yes, thanks for pointing that out! In fact the νMSM (nu-minimal SM) is covered in a concise way in the 2009 paper by him and Wetterich. I should have mentioned that:

    ==quote Shaposhnikov Wetterich http://arxiv.org/abs/0912.0204 ==
    Within this setting a very economical description of all interactions in Nature may be possible. One can assume that there is no new physics associated with any intermediate energy scale (such as Grand Unified scale or low energy supersymmetry) between the weak scale and ktr. All confirmed observational signals in favor of physics beyond the Standard Model [such] as neutrino masses and oscillations, dark matter and dark energy, baryon asymmetry of the Universe and inflation can be associated with new physics below the electroweak scale, for reviews see [20, 21] and references therein. The minimal model – νMSM, contains, in addition to the SM particles, 3 relatively light singlet Majorana fermions and the dilaton. These fermions could be responsible for neutrino masses, dark matter and baryon asymmetry of the Universe. The dilaton may lead to dynamical dark energy [22, 23] and realizes spontaneously broken scale invariance which either emerges from the cosmological approach to a fixed point [22, 24] or is an exact quantum symmetry [25, 26]. Inflation can take place either due to the SM Higgs [27] or due to the asymptotically safe character of gravity [28]. Yet another part of new physics, related, for example, to the strong CP problem or to the flavor problem, may be associated with the Planck energy. In this Letter we show that this scenario leads to a prediction of the Higgs mass, which can be tested at the LHC...
    ==endquote==
     
  12. Dec 21, 2011 #11
    They say no new physics between the weak and Planck scales. There could still be new physics below the weak scale that went undetected because it interacts weakly.

    I am terribly rusty with this kind of calculation and I never learnt it properly anyway, so am not competent to judge its validity. It is a striking result though.

    There seems to be the consensus that 126 GeV is the border where the SM becomes inconsistent. I wonder if calcuation that leads to this result is isomorphic to the SW calcuation, with a different interpretation. After all, they use the same in-data (e.g. top mass)
     
  13. Jan 20, 2012 #12

    atyy

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    Motl links to Dimopoulous's talk at the IFT Inaugural conference, in which he discusses Shaposhnikov and Wetterich's prediction after 8 minutes from the start.
     
  14. Jan 22, 2012 #13

    MTd2

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    Besides a Higgs at 126+-2 GeV being an indirect evidence of QG, THE FIRST ONE, what other thing we should see to have more confidence that we are seeing AS?
     
  15. Jan 23, 2012 #14

    ohwilleke

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    There is a nice annotated bibliography on the asymptotic safety of gravity at http://www.percacci.it/roberto/physics/as/biblio.html. Experimental tests are suggested in the area of cosmological inflation.

    The discussion of fractal dimensions in the emergent dimensionality of loop quantum gravity is suggestive of the possibility that some slight fractional deviation from four dimensionality in an experiment sensitive to fractal dimensionality of space-time might be observable.

    Not really too the point but interesting and potentially practically relevant is this paper suggesting that some of the mathematical and calculation intractability of full fledged Einstein gravity may be due to our failure to discern that lots of problematic to calculate terms cancel out:

    Z. Bern, J.J. Carrasco, D. Forde, H. Ita, H. Johansson (2007)
    Unexpected Cancellations in Gravity Theories.
    Phys. Rev. D77, 025010
    arXiv:0707.1035 [hep-th]
    Presents evidence that pure Einstein theory may have unexpected cancellations.

    A paper by B.F.L. Ward addresses another topic that is one of the less discused but most fundamental theoretical inconsistencies between the Standard Model and GR:

    B.F.L. Ward (2004)
    Massive elementary particles and black holes.
    JCAP 0402, 011.
    arXiv:hep-ph/0312188
    Performs a resummation of perturbative series using the Yennie-Frautschi-Suura method and shows that point particles are not black holes as a consequence of quantum effects.

    And, for people who are worried about how to make dark energy work there are a series of papers along the lines of:

    F. Bauer and L. Schrempp (2008)
    Relaxing neutrino mass bounds by a running cosmological constant.
    JCAP 0804, 006
    arXiv:0711.0744 [astro-ph]

    The most recent exposition of the basic idea of the 2009 paper is found at:

    J.C.C. Felipe, L.C.T. Brito, M. Sampaio and M.C. Nemes (2011)
    Quantum gravitational contributions to the beta function of quantum electrodynamics.
    Phys. Lett. B700, 86-89 (2011)
    arXiv:1103.5824 [hep-th]
    A perturbative evaluation of the quadratic divergences due to gravity, emphasizing the source of ambiguities.

    Since the AS Gravity effects manifest via the beta functions of the Standard Model, it follows that sufficiently precise precision tests of those beta functions at sufficiently high energies ought to be able to discern divergences between the non-quantum gravity corrected versions and those that are quantum gravity corrected long before they have any macroscopic impact. I personally have always been concerned about the strong importance SUSY gives to making the coupling constants converge at a triple point at high energies when there might be something inaccurate about the beta functions at high energies and AS Gravity supplies just such a potential correction.

    Finally, for the fan club, PFs BSM favorite, had a paper on the subject shortly after it was proposed by Weinberg and a couple of his peers before going his own way with early LQG:

    Lee Smolin (1982)
    A fixed point for quantum gravity.
    Nucl. Phys. B 208, 439-466
    It was shown in this paper that a fixed point must exist in 4-d gravity in the leading order of a 1/N approximation.
     
    Last edited: Jan 23, 2012
  16. Feb 7, 2012 #15

    marcus

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    Ohwilleke, thanks for the links.

    Anyone following this might want to note some papers that came out today 7 Feb. For instance:
    https://cdsweb.cern.ch/record/1421964/files/hcomb.pdf [Broken]
    "An excess of events is observed around mH∼126 GeV with a local significance of 3.5 standard deviations (σ)"

    Taking account of look-elsewhere effect reduces the significance considerably
    https://cdsweb.cern.ch/record/1421948/files/hgg.pdf
    "..., the largest excess with respect to the background-only hypothesis in the mass range 110-150 GeV is observed at 126.5 GeV with a local significance of 2.9 standard deviations. The uncertainty on the mass position (±0.7 GeV) due to the imperfect knowledge of the photon energy scale has a small effect on the significance. When this uncertainty is taken into account using pseudo experiments, the significance is 2.8 standard deviations; this becomes 1.5 standard deviations when the look elsewhere effect [42] for the mass range 110-150 GeV is included."

    So it's interesting but still too early to draw conclusions.
     
    Last edited by a moderator: May 5, 2017
  17. Feb 7, 2012 #16

    marcus

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    As you might expect, 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.

    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 evolu- tion. 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.
     
    Last edited: Feb 7, 2012
  18. Feb 8, 2012 #17

    tom.stoer

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    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.
     
  19. Feb 8, 2012 #18

    marcus

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    Hi Tom!
    As you can imagine, I have heard that said many times, since I've been reporting AsymSafe research here since, I guess, 2004 or 2005.
    I'm not sure it has any meaning, except emotional, however.

    It may be that LQG is wrong whether or not AS is right. We just have to see.
    I suppose it could also be that LQG will eventually explain why gravity is asymptotically safe.
    Both could provide good approximations to nature in the appropriate circumstances.

    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.

    I'm an agnostic. I don't "pick winners" and as long as it's mathematically OK and not ruled out by observation I don't declare in advance that such and such is wrong. You claim to be certain that AS and LQG are incompatible? I don't claim to know that. Maybe they are, maybe not.

    What matters to me is that right now both research programs have energy, are going places, getting new ideas, involving people i respect.

    Reuter as I recall was one of the invited plenary speakers at the Loops 2005 conference. I remember being very impressed by his talk. Since then AS has not progressed as fast or drawn in as many researchers as I thought it would, but that's OK. On the other hand Loop has generally exceeded my expectations since then. Both programs remain very interesting. Perhaps you agree?
     
    Last edited: Feb 8, 2012
  20. Feb 8, 2012 #19

    tom.stoer

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    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.
     
  21. Feb 8, 2012 #20

    marcus

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    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:
    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.
     
    Last edited: Feb 8, 2012
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