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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.
