Asymptotic safety of gravity and the Higgs boson mass (0912.0208v2)

Abstract: 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.

• The paper demonstrates that gravitational corrections drive the Higgs self-coupling toward an ultraviolet fixed point, predicting a mass near 126 GeV.
• The analysis employs the Functional Renormalization Group Equation within the Einstein-Hilbert framework to assess gravity's non-perturbative behavior.
• The findings imply that integrating asymptotically safe gravity with the Standard Model could validate high-energy physics without requiring new physics below the Planck scale.

Asymptotic Safety of Gravity and the Higgs Boson Mass

The paper "Asymptotic Safety of Gravity and the Higgs Boson Mass" by Mikhail Shaposhnikov and Christof Wetterich discusses the intriguing possibility that gravity is asymptotically safe. The research suggests that the Standard Model (SM) of particle physics, when coupled with gravity, might be valid up to extremely high energies, potentially without the need for new physics beyond the Planck scale. This notion raises the question of whether the Higgs boson mass can be predicted under certain assumptions about the nature of gravitational contributions to the renormalization group flow of physical constants.

The primary focus is on the gravitational corrections to the running of the Higgs self-coupling constant, λ, and the implications this has for the Higgs boson mass. The authors posit a positive gravity-induced anomalous dimension (λ > 0), which leads to an ultraviolet fixed point at zero for the quartic scalar self-interaction beyond the Planck scale. This fixed point behavior provides the remarkable prediction of a Higgs boson mass of approximately 126 GeV, with minimal uncertainty. Notably, this prediction appears robust against a range of extensions to the Standard Model, highlighting the potentially universal nature of the result.

Shaposhnikov and Wetterich also explore the scenario where Aλ is negative. In such a case, the Higgs mass is expected to lie in a broader range, specifically between the minimum value of roughly 126 GeV and a maximum value of about 174 GeV. This scenario showcases an increased sensitivity to short-distance physics and the precise form of the anomalous gravitational contributions to the beta functions.

The research builds on the notion that gravity, though non-renormalizable by traditional perturbative means, might find a non-trivial fixed point in a non-perturbative setting, rendering it suitable for integration into a quantum framework up to the highest energy scales. Employing the Functional Renormalization Group Equation (FRGE), evidence for such a fixed point in the context of the Einstein-Hilbert truncation of gravity has been presented in previous studies. The implications of these findings suggest a profound shift in how we view the quantum behavior of gravity and its impact on fundamental constants within the Standard Model.

From the analysis, a further extension is proposed, suggesting that the Standard Model, complemented by asymptotically safe gravity, may act as a fundamental theory rather than merely an effective field theory at high energies. The authors assert that under certain conditions – namely, that all Standard Model couplings, except the Higgs self-coupling, are asymptotically free and λ is drawn towards an approximate fixed point at zero – the Higgs mass is predictably close to the lower bound of the infrared interval established by the model's dynamics. Such a prediction emphasizes the critical role of gravity's anomalous dimensions in potentially eliminating the need for new physics at scales between the electroweak and Planck regimes.

In conclusion, this paper challenges the traditional boundaries of our understanding of both gravity and the Standard Model, suggesting that insights from non-perturbative physics could hold the key to unlocking a clearer understanding of the universe's fundamental forces. For future research, a deeper examination of the signs and magnitudes of gravitational corrections and their implications for other fields and potentials within the Standard Model landscape may prove rewarding, particularly in the context of experimental verification at high-energy particle colliders like the LHC. The possibility that gravitational corrections could align with specific empirical results – such as a Higgs mass around 126 GeV – underscores the transformative potential of theoretical advances in this domain.