Naturalness of asymptotically safe Higgs

Abstract

We extend the list of theories featuring a rigorous interacting ultraviolet fixed point by constructing the first theory featuring a Higgs-like scalar with gauge, Yukawa and quartic interactions. We show that the theory enters a perturbative asymptotically safe regime at energies above a physical scale $\Lambda$. We determine the salient properties of the theory and use it as a concrete example to test whether scalars masses unavoidably receive quantum correction of order $\Lambda$. Having at our dispose a calculable model allowing us to precisely relate the IR and UV of the theory we demonstrate that the scalars can be lighter than $\Lambda$. Although we do not have an answer to whether the Standard Model hypercharge coupling growth towards a Landau pole at around $\Lambda \sim 10^{40}$ GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful, it might also offer an explanation for the unbearable lightness of the Higgs.

17 pages. v2: final version; extra argument in the conclusions makes obvious why our claims are correct

References in corpus (5)

• Conformal Window 2.0: The Large $N_f$ Safe Story
• Asymptotically Safe Grand Unification
• Precision check on triviality of phi^4 theory by a new simulation method
• The Conformal Constraint in Canonical Quantum Gravity
• Quantum Electrodynamics at Extremely Small Distances

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• Seeking leptoquarks in the $\mathbf{t}\bar{\mathbf{t}}$ plus missing energy channel at the high-luminosity LHC
• High scale boundary conditions with an additional complex singlet
• High Scale Boundary Conditions in Models with Two Higgs Doublets
• Radiative decays of a singlet scalar boson through vector-like quarks
• Leptoquarks in B-meson anomalies: simplified models and HL-LHC discovery prospects
• Two-Loop Renormalization Group Equations and Gauge Couplings Unification