Minimal scenario of criticality for electroweak scale, neutrino masses, dark matter, and inflation

We propose a minimal model that can explain the electroweak scale, neutrino masses, Dark Matter (DM), and successful inflation all at once based on the multicritical-point principle (MPP). The model has two singlet scalar fields that realize an analogue of the Coleman–Weinberg mechanism, in addition to the Standard Model with heavy Majorana right-handed neutrinos. By assuming a $$Z_2 $$ Z 2 symmetry, one of the scalars becomes a DM candidate whose property is almost the same as the minimal Higgs-portal scalar DM. In this model, the MPP can naturally realize a saddle point in the Higgs potential at high energy scales. By the renormalization-group analysis, we study the critical Higgs inflation with non-minimal coupling $$\xi |H|^2 R$$ ξ | H | 2 R that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for $$\xi =25$$ ξ = 25 and that the heaviest right-handed neutrino is predicted to have a mass around $$10^{14}$$ 10 14 $$\mathrm{GeV}$$ GeV to meet the current cosmological observations. Such a small value of $$\xi $$ ξ can be realized by the Higgs-portal coupling $$\lambda _{SH}\simeq 0.32$$ λ SH ≃ 0.32 and the vacuum expectation value of the additional neutral scalar $$\langle \phi \rangle \simeq 2.7$$ ⟨ ϕ ⟩ ≃ 2.7 TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section $$1.8\times 10^{-9}$$ 1.8 × 10 - 9 pb, and the mass of additional neutral scalar 190 GeV.

A theory of giant vortices

We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number n. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-n corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.

A natural mechanism for approximate Higgs alignment in the 2HDM

The 2HDM possesses a neutral scalar interaction eigenstate whose tree-level properties coincide with the Standard Model (SM) Higgs boson. In light of the LHC Higgs data which suggests that the observed Higgs boson is SM-like, it follows that the mixing of the SM Higgs interaction eigenstate with the other neutral scalar interaction eigenstates of the 2HDM should be suppressed, corresponding to the so-called Higgs alignment limit. The exact Higgs alignment limit can arise naturally due to a global symmetry of the scalar potential. If this symmetry is softly broken, then the Higgs alignment limit becomes approximate (although still potentially consistent with the current LHC Higgs data). In this paper, we obtain the approximate Higgs alignment suggested by the LHC Higgs data as a consequence of a softly broken global symmetry of the Higgs Lagrangian. However, this can only be accomplished if the Yukawa sector of the theory is extended. We propose an extended 2HDM with vector-like top quark partners, where explicit mass terms in the top sector provide the source of the soft symmetry breaking of a generalized CP symmetry. In this way, we can realize approximate Higgs alignment without a significant fine-tuning of the model parameters. We then explore the implications of the current LHC bounds on vector-like top quark partners for the success of our proposed scenario.

Sensitivity to invisible scalar decays at CLIC

We studied the possibility of constraining production of new scalar particles at CLIC running at 380 GeV and 1.5 TeV, assuming the associated production of Higgs-like neutral scalar with $$\mathrm{Z}{}{} $$ Z boson and its invisible decays. The analysis is based on the Whizard event generation and fast simulation of the CLIC detector response with Delphes. We considered $${\mathrm{e}{}{}}^{+} {\mathrm{e}{}{}}^{-} $$ e + e - background processes but also relevant $$\upgamma {}{} \upgamma {}{} $$ γ γ and $$\upgamma {}{} \mathrm{e}{}{} ^{\pm }$$ γ e ± interactions. The approach consisting of a two-step analysis was used to optimise separation between signal and background processes. First, a set of preselection cuts was applied; then, multivariate analysis methods were employed to optimise the significance of observations. We first estimated the expected limits on the invisible decays of the 125 GeV Higgs boson, which were then extended to the cross section limits for production of an additional neutral scalar, assuming its invisible decays, as a function of its mass. Extracted model-independent branching ratio and cross section limits were then interpreted in the framework of the Higgs-portal models to set limits on the mixing angle between the SM-like Higgs boson and the new scalar of the “dark sector”.

The Casimir energy anomaly for a point interaction

The Casimir energy for a massless, neutral scalar field in presence of a point interaction is analyzed using a general zeta-regularization approach developed in earlier works. In addition to a regular bulk contribution, there arises an anomalous boundary term which is infinite despite renormalization. The intrinsic nature of this anomaly is briefly discussed.

The signatures of the new particles $$h_{2}$$ and $$Z^{}_{\mu \tau }$$ at e-p colliders in the $${U(1)}_{L^{}_{\mu } - L^{}_{\tau } }$$ model

Considering the superior performances of the future e-p colliders, LHeC and FCC-eh, we discuss the feasibility of detecting the extra neutral scalar $$h_{2}$$h2 and the light gauge boson $$Z^{}_{\mu \tau }$$Zμτ, which are predicted by the $${U(1)}_{L^{}_{\mu } - L^{}_{\tau }}$$U(1)Lμ-Lτ model. Taking into account the experimental constraints on the relevant free parameters, we consider all possible production channels of $$h_{2}$$h2 and $$Z^{}_{\mu \tau }$$Zμτ at e-p colliders and further investigate their observability through the optimal channels in the case of the beam polarization $$\hbox {P}(e^{-})= -0.8$$P(e-)=-0.8. We find that the signal significance above $$5\sigma $$5σ of $$h_{2}$$h2 as well as $$Z^{}_{\mu \tau }$$Zμτ detecting can be achieved via "Equation missing" process and a $$5\sigma $$5σ sensitivity of $$Z^{}_{\mu \tau }$$Zμτ detecting can be gained via "Equation missing" process at e-p colliders with appropriate parameter values and a designed integrated luminosity. However, the signals of $$h_{2}$$h2 decays into pair of SM particles are difficult to be detected.

A New Mechanism for Generating Particle Number Asymmetry through Interactions

A new mechanism for generating particle number asymmetry (PNA) has been developed. This mechanism is realized with a Lagrangian including a complex scalar field and a neutral scalar field. The complex scalar carries U(1) charge which is associated with the PNA. It is written in terms of the condensation and Green’s function, which is obtained with two-particle irreducible (2PI) closed time path (CTP) effective action (EA). In the spatially flat universe with a time-dependent scale factor, the time evolution of the PNA is computed. We start with an initial condition where only the condensation of the neutral scalar is nonzero. The initial condition for the fields is specified by a density operator parameterized by the temperature of the universe. With the above initial conditions, the PNA vanishes at the initial time and later it is generated through the interaction between the complex scalar and the condensation of the neutral scalar. We investigate the case that both the interaction and the expansion rate of the universe are small and include their effects up to the first order of the perturbation. The expanding universe causes the effects of the dilution of the PNA, freezing interaction, and the redshift of the particle energy. As for the time dependence of the PNA, we found that PNA oscillates at the early time and it begins to dump at the later time. The period and the amplitude of the oscillation depend on the mass spectrum of the model, the temperature, and the expansion rate of the universe.