Higgs mass naturalness and scale invariance in the ultraviolet

Abstract

It has been suggested that electroweak symmetry breaking in the Standard Model may be natural if the Standard Model merges into a conformal field theory (CFT) at short distances. In such a scenario the Higgs mass would be protected from quantum corrections by the scale invariance of the CFT. In order for the Standard Model to merge into a CFT at least one new ultraviolet (UV) scale is required at which the couplings turn over from their usual Standard Model running to the fixed point behavior. We argue that the Higgs mass is sensitive to such a turn-over scale even if there are no associated massive particles and the scale arises purely from dimensional transmutation. We demonstrate this sensitivity to the turnover scale explicitly in toy models. Thus if scale invariance is responsible for Higgs mass naturalness, then the transition to CFT dynamics must occur near the TeV scale with observable consequences at colliders. In addition, the UV fixed point theory in such a scenario must be interacting because logarithmic running near a free fixed point constitutes hard breaking of scale invariance and spoils the Higgs mass protection.

Very light dilaton and naturally light Higgs boson

“…This property is not spoiled under any radiative corrections from the UV physics of the Higgs sector with spontaneously broken scale-symmetry, because one can always compensate the radiative corrections by shifting the dilaton field, as we have shown in this appendix A.2. The constraint on the Higgs mass, studied in [23], therefore does not apply to our model that has light dilaton from the spontaneously broken scale-symmetry, noted also in [49].…”

“…The scale M defines the intrinsic scale of the UV theory such as the dynamical mass in eq. (4.8) or the scale of phase transitions in [23].…”

“…2 Being parameters of the low-energy effective theory, the Higgs mass M and the quartic coupling λ include all the ultraviolet contributions from the UV theory above the cutoff scale that are relevant at low energy. Especially the mass term includes the contributions from the massive modes in the UV theory or certain intrinsic scales of the UV sector such as the scale for the conformal phase transition in the case of conformal UV theories [23]. In the case of the composite Higgs model, that we will focus on later as a possible model that realizes our mechanism, the Higgs mass is protected by the shift symmetry and generated by the Higgs interactions with the standard model particles such as top quark or EW gauge bosons, the mass term in eq.…”

Cosmological Signatures of a UV-Conformal Standard Model

“…In that respect, the idea that nature may be exactly scale invariant at high energies (in the UV) [3] as an explanation for the lightness of the Higgs boson [4,5] has recently attracted renewed interest; see, e.g., [6][7][8][9] (exact UV scale invariance has also been widely discussed in the context of asymptotic safety, see [10] for a recent review). Scale invariance would have to be broken at some energy scale f c , above which all quantum corrections to m h would be forbidden by the symmetry.…”

“…Scale invariance would have to be broken at some energy scale f c , above which all quantum corrections to m h would be forbidden by the symmetry. The mass of the Higgs boson being sensitive to f c [6], this new scale should be of order of the TeV energy scale. However, it has been recently shown [9] that when the breaking of scale invariance originates in a hidden sector and is mediated to the SM sector via gauge interactions (in analogy to gauge mediation in the context of supersymmetry breaking theories), f c could be significantly higher.…”