Asymptotic safety of gravity and the Higgs-boson mass

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 λ > 0 the running of the quartic scalar self interaction λ at scales beyond the Planck mass is determined by a fixed point at zero. This results in m H = m 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 λ < 0 one finds m H in the interval m min < m H < m max ≃ 174 GeV, now sensitive to A λ and other properties of the short distance running. The case A λ > 0 is favored by explicit computations existing in the literature. The "flowing action" or "effective average action" Γ k includes all quantum fluctuations with momenta larger than an infrared cutoff scale. For k → ∞ no fluctuations are included and Γ k→∞ coincides with the classical or microscopic action, while for k → 0 the flowing action includes all quantum fluctuations and becomes the generating functional of the one-particle irreducible Green's functions. The scale dependence of Γ k obeys an exact functional renormalization group equation [4]. It is of a simple one loop type, but nevertheless can be solved only approximately by suitable non-perturbative truncations of its most general functional form. From the studies of the functional renormalization group for Γ k one infers a characteristic scale dependence of the gravitational constant or Planck mass,where M P = (8πG N ) −1/2 = 2.4 × 10 18 GeV is the low energy Planck mass, and ξ 0 is a pure number, the exact

Dark matter meets quantum gravity

“…The predictive quality of the quartic scalar coupling [39] stems from the fact that it is UV repulsive at this (almost) Gaußian fixed point [46,47]. This entails that only one trajectory leads to the fixed point and the coupling value is fully determined at the Planck scale.…”

“…The first prediction of asymptotically safe quantum gravity was the Higgs boson mass [39]: asymptotic safety predicts that the quartic scalar coupling is roughly vanishing at the Plank scale. This yields a Higgs boson mass in the range from roughly 126 to 136 GeV, depending for instance on the value of the top mass.…”

Systematic analysis of radiative symmetry breaking in models with extended scalar sector

“…Looking for a concept of conformal invariance not present in a fundamental theory, the existence of a UV fixed point near M Pl based on inclusion of gravity was discussed in ref. [14] and related to the concept of "asymptotic safety", see e.g. refs.…”

“…In this case the tree-level potential is comparable to the one-loop contribution. 14 The scalar contributions to V (1) should be dropped, but apart from that no further simplifications occur. 15 Nonetheless, with this approximation the SM and SU(2) X one-loop contributions to the effective potential decouple (the former depends only on h and the latter only on ϕ) and the stationary point equations, eqs.…”

Alternative flow equation for the functional renormalization group

“…Ref. [17]), and to derive the beta functions and identify the fixed points of various interacting quantum field theories, notably in the context of the on-going asymptotic safety program of quantum gravity [18][19][20][21][22] (for reviews, see Refs. [23][24][25][26]), as initiated by Weinberg [27].…”