Abstract
We discover that asymptotically safe quantum gravity could predict the top-quark mass. For a broad range of microscopic gravitational couplings, quantum gravity could provide an ultraviolet completion for the Standard Model by triggering asymptotic freedom in the gauge couplings and bottom Yukawa and asymptotic safety in the top-Yukawa and Higgs-quartic coupling. We find that in a part of this range, a difference of the top and bottom mass of approximately 170GeV is generated and the Higgs mass is determined in terms of the top mass. Assuming no new physics below the Planck scale, we construct explicit Renormalization Group trajectories for Standard Model and gravitational couplings which link the transplanckian regime to the electroweak scale and yield a top pole mass of Mt,pole≈171GeV.
Highlights
We discover that asymptotically safe quantum gravity could predict the top-quark mass
We explore a regime of asymptotically safe quantum gravity, in which a UV completion for the Standard Model (SM) is triggered
The following holds in a truncation of the Renormalization Group (RG) flow: All gauge couplings of the SM become asymptotically free under the impact of quantum gravity fluctuations [7, 8, 20, 21]
Summary
Astrid Eichhorn1, ∗ and Aaron Held1, † 1Institut fur Theoretische Physik, Universitat Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany. It is expected to break down, due to the triviality problem signaled by Landau poles in the Abelian hypercharge [3] and the Higgs-Yukawa sector [4] The resulting model would contain quantum gravity and all SM fields, be UV complete and have a higher predictive power than the SM, cf Fig. 1: In a specific range of microscopic gravitational couplings, the asymptotic safety scenario might predict the top mass in terms of the bottom mass, and generate a difference of ∼ 170 GeV between them. Asymptotic safety generalizes asymptotic freedom: The latter posits that a model evolves along a Renormalization Group (RG) trajectory which emanates from the free fixed point in the deep UV, whereas the former is based on a fixed point at finite values of the couplings Both settings have in common that their free parameters are the relevant couplings which parameterize the deviation of the model from the fixed point. The sizable value of the top Yukawa
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