Abstract
In the quest for unification of the Standard Model with gravity, classical scale invariance can be utilized to dynamically generate the Planck mass MPl. However, the relation of Planck scale physics to the scale of electroweak symmetry breaking μH requires further explanation. In this paper, we propose a model that uses the spontaneous breaking of scale invariance in the scalar sector as a unified origin for dynamical generation of both scales. Using the Gildener-Weinberg approximation, only one scalar acquires a vacuum expectation value of υS ∼ (1016−17) GeV, thus radiatively generating {M}_{mathrm{P}1}approx {beta}_S^{1/2}{upsilon}_S and μH via the neutrino option with right handed neutrino masses mN = yMυS ∼ 107 GeV. Consequently, active SM neutrinos are given a mass with the inclusion of a type-I seesaw mechanism. Furthermore, we adopt an unbroken Z2 symmetry and a Z2-odd set of right-handed Majorana neutrinos χ that do not take part in the neutrino option and are able to produce the correct dark matter relic abundance (dominantly) via inflaton decay. The model also describes cosmic inflation and the inflationary CMB observables are predicted to interpolate between those of R2 and linear chaotic inflationary model and are thus well within the strongest experimental constraints.
Highlights
Ratio r of tensor to scalar power spectra of fluctuations can be nearly zero
The mass parameter μH can logarithmically run all the way to the Planck scale so that, according to Bardeen [60], the SM does not, by itself, have a fine-tuning problem. We regard this as a strong evidence [61] for extending the SM in a scale invariant way [62, 63], because the logarithmic running of μH up to the Planck scale means that scale invariance is broken only by the scale anomaly [64, 65], except by the soft breaking due to μH
Our total Lagrangian LT consists of four parts: (i) LCW is, after including quantum corrections, responsible for the spontaneous breaking of global conformal symmetry and the generation of a unified scale. (ii) LGR is responsible for the identification of the Planck scale, thereby generating the Einstein-Hilbert action. (iii) LSM describes the SM interactions, and (iv) LNχ is responsible for generating light neutrino masses via a type-I see-saw mechanism which at the same time radiatively induces the Higgs mass term and accommodates for dark matter
Summary
Our total Lagrangian LT consists of four parts: (i) LCW is, after including quantum corrections, responsible for the spontaneous breaking of global conformal symmetry and the generation of a unified scale. (ii) LGR is responsible for the identification of the Planck. Our total Lagrangian LT consists of four parts: (i) LCW is, after including quantum corrections, responsible for the spontaneous breaking of global conformal symmetry and the generation of a unified scale. (iii) LSM describes the SM interactions, and (iv) LNχ is responsible for generating light neutrino masses via a type-I see-saw mechanism which at the same time radiatively induces the Higgs mass term and accommodates for dark matter. We will see that the real scalar S has a triple role: (i) It is the only scalar that forms a condensate and thereby breaks global conformal invariance spontaneously, (ii) it is the mediator that transmits the energy scale inherent in the condensate to the gravity (LGR) and neutrino (LNχ) sectors, and subsequently to the SM sector, and (iii) it serves as the inflaton
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