A simple route far beyond the Cape of Grand Unification
We have studied the SM in its full perturbative validity range up to the Landau pole, assuming that the gravity does not signiﬁcantly affect the SM predictions at energies above the Planck scale. The SM without gravity can be regarded as a consistent quantum ﬁeld theory all the way between ΛQCD and the UV Landau pole of the U(1)Y gauge coupling. However, when viewed in isolation from any potential new physics, as we have assumed in this work, the SM suffers from a false vacuum problem at the EW scale, which is caused by the negative Higgs quartic coupling at an intermediate energy scale. We have proposed the most minimal extension of the SM by one complex singlet ﬁeld that solves the wrong vacuum problem, generates EWSB dynamically via dimensional transmutation, provides the correct amount of DM, and is a candidate for the inﬂaton. Compared to previous such attempts to formulate the new SM, ours has less parameters as well as less new dynamical degrees of freedom.
In this framework the false SM vacuum is avoided due to the modiﬁcation of the SM Higgs boson quartic coupling RGE by the singlet couplings. The electroweak scale can be generated from a classically scale invariant Lagrangian through dimensional transmutation in the scalar sector, by letting the quartic coupling of the CP-even scalar run negative close to the EW scale. The VEV of this scalar then induces the standard model Higgs VEV through a portal coupling. We studied the perturbative validity range of this model and found that the scalar quartic Landau pole appears below the SM U(1)Y Landau pole. This happens because we demand EWSB to happen via dimensional transmutation. If more than one singlet is added to the model, this constraint can be avoided. Because dimensional transmutation depends only logarithmically on the energy scale, large hierarchies can be accommodated in our model.
...and a fair amount of fine-tuning?
Thus, obtaining the right EW scale form the high scale Landau pole is technically natural in our framework provided that the couplings have the right numerical values. Needless to say, we do not have any prediction why the fundamental Yukawa and scalar self-couplings must have the needed values. In order for our model to work, some of the scalar couplings at the EW scale have to be as small as 10−4 to provide the correct EW scale. We here simply remind the reader that couplings of this order are already present in the SM in the form of Yukawa couplings. Anthropic selection might be a possibility to explain the smallness of those couplings, if a suitable measure on the space of couplings can be deﬁned. For a recent discussion of ﬁne-tuning in a similar model framework we refer the reader to .
The model also naturally provides a DM candidate in the form of the CP-odd scalar that is stable due to the CP-invariance of the scalar potential. We demonstrated that this model allows the DM particle to be produced with the correct relic density while fulﬁlling all experimental constraints on Higgs boson and DM phenomenology. Detecting the DM directly at colliders is very challenging due to the small mixing between the Higgs dou- blet and the singlet. However, this framework is potentially testable in the planned DM direct detection experiments.
We also demonstrated that inﬂation can be accommodated in this model without introducing additional degrees of freedom. In this case the scalar couplings must be very ﬁnely tuned. Our framework does not differ from generic large scale inﬂation models in that respect.
A first shot in the unknown, waiting for more tools...
Our SM model extension does not provide a complete solution to the known open questions in particle physics. Obviously, there is no model of gravity in our framework that could support our initial assumptions and explain the observed cosmological constant value. We simply assume that the presently unknown UV theory of gravity does not spoil our assumptions. Recent theoretical developments may support this view on gravity. The baryon asymmetry of the universe also requires additional dynamics, which we do not discuss. Leptogenesis remains the favourite candidate mechanism and can easily be incorporated in our framework together with neutrino masses. In the context of particle physics, the strong CP problem remains unexplained, and likely requires additional degrees of freedom to be added to this minimal model. Clearly our results and conclusions remain valid under the assumption that these new degrees of freedom somehow decouple from the relevant degrees of freedoms that contribute to our scalar sector.
Finally we want to remark that even if the Planck scale is indeed a physical cutoff for the validity of the Standard Model, our conclusions remain mostly valid. The extra scalars would still avert the metastability problem of the EW vacuum, and the low energy phenomenology of the model, including the dynamical generation of the EW scale and the DM model, remains intact. If our framework turns out to be the right approach for extending the validity of the SM above the Planck scale, there are concrete predictions of our model that could be tested by future DM and collider experiments.