The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking

Abstract

We present a comprehensive non-perturbative study of the phase structure of the asymptotically safe Standard Model. The physics scales included range from the asymptotically safe trans-Planckian regime in the ultraviolet, the intermediate high-energy regime with electroweak symmetry breaking to strongly correlated QCD in the infrared. All flows are computed with a self-consistent functional renormalisation group approach, using a vertex expansion in the fluctuation fields. In particular, this approach takes care of all physical threshold effects and the respective decoupling of ultraviolet degrees of freedom. Standard Model and gravity couplings and masses are fixed by their experimental low energy values. Importantly, we accommodate for the difference between the top pole mass and its Euclidean analogue. Both, the correct mass determination and the threshold effects have a significant impact on the qualitative properties, and in particular on the stability properties of the specific ultraviolet-infrared trajectory with experimental Standard Model physics in the infrared. We show that in the present rather advanced approximation the matter part of the asymptotically safe Standard Model has the same number of relevant parameters as the Standard Model, and is asymptotically free. This result is based on the novel UV fixed point found in the present work: the fixed point Higgs potential is flat but has two relevant directions. These results and their analysis are accompanied by a thorough discussion of the systematic error of the present truncation, also important for systematic improvements.

41 pages, 19 figures. v3: summary of approximations and suggestions from referees v2: discussion of full eigenfunctions of fixed point solution added in Section V, typos corrected, citations added

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Cited by in corpus (12)

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• Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• Lectures in Quantum Gravity
• On the phase structure of extra-dimensional gauge theories with fermions
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Stabilizing dark matter with quantum scale symmetry
• The quantum criticality of the Standard Model and the hierarchy problem
• Indications against dynamical CPT symmetry restoration in quantum gravity
• Charting GLOBs in Asymptotically Safe Gravity
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory