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.
Highlights
√ The Large Hadron Collider (LHC) data at s = 13 TeV confirm the Standard Model (SM) and give strong bounds on supersymmetry, on composite Higgs and on other SM extensions that were put forward to tame the quadratically divergent corrections to the Higgs mass in a natural way
Physical corrections to the Higgs mass are small in the SM, and can remain small once it is extended to account for dark matter, neutrino masses [1], gravity, and inflation [2]
This is not interpreted as a large photon mass because it is presumed that some unknown physical cut-off regulates divergences while respecting gauge invariance, that forces the photon to be massless
Summary
Gravity itself could be described by small dimension-less parameters [2,3,4], such that it makes sense to extrapolate the SM RGE above the Planck scale In this context, one possibility is devising realistic weakscale extensions of the SM such that all gauge, Yukawa, and quartic couplings flow to zero at infinite energy [3, 4]. Litim and Sannino (LS) [19] presented the first fourdimensional example of a perturbative quantum field theory where all couplings that are small at low energy flow to a constant value at higher energy persisting up to infinite energy This model involves a gauge group SU(Nc) with large Nc, a neutral scalar S and vector-like charged fermions, with asymptotically safe Yukawa couplings and scalar quartics.
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