Mass Difference for Charged Quarks from Asymptotically Safe Quantum Gravity

Abstract

We propose a scenario to retrodict the top and bottom mass and the Abelian gauge coupling from first principles in a microscopic model including quantum gravity. In our approximation, antiscreening quantum-gravity fluctuations induce an asymptotically safe fixed point for the Abelian hypercharge leading to a uniquely fixed infrared value that is observationally viable for a particular choice of microscopic gravitational parameters. The unequal quantum numbers of the top and bottom quark lead to different fixed-point values for the top and bottom Yukawa under the impact of gauge and gravity fluctuations. This results in a dynamically generated mass difference between the two quarks. To work quantitatively, the preferred ratio of electric charges of bottom and top in our approximation lies in close vicinity to the Standard-Model value of Q b Qt = −1 2.

Dark matter meets quantum gravity

“…The hypercharge and the Yukawa couplings would not be compatible if the values for f g and f y in (22) and (10) were too small. This results in lower limits f g ≥ 9.8 · 10 −3 and f y ≥ 10 −4 , assuming only SM matter content [41]. These values can be achieved with non-perturbative computations, see, e.g., (6).…”

“…Importantly, f g is positive for all relevant values of the gravity couplings, see [66], which makes the contribution to the beta function negative. Typical values of f g are of the order O(10 −2 ) [41] and here we use f g ≤ 0.04. Gravity supports asymptotic freedom for non-abelian gauge theories and the gauge couplings run in the Gaußian fixed point g * = 0 [64,66].…”

“…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. Also, a retrodiction of the top mass [40] and the difference between the top and the bottom mass [41] were attempted. See also [42][43][44][45] for further works in this context.…”

Resolving Spacetime Singularities within Asymptotic Safety

“…By now, the Wetterich equation has proven its merits in statistical physics [25], non-equilibrium physics [26] and gauge theories [27]. Starting from the pioneering work [28], which introduced the functional renormalization group in the context of gravity, there is now solid evidence supporting the existence of a non-trivial renormalization group fixed point for four-dimensional gravity [11, and many gravity-matter systems potentially including the standard model of particle physics [13,[51][52][53][54][55][56][57][58][59][60][61][62]. In particular, the full momentum dependence of the gravitational propagators starting from Γ k given by the Einstein-Hilbert action has been studied in [63,64].…”

Asymptotic safety, the Higgs boson mass, and beyond the standard model physics

“…There are a few issues which require separate discussion. First of all, to obtain the running of the considered couplings one can solve the full Wetterich equation, see for example [21,[79][80][81]. While Wetterich equation is exact, however it is very difficult (or even impossible) to be solved, because one has to take into account all of the operators which coincide with the symmetries.…”