Higgs stability-bound and fermionic dark matter

Higgs-portal interactions of fermionic dark matter -- in contrast to fermions coupled via Yukawa interactions -- can have a stabilizing effect on the standard-model Higgs potential. A non-perturbative renormalization-group analysis reveals that, similar to higher-order operators in the Higgs potential itself, the fermionic portal coupling can increase the metastability scale by only about one order of magnitude. Furthermore, this regime of very weakly coupled dark matter is in conflict with relic-density constraints. Conversely, fermionic dark matter with the right relic abundance requires either a low cutoff scale of the effective field theory or a strongly interacting scalar sector. This results in a triviality problem in the scalar sector which persists at the non-perturbative level. The corresponding breakdown of the effective field theory suggests a larger dark sector to be present not too far above the dark-fermion mass-scale.Comment: 12 pages; 3 figure

Top mass from asymptotic safety

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 $170\, \rm GeV$ 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 $M_\text{t,pole} \approx 171\, \rm GeV$.Comment: Matches version accepted in Phys. Lett. B; counting of degrees of freedom in Eq.(7) changed, resulting in M_t=171 GeV and M_h=132 GeV; conclusions unchange

Quantum-gravity predictions for the fine-structure constant

Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approached as the momentum scale is lowered in the transplanckian regime, leading to a uniquely predicted value of the gauge coupling at the Planck scale. The precise value of the predicted fine-structure constant depends on the matter content of the grand unified model. It is proportional to the gravitational fluctuation effects for which computational uncertainties remain to be settled.Comment: 4 pages plus references, 2 figure

From particle physics to black holes: The predictive power of asymptotic safety

At the Planck scale, matter, space, and time fluctuate collectively. This thesis explores the phenomenology of a suggested joint theory of quantum gravity and matter. The discovery of the Higgs boson has completed the Standard Model of particle physics, realizing a delicate balance of the measured masses and couplings for which the Higgs potential provides a strong hint for Planckian quantum scale symmetry. The latter could also tame gravitational and Abelian interactions and render both General Relativity and the Standard Model asymptotically safe. A pivotal weak-gravity mechanism could facilitate a gravitationally induced UV-completion of the Standard Model. Within this scenario, the asymptotic-safety paradigm potentially enhances the predictive power of the Standard Model. It could uniquely fix the Abelian gauge and various Yukawa couplings from first principles. We uncover mechanisms which could link the mass difference of top and bottom quark to their charge ratio, could dynamically favor small Dirac neutrino masses, and might allows for phenomenologically appealing transitions between different fixed points of the CKM-mixing matrix. In the absence of intermediate scales, those Planckian predictions are connected to the electroweak scale by Renormalization Group flows. This could permit testing quantum gravity at accessible energy scales. Thereupon, we generalize the paradigm of quantum scale symmetry and the associated enhanced predictivity to grand unification where it potentially restores the predictivity of the complicated chain of spontaneous symmetry breaking. Asymptotically safe quantum fluctuations could also resolve the singularity at the center of black holes. We obtain the shadow boundary for nonspinning and spinning regular black holes. In comparing to the shadow image obtained by the Event Horizon Telescope, we find that horizonless objects can not yet be excluded

Asymptotic safety in the dark

We explore the Renormalization Group flow of massive uncharged fermions -- a candidate for dark matter -- coupled to a scalar field through a Higgs portal. We find that fermionic fluctuations can lower the bound on the scalar mass that arises from vacuum stability. Further, we discuss that despite the perturbative nonrenormalizability of the model, it could be ultraviolet complete at an asymptotically safe fixed point. In our approximation, this simple model exhibits two mechanisms for asymptotic safety: a balance of fermionic and bosonic fluctuations generates a fixed point in the scalar self-interaction; asymptotic safety in the portal coupling is triggered through a balance of canonical scaling and quantum fluctuations. As a consequence of asymptotic safety in the dark sector, the low-energy value of the portal coupling could become a function of the dark fermion mass and the scalar mass, thereby reducing the viable parameter space of the model.Comment: 16 pages plus appendix; 5 figure