Perspective of Direct Search for Dark Components in the Universe with Multi-Wavelengths Stimulated Resonant Photon-Photon Colliders

We explore a possibility to detect dark components in the Universe via stimulated photon–photon collisions by focusing two-frequency coherent electromagnetic fields in a vacuum. Those fields are assumed to be pulsed reaching Fourier transform limits in near-infrared, THz, and GHz frequency bands, respectively. The numbers of signal photons as a result of exchange of a pseudoscalar-type pseudo Nambu–Goldstone boson have been evaluated in the individual frequency bands. Within presently available beam intensities, we found that the QCD axion scenarios are thoroughly testable in the mass range 10−6–100 eV based on the common method. Furthermore, we show a possibility to reach the weak coupling domain even beyond the gravitationally weak coupling strength if pulse compression in the GHz band is realized in the near future development.

Spontaneously Broken Symmetries

The phenomenon of spontaneous symmetry breaking is a common feature of phase transitions in both classical and quantum physics. In a first part we study this phenomenon for the case of a global internal symmetry and give a simple proof of Goldstone’s theorem. We show that a massless excitation appears, corresponding to every generator of a spontaneously broken symmetry. In a second part we extend these ideas to the case of gauge symmetries and derive the Brout–Englert–Higgs mechanism. We show that the gauge boson associated with the spontaneously broken generator acquires a mass and the corresponding field, which would have been the Goldstone boson, decouples and disappears. Its degree of freedom is used to allow the transition from a massless to a massive vector field.

The Weak Interactions

We present the phenomenology of the weak interactions in a historical perspective, from Fermi’s four-fermion theory to the V−A current×current interaction. The experiments of C.S. Wu, which established parity violation, and M. Goldhaber, which measured the neutrino helicity, are described. We study in turn the leptonic, semi-leptonic and non-leptonic weak interactions. We introduce the concept of the conserved vector current and the partially conserved axial current and show that the latter is the result of spontaneously broken chiral symmetry with the pion the corresponding pseudo-Goldstone boson. We study Gell–Mann’s current algebra and derive the Adler–Weisberger relation. Strangeness changing weak interactions and the Cabibbo theory are described. We present a phenomenological analysis of CP-violation in the neutral kaon system and we end with the intermediate vector boson hypothesis.

Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

Two-loop $$ \mathcal{O} $$((αt + αλ + ακ)2) corrections to the Higgs boson masses in the CP-violating NMSSM

We present our computation of the $$ \mathcal{O} $$ O ((αt + αλ + ακ)2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed $$ \overline{\mathrm{DR}} $$ DR ¯ -on-shell (OS) renormalisation scheme for the Higgs sector and apply both $$ \overline{\mathrm{DR}} $$ DR ¯ and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising λ and κ, remaining overall below about 3% compared to our previously computed $$ \mathcal{O} $$ O (αt(αt + αs)) corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.

Extranatural flux inflation

We propose a new inflation scenario in flux compactification, where a zero mode scalar field of extra components of the higher dimensional gauge field is identified with an inflaton. The scalar field is a pseudo Nambu-Goldstone boson of spontaneously broken translational symmetry in compactified spaces. The inflaton potential is non-local and finite, which is protected against the higher dimensional non-derivative local operators by quantum gravity corrections thanks to the gauge symmetry in higher dimensions and the shift symmetry originated from the translation in extra spaces. We give an explicit inflation model in a six dimensional scalar QED, which is shown to be consistent with Planck 2018 data.

Searching for pseudo Nambu-Goldstone boson dark matter production in association with top quarks

Pseudo Nambu-Goldstone bosons (pNGBs) are attractive dark matter (DM) candidates, since they couple to the Standard Model (SM) predominantly through derivative interactions. Thereby they naturally evade the strong existing limits inferred from DM direct detection experiments. Working in an effective field theory that includes both derivative and non-derivative DM-SM operators, we perform a detailed phenomenological study of the Large Hadron Collider reach for pNGB DM production in association with top quarks. Drawing on motivated benchmark scenarios as examples, we compare our results to other collider limits as well as the constraints imposed by DM (in) direct detection experiments and the relic abundance. We furthermore explore implications on the viable parameter space of pNGB DM. In particular, we demonstrate that DM direct detection experiments become sensitive to many pNGB DM realisations once loop-induced interactions are taken into account. The search strategies and pNGB DM benchmark models that we discuss can serve as a starting point for dedicated experimental analyses by the ATLAS and the CMS collaborations.

Dynamical inverse seesaw mechanism as a simple benchmark for electroweak breaking and Higgs boson studies

The Standard Model (SM) vacuum is unstable for the measured values of the top Yukawa coupling and Higgs mass. Here we study the issue of vacuum stability when neutrino masses are generated through spontaneous low-scale lepton number violation. In the simplest dynamical inverse seesaw, the SM Higgs has two siblings: a massive CP-even scalar plus a massless Nambu-Goldstone boson, called majoron. For TeV scale breaking of lepton number, Higgs bosons can have a sizeable decay into the invisible majorons. We examine the interplay and complementarity of vacuum stability and perturbativity restrictions, with collider constraints on visible and invisible Higgs boson decay channels. This simple framework may help guiding further studies, for example, at the proposed FCC facility.

Probing effective field theory approach in the CP violating minimal linear $$\sigma $$ model

The Minimal Linear $$\sigma $$ σ Model is a useful theoretical laboratory. One can investigate in a perturbative renormalisable model the properties of the Higgs boson as a pseudo-Goldstone boson, the phenomenological effects of the radial mode of the field $$\texttt {s}$$ s which spontaneously breaks the global SO(5) symmetry and the validity of conclusions based on the Effective Field Theory approach with the field $$\texttt {s}$$ s in the spectrum, after the decoupling of heavy degrees of freedom. In this paper all those issues are discussed in the framework of the Minimal Linear $$\sigma $$ σ Model with CP violating phases leading to pseudoscalar components in the effective Standard Model Yukawa couplings. Also the character of the electroweak phase transition in the presence of the field $$\texttt {s}$$ s is investigated.

The hubble tension as a hint of leptogenesis and neutrino mass generation

The majoron, a neutrinophilic pseudo-Goldstone boson conventionally arising in the context of neutrino mass models, can damp neutrino free-streaming and inject additional energy density into neutrinos prior to recombination. The combination of these effects for an eV-scale mass majoron has been shown to ameliorate the outstanding $$H_0$$ H 0 tension, however only if one introduces additional dark radiation at the level of $$\Delta N_{\mathrm{eff}} \sim 0.5$$ Δ N eff ∼ 0.5 . We show here that models of low-scale leptogenesis can naturally source this dark radiation by generating a primordial population of majorons from the decays of GeV-scale sterile neutrinos in the early Universe. Using a posterior predictive distribution conditioned on Planck2018+BAO data, we show that the value of $$H_0$$ H 0 observed by the SH$$_0$$ 0 ES collaboration is expected to occur at the level of $$\sim 10\%$$ ∼ 10 % in the primordial majoron cosmology (to be compared with $$\sim 0.1\%$$ ∼ 0.1 % in the case of $$\Lambda $$ Λ CDM). This insight provides an intriguing connection between the neutrino mass mechanism, the baryon asymmetry of the Universe, and the discrepant measurements of $$H_0$$ H 0 .