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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 [tex]m_H[/tex] can be predicted. For a positive gravity induced anomalous dimension [tex]A_\lambda>0[/tex] the running of the quartic scalar self interaction [tex]\lambda[/tex] at scales beyond the Planck mass is determined by a fixed point at zero. This results in [tex]m_H=m_{\rm min}=126[/tex] 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 [tex]A_\lambda <0[/tex] one finds [tex]m_H[/tex] in the interval [tex]m_{\rm min}< m_H < m_{\rm max}\simeq 174[/tex] GeV, now sensitive to [tex]A_\lambda[/tex] and other properties of the short distance running. The case [tex]A_\lambda>0[/tex] 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.

Theone other model in the same spiritthat Nicolai citedwas that of Shaposhnikov. The only other elegant minimalist way to extend standard model coverage up to 10^{16}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 wassomething 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.

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# Predict Higgs mass by AsymSafety: Shaposhnikov and Wetterich

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