Multiple Point Criticality Principle Research Articles

Multiple point criticality principle and Coleman-Weinberg inflation

We apply the multiple point criticality principle to inflationary model building and study Coleman-Weinberg inflation when the scalar potential is quadratic in the logarithmic correction. We analyze also the impact of a non-minimal coupling to gravity under two possible gravity formulation: metric or Palatini. We compare the eventual compatibility of the results with the final data release of the Planck mission.

Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

Natural solution to the naturalness problem: The universe does fine-tuning

We propose a new mechanism to solve the fine-tuning problem. We start from a multi-local action $ S=\sum_{i}c_{i}S_{i}+\sum_{i,j}c_{i,j}S_{i}S_{j}+\sum_{i,j,k}c_{i,j,k}S_{i}S_{j}S_{k}+\cdots$, where $S_{i}$'s are ordinary local actions. Then, the partition function of this system is given by \begin{equation} Z=\int d\overrightarrow{\lambda} f(\overrightarrow{\lambda})\langle f|T\exp\left(-i\int_{0}^{+\infty}dt\hat{H}(\overrightarrow{\lambda};a_{cl}(t))\right)|i\rangle,\nonumber\end{equation} where $\overrightarrow{\lambda}$ represents the parameters of the system whose Hamiltonian is given by $\hat{H}(\overrightarrow{\lambda};a_{cl}(t))$, $a_{cl}(t)$ is the radius of the universe determined by the Friedman equation, and $f(\overrightarrow{\lambda})$, which is determined by $S$, is a smooth function of $\overrightarrow{\lambda}$. If a value of $\overrightarrow{\lambda}$, $\overrightarrow{\lambda}_{0}$, dominates in the integral, we can interpret that the parameters are dynamically tuned to $\overrightarrow{\lambda}_{0}$. We show that indeed it happens in some realistic systems. In particular, we consider the strong CP problem, multiple point criticality principle and cosmological constant problem. It is interesting that these different phenomena can be explained by one mechanism.

Vanishing Higgs potential in minimal dark matter models

We consider the Standard Model with a new particle which is charged under SU(2)L with the hypercharge being zero. Such a particle is known as one of the dark matter (DM) candidates. We examine the realization of the multiple point criticality principle (MPP) in this class of models. Namely, we investigate whether the one-loop effective Higgs potential Veff(ϕ) and its derivative dVeff(ϕ)/dϕ can become simultaneously zero at around the string/Planck scale, based on the one/two-loop renormalization group equations. As a result, we find that only the SU(2)L triplet extensions can realize the MPP. More concretely, in the case of the triplet Majorana fermion, the MPP is realized at the scale ϕ=O(1016 GeV) if the top mass Mt is around 172 GeV. On the other hand, for the real triplet scalar, the MPP can be satisfied for 1016 GeV≲ϕ≲1017 GeV and 172 GeV≳Mt≳171 GeV, depending on the coupling between the Higgs and DM.

Eternal Higgs inflation and the cosmological constant problem

We investigate the Higgs potential beyond the Planck scale in the superstring theory, under the assumption that the supersymmetry is broken at the string scale. We identify the Higgs field as a massless state of the string, which is indicated by the fact that the bare Higgs mass can be zero around the string scale. We find that, in the large field region, the Higgs potential is connected to a runaway vacuum with vanishing energy, which corresponds to opening up an extra dimension. We verify that such universal behavior indeed follows from the toroidal compactification of the non-supersymmetric $SO(16)\times SO(16)$ heterotic string theory. We show that this behavior fits in the picture that the Higgs field is the source of the eternal inflation. The observed small value of the cosmological constant of our universe may be understood as the degeneracy with this runaway vacuum, which has vanishing energy, as is suggested by the multiple point criticality principle.

Gravitational effects on vanishing Higgs potential at the Planck scale

We investigate gravitational effects on the so-called multiple point criticality principle (MPCP) at the Planck scale. The MPCP requires two degenerate vacua, whose necessary conditions are expressed by vanishing Higgs quartic coupling $\lambda(M_{\rm Pl})=0$ and vanishing its $\beta$ function $\beta_\lambda(M_{\rm Pl})=0$. We discuss a case that a specific form of gravitational corrections are assumed to contribute to $\beta$ functions of coupling constants although it is accepted that gravitational corrections do not alter the running of the standard model (SM) couplings. To satisfy the above two boundary conditions at the Planck scale, we find that the top pole mass and the Higgs mass should be $170.8\,{\rm GeV} \lesssim M_t\lesssim 171.7\,{\rm GeV}$ and $M_h=125.7\pm0.4\,{\rm GeV}$, respectively, as well as include suitable magnitude of gravitational effects (a coefficient of gravitational contribution as $|a_\lambda| > 2$). In this case, however, since the Higgs quartic coupling $\lambda$ becomes negative below the Planck scale, two vacua are not degenerate. We find that $M_h \gtrsim 131.5\,{\rm GeV}$ with $M_t \gtrsim 174\,{\rm GeV}$ is required by the realization of the MPCP. Therefore, the MPCP at the Planck scale cannot be realized in the SM and also the SM with gravity since $M_h \gtrsim 131.5\,{\rm GeV}$ is experimentally ruled out.

Vanishing Higgs potential at the Planck scale in a singlet extension of the standard model

We discuss the realization of a vanishing effective Higgs potential at the Planck scale, which is required by the multiple-point criticality principle (MPCP), in the standard model with singlet scalar dark matter and a right-handed neutrino. We find the scalar dark matter and the right-handed neutrino play crucial roles for realization of the MPCP, where a neutrino Yukawa becomes effective above the Majorana mass of the right-handed neutrino. Once the top mass is fixed, the MPCP at the (reduced) Planck scale and the suitable dark matter relic abundance determine the dark matter mass, $m_S$, and the Majorana mass of the right-handed neutrino, $M_R$, as $8.5~(8.0)\times10^2~{\rm GeV}\leq m_S\leq1.4~(1.2)\times10^3~{\rm GeV}$ and $6.3~(5.5)\times10^{13}~{\rm GeV}\leq M_R\leq1.6~(1.2)\times10^{14}~{\rm GeV}$ within current experimental values of the Higgs and top masses. This scenario is consistent with current dark matter direct search experiments, and will be checked by future experiments such as LUX with further exposure and/or the XENON1T.

Multiple Model of Anti-Grand Unification, The Regularization with Wilson Loop Action and Critical Coupling Constants

The present work considers the phase transition between the confinement and "Coulomb" phases in U(1) gauge theory described by Wilson loop action. It was shown (using as an example the approximation of circular loops) that the critical coupling constant is rather independent of the regularization method. Taking into account the renormalization by artefact monopole contributions and the existence of strings in confinement phase assuming the maximal value of the effective fine structure constant equal to α max =π/12≈0.26, we obtain α c ≈0.204, in agreement with Monte Carlo lattice simulation result: α c ≈0.20. Such an approximate regularization independence ("universality") of the critical couplings is needed for the fine structure constant predictions claimed from "the multiple-point criticality principle".

THE HIGGS PHENOMENON

We briefly discuss why we are forced to use the Higgs–Kibble mechanism just, for example, to be able to "present" masses and what in this sense the so-called Higgs phenomenon really means. But, independent of this fact that we cannot calculate physical masses, we, in spite of this reality, briefly demonstrate presently available theoretical methods for understanding the top-Higgs-mass correlations, for example, especially since the discovery of the top quark at FNAL. It is possible that model-dependent ways, using SUSY and SUGRA models, for example, to overcome the so-called scale dependence (just from the Planck down to the Fermi scale), nonlinear realizations of SUSY and also the requirement of phase coexistence of the two minima of the effective potential with one-loop corrections and its degeneracy ("multiple point criticality principle"), might indicate that in this sense the existence of supersymmetry can be "partially" ruled out. In this context the top-Higgs-mass spectrum belongs neither to the SM nor to SUSY. Also, the loss of quantum coherence, which is very small at low energies for everything except scalar fields, leads to the prediction that we may never observe the Higgs particle either.

Standard model criticality prediction top mass 173 ± 5 GeV and Higgs mass 135 ± 9 GeV

Imposing the constraint that the Standard Model effective Higgs potential should have two degenerate minima (vacua), one of which should be — order of magnitude wise — at the Planck scale, leads to the top mass being 173 ± 5 GeV and the Higgs mass 135 ± 9 GeV. This requirement of the degeneracy of different phases is a special case of what we call the multiple point criticality principle. In the present work we use the Standard Model all the way to the Planck scale, and do not introduce supersymmetry or any extension of the Standard Model gauge group. A possible model to explain the multiple point criticality principle is lack of locality fundamentally.