Abstract
We argue that the Standard Model (SM) in the Higgs phase does not suffer from a "hierarchy problem" and that similarly the "cosmological constant problem" resolves itself if we understand the SM as a low energy effective theory emerging from a cutoff-medium at the Planck scale. We actually take serious Veltman's "The Infrared - Ultraviolet Connection" addressing the issue of quadratic divergences and the related huge radiative correction predicted by the SM in the relationship between the bare and the renormalized theory, usually called "the hierarchy problem" and claimed that this has to be cured. We discuss these issues under the condition of a stable Higgs vacuum, which allows to extend the SM up to the Planck cutoff. The bare Higgs boson mass then changes sign below the Planck scale, such that the SM in the early universe is in the symmetric phase. The cutoff enhanced Higgs mass term as well as the quartically enhanced cosmological constant term provide a large positive dark energy which triggers the inflation of the early universe. Reheating follows via the decays of the four unstable heavy Higgs particles, predominantly into top-antitop pairs, which at this stage are still massless. Preheating is suppressed in SM inflation since in the symmetric phase bosonic decay channels are absent at tree level. The coefficients of the shift between bare and renormalized Higgs mass as well as of the shift between bare and renormalized vacuum energy density exhibit close-by zeros at about $7.7 \times 10^{14}$ GeV and $3.1 \times 10^{15}$ GeV, respectively. The zero of of the Higgs mass counter term triggers the electroweak phase transition from the low energy Higgs phase and to the symmetric phase above the transition point. The scenario highly favors to understand the SM and its main properties as a natural structure emerging at long distance.
Highlights
Invited talk at the Workshop “Naturalness, Hierarchy and Fine Tuning” RWTH Aachen, 28 February 2018 to 2 March 2018, Aachen,Germany dependence is illustrated in Fig. 1 assuming the cutoff as a renormalization scale and the Standard Model (SM) Renormalization Group (RG) ruling the scale dependence of the SM couplings
In contrast to other inflation models, Higgs inflation is special because of almost all properties are known or predictable! Below, I will argue that the SM in the Higgs phase does not suffer from a “hierarchy problem” and that the “cosmological constant problem” resolves itself if we understand the SM as a low energy effective theory emerging from a cutoff-medium at the Planck scale
A cutoff regularized SM with the Planck mass as a cutoff is considered to exhibit the relevant features of the physical Planck world in the sense that it resides in the same universality class with respect to its long-range behavior
Summary
With the discovery of the Higgs boson by ATLAS [40] and CMS [41] in 2012 a last major but often questioned building block of the electroweak SM has been experimentally verified. One important point is missing : the physical on-shell parameters are determined from experimental data by unfolding the raw data from radiation and detector effects They represent pseudo-observables depending on theory input that relies on approximations. My quintessence: while the matching conditions are known to two loops, the input parameters have not yet been determined at the same level of accuracy, i.e. likely reported errors are underestimated. These issues have to be reminded before one can claim that metastability of the electroweak vacuum is a proven fact
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