Top mass from asymptotic safety

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 $170\, \rm GeV$ 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

Upper bound on the Abelian gauge coupling from asymptotic safety

“…These two sections are self-contained and can be read without section 3, which details the techniques underlying our calculation and provides an overview of our results. In the final section, section 5, we consider the possible implications of our result together with that in [1] for the perspective of a predictive UV completion of the Standard Model. We highlight the potential for the existence of a microscopic model including quantum gravity degrees of freedom and fixing several of the free parameters of the Standard Model.…”

“…The weakly-coupled gravity regime required by a quantitatively accurate prediction of the IR value of the hypercharge coupling, as well as the top mass [1] within our truncation, is simultaneously a regime where first extensions of the truncation show signs of stability: as gravity is weakly-coupled, all effects of induced couplings appear suppressed. Specifically, the effect of induced photon self-interactions on g Y appears to be negligible, as the inducing quantum-gravity effects are of course also suppressed at Λ 0.…”

“…Physically, marginal irrelevance means a growth of the coupling towards the ultraviolet. Asymptotically safe quantum gravity adds a contribution to the beta function of all matter couplings that is linear in the matter coupling [1,16,[33][34][35][36][37][38][39][40][41][42][43][44][45][46]. If the sign of the gravitational contribution is negative, a fundamental change is triggered in the high-energy behavior of the corresponding coupling: the UV-repulsive free fixed point is turned into a UV attractive fixed point.…”

“…As the fixed-point value of g Y depends on the UV value of the gravity couplings, each point in the G, Λ plane is mapped onto an IR value of g Y along the corresponding critical The structural similarity to the dependence of the IR value of the top mass on the microscopic gravity parameters [1] is due to a similar form of the beta functions, with the only difference being the numerical prefactor of the gravity contribution as well as the critical value of Λ, at which the critical exponent switches its sign and an interacting, predictive fixed point is induced. trajectory, cf.…”

“…For our quantitative analysis, we are particularly interested in the region Λ < 0, where a prediction of the top mass and Higgs mass from asymptotic safety might be possible [1,87,88]. It is a highly nontrivial result of our analysis, that the same region of the gravity parameter space in our truncation also allows a prediction of the IR value of the U(1) coupling which is in the vicinity of the experimentally observed value, cf.…”