Higgs mass bounds from renormalization flow for a simple Yukawa model

Abstract

We study the functional renormalization group flow of a Higgs-Yukawa toy model mimicking the top-Higgs sector of the standard model. This approach allows for treating arbitrary bare couplings. For the class of standard bare potentials of ϕ 4 type at a given ultraviolet cutoff, we show that a finite infrared Higgs mass range emerges naturally from the renormalization group flow itself. Higgs masses outside the resulting bounds cannot be connected to any conceivable set of bare parameters in this standard model ϕ 4 class. By contrast, more general bare potentials allow us to diminish the lower bound considerably. We identify a simple renormalization group mechanism for this depletion of the lower bound. If this depletion is also active in the full standard model, Higgs masses smaller than the conventional infrared window do not necessarily require new physics at low scales or give rise to instability problems. 1 In fact, the upper bound is often motivated from the requirement that the standard model per definitionem should be describable within perturbation theory in the UV. Since this is, if at all, an aesthetic but not a physical criterion, we rely on the criterion of triviality in the present work.PHYSICAL REVIEW D 89, 045012 (2014) 1550-7998=2014=89(4)=045012 (13) 045012-1

The Higgs mass and the scale of new physics

“…When we include the strong coupling in the bottom left panel of figure 1 the top Yukawa coupling decreases toward the ultraviolet. This allows for lower Higgs mass bounds from vacuum stability compared to the pure Z 2 model [54]. With the additional approximate effects from the weak coupling we also reproduce the back-bending toward positive λ 4 in the deep ultraviolet, as it occurs in the Standard Model, shown in the bottom right panel of figure 1.…”

“…New physics only has to set in at the Planck scale, tunneling rates to the true vacuum have to be small, and our electroweak vacuum is meta-stable [45]. The third, less studied option [51][52][53][54][55][56][57][58] includes higher-dimensional operators which stabilize the Higgs vacuum beyond 10 10 GeV. Such operators will appear in theories with physical cutoff or matching scales.…”

“…(2.9). The additional logarithmic contribution to the quartic potential term contributes to the Higgs mass as [54,[64][65][66] …”

“…Higher orders can easily be included, but do not lead to any significant change of results. For the pure Z 2 model, the local convergence has been checked to order ∼ λ 40 H 40 [54].…”

“…(12) in ref. [54] remains unaffected, the flow of the Yukawa coupling receives direct contributions from the gauge sector. Also for numerical purposes, it is convenient to write this β-function as Table 1.…”