Predict Higgs mass by AsymSafety: Shaposhnikov and Wetterich

[marcus]

http://arxiv.org/abs/0912.0208
Asymptotic safety of gravity and the Higgs boson mass
Mikhail Shaposhnikov, Christof Wetterich
12 pages
(Submitted on 1 Dec 2009)
"There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson $$m_H$$ can be predicted. For a positive gravity induced anomalous dimension $$A_\lambda>0$$ the running of the quartic scalar self interaction $$\lambda$$ at scales beyond the Planck mass is determined by a fixed point at zero. This results in $$m_H=m_{\rm min}=126$$ GeV, with only a few GeV uncertainty. This prediction is independent of the details of the short distance running and holds for a wide class of extensions of the SM as well. For $$A_\lambda <0$$ one finds $$m_H$$ in the interval $$m_{\rm min}< m_H < m_{\rm max}\simeq 174$$ GeV, now sensitive to $$A_\lambda$$ and other properties of the short distance running. The case $$A_\lambda>0$$ is favored by explicit computations existing in the literature."

In my humble estimation, Shaposhnikov and Wetterich are big guns. It is interesting to see them working on the AsymSafe program, deducing consequences, elaborating, deriving testable predictions.
To give an idea of Shapo's standing: my pick for the best conference of 2009 was the Planck Scale meeting in early July. And the most interesting talk there was arguably the one by Hermann Nicolai where he presented the Nicolai Meissner model which makes LHC-testable predictions, is minimalist (no extra dimensions or other made-up complications), and goes all the way to Planck scale.
The one other model in the same spirit that Nicolai cited was that of Shaposhnikov. The only other elegant minimalist way to extend standard model coverage up to 10¹⁶ TeV.
I looked up the Shaposhnikov papers that Nicolai cited and I don't recall that AsymSafety played a part. So this is something new.

And about Wetterich, remember that Weinberg proposed AsymSafe gravity over 30 years ago but couldn't make it work and gave up, so it had to be revived by Martin Reuter some 20 years later, in 1998. And the key method that Reuter brought to it was something he got from Wetterich. Exact Renormalization Group Equation (ERGE). It was Wetterich's math technique that enabled Reuter to revive Weinberg's program.

So I have to pay attention when those two guys show up on the train. It is almost like when Weinberg himself got on board---with his July 2009 CERN talk.

 

[MTd2]

Marcus, you are overlooking the most important discovery in this paper. Up to now, it was thought that the value of the Top mass, according to the IR fixed point of the SM, was 233GeV, whereas only by the use of supersymmetry one could get the actual value in the infrared.

"The value of the fixed point is fairly precisely determined in the Standard Model, leading to a predicted top quark mass of 230 GeV. If there is more than one Higgs doublet, the value will be reduced by Higgs mixing angle effects. The observed top quark mass is slightly lower, about 171 GeV (see Top quark). In the minimal supersymmetric extension of the Standard Model (the MSSM), there are two Higgs doublets and the renormalization group equation for the top quark Yukawa coupling is slightly modified. This leads to a fixed point where the top mass is smaller, 170–200 GeV. Some theorists believe this is supporting evidence for the MSSM."

http://en.wikipedia.org/wiki/Infrared_fixed_point

 

[ensabah6]

Does Asym predict a single HIggs and nothing more?

 

[marcus]

MTd2,
so low energy supersymmetry is another thing that might not be needed! They seem to be able to get the SM top quark down into an experimentally comfortable range around 170 GeV, if they need to.
BTW although I think it's obvious to most of us, we should probably say explicitly that what you predict depends on the model of gravity+matter that you construct. Asymptotic Safety is only part of the basis, and by itself does not predict stuff about matter. Indeed, Asymptotic Safety is further evidence that string theory (and elaborate inventions like that) is probably unnecessary. But it doesn't do everything by itself. You still have to decide on a version of the SM to inhabit the AS geometry.

Accordingly, in this paper you can see Shapo and Wetterich making assumptions and adjusting numbers in their barebones version of SM, and then deriving results dependent on those assumptions.

Maybe I missed something but I didn't think they got a definite prediction of the top quark mass. I can see them working with it, and constraining it, based on various provisional assumptions. I will get a page reference later, have to go do something else now.

But the only reasonably firm thing I see them say is this 126 GeV figure for Higgs.
MTd2 maybe you can point me to where they say something definite about top quark?

I had to be involved with other stuff and just got back----I see on page 8, about 2/3 of the way down that it is easy for them, without SUSY, to have top quark = 171.3 GeV, the central experimental value. And so they just SET the top quark equal to that, and that is how they derive their 126 GeV for the Higgs. Their prediction for the Higgs seems to depend on what the top quark turns out to be.

 

[MTd2]

It doesn't matter what depends on what. The great thing it is that the Top mass is consistent with a Higgs mass within experimental bounds. Before that, one had to appeal to susy to make things fit. That's all.

One more interesting bit to this story. On this blog post

http://dorigo.wordpress.com/2008/06/11/massimo-passera-the-muon-anomaly-and-the-higgs-mass-part-ii/

Tommaso Dorigo was discussing about a way of correcting the discrepancy of 3.2 standard deviations between the SM and expirments of the anomalous magnetic momento f the muon. It seems that instead of trying new physics, it could be that the contribution of QCD to the fine structure constant could be wrong given that on low energies, QCD is non perturbative. Adjusting the contribution of QCD, should impose bounds to the Higgs mass. The optimum value for that is around 130GeV!

Here is the article on which Tommaso based his post:http://arxiv.org/abs/0804.1142
The muon g-2 and the bounds on the Higgs boson mass
M. Passera, W.J. Marciano, A. Sirlin
(Submitted on 8 Apr 2008 (v1), last revised 6 Jun 2008 (this version, v2))
After a brief review of the muon g-2 status, we analyze the possibility that the present discrepancy between experiment and the Standard Model (SM) prediction may be due to hypothetical errors in the determination of the hadronic leading-order contribution to the latter. In particular, we show how an increase of the hadro-production cross section in low-energy e^+e^- collisions could bridge the muon g-2 discrepancy, leading however to a decrease on the electroweak upper bound on M_H, the SM Higgs boson mass. That bound is currently M_H < ~ 150GeV (95%CL) based on the preliminary top quark mass M_t = 172.6(1.4)GeV and the recent determination \Delta \alpha_{\rm had}^{(5)}(M_Z) = 0.02768(22), while the direct-search lower bound is M_H > 114.4GeV (95%CL). By means of a detailed analysis we conclude that this solution of the muon g-2 discrepancy is unlikely in view of current experimental error estimates. However, if this turns out to be the solution, the 95%CL upper bound on M_H is reduced to about 130GeV which, in conjunction with the experimental lower bound, leaves a narrow window for the mass of this fundamental particle.

 

[marcus]

The main focus of this thread is on this Shaposhnikov Wetterich article, which predicts a Higgs mass in the range 126-174 GeV. The abstract was given in the initial post, but to refresh our memory I will copy it here. In the meantime, since this thread was started, the paper was published in Physics Letters B.
http://arxiv.org/abs/0912.0208
Asymptotic safety of gravity and the Higgs boson mass
Mikhail Shaposhnikov, Christof Wetterich
12 pages. Phys.Lett.B683:196-200,2010
(Submitted on 1 Dec 2009)
"There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson $$m_H$$ can be predicted. For a positive gravity induced anomalous dimension $$A_\lambda>0$$ the running of the quartic scalar self interaction $$\lambda$$ at scales beyond the Planck mass is determined by a fixed point at zero. This results in $$m_H=m_{\rm min}=126$$ GeV, with only a few GeV uncertainty. This prediction is independent of the details of the short distance running and holds for a wide class of extensions of the SM as well. For $$A_\lambda <0$$ one finds $$m_H$$ in the interval $$m_{\rm min}< m_H < m_{\rm max}\simeq 174$$ GeV, now sensitive to $$A_\lambda$$ and other properties of the short distance running. The case $$A_\lambda>0$$ is favored by explicit computations existing in the literature."

...about Wetterich, remember that Weinberg proposed AsymSafe gravity over 30 years ago but couldn't make it work and gave up, so it had to be revived by Martin Reuter some 20 years later, in 1998. And the key method that Reuter brought to it was something he got from Wetterich. Exact Renormalization Group Equation (ERGE). It was Wetterich's math technique that enabled Reuter to revive Weinberg's program...

Also (as MTd2 points out) Shaposhnikov gave a slide presentation based on this paper at a conference in June 2010.
http://quarks.inr.ac.ru/presentations/Shaposhnikov.pdf
AFAICS the slide talk is not in depth and does not offer any new results, although it does give graphics illustrating points in the paper.