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 . 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 . 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 . Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around ∼ 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.

Agravity up to infinite energy

“…(51). We do not know of any previous determinations of the RGE in (25) and (26). We do not show the RGE of the gauge couplings because they are not modified by the gravitational couplings (see the first paper in [41][42][43][44] and [4,45,46]).…”

“…The RGE are those of gauge-fixed conformal gravity (see Eqs. (24), (25) and (26)). Proceeding as in Appendix B, the RGE of the Higgs mass is…”

“…An unpleasant feature of the model is that the mixed quartic λ H S must be very small, in order to avoid inducing an unnaturally large contribution to the Higgs mass (M 2 h = λ H S s 2 , which appears in the potential as −M 2 h |H | 2 /2). References [4,6,7] showed that λ H S can be naturally small, despite being generated at loop level through gravity loops as A peculiar RG running behavior at a very large scale, such as 0 10 10 16 GeV, does not imply perturbative contributions to scalar masses of the same order, as long as no new physics nor vacuum expectation values nor condensates develop at that scale [25]. Non-perturbative ultra-Planckian contributions to the cosmological constant and the Planck mass from a f 0 ∼ 4π are forbidden by the global shift symmetry σ → σ + δσ .…”

“…The Quantum Field Theory (QFT) part can have this property. Realistic TeV-scale extensions of the Standard Model (SM) can be asymptotically free [23,24], and it is not known whether the SM itself can be asymptotically safe, in a non-perturbative regime [25]. The gravitational coupling f 2 is asymptotically free.…”

Is scale-invariance in gauge-Yukawa systems compatible with the graviton?

“…The corresponding models feature similar building blocks to the Standard Model. Thus, the asymptotic-safety paradigm could potentially play a role in beyond-Standard-Model physics at scales below the Planck scale [17,18], with possible consequences for phenomenological questions [19][20][21][22]. On the other hand, there are compelling hints for asymptotic safety of gravity without [23] and with [24] matter beyond the Planck scale, for reviews, see [25].…”